mm-4809 === Subject: Re: Clep test for Calculus > I am tutoring someone in Calculus in preparation for a Clep test. We're > behind and I need to cut some things. Would it be safe to cut hyperbolic > functions in favor of integration techniques (parts, trig substitution, > etc.)? oh the damned institutional failure of tests on global schedules in the words of a famous philosopher can the world be as sad as it seems? does it make no sense to those who make the rules that students can be ready at their own pace and the tests still measure what they always measure? another example of cutting education to meet the deadline of a test... === Subject: Re: Clep test for Calculus another example of cutting education to meet the deadline of a test... I would prefer not to cut anything, but with such a tight deadline, it's almost inevitable that I'll have to. Dave === Subject: prime puzzle I am trying to see if there is a solution to the following; I have many paper bags, each filled with a collection of wooden squares with a prime number (or 1) written on each square. For each experiment, I draw a prime (or a 1) from each bag, multiply the primes together, and write down the resulting number. I then return the primes to the bag they came from, and repeat the experiement over and over again. I always draw from the same bags in the same order, for each experiment. My question is this; is it possible to load each bag with specific collections of primes such that my collection of results will span a specific numeric range from 1 to N inclusive, but without exceeeding N? N is allowed to be special; that is, I would be happy to find a solution for a specific N, even if there is no general solution. If the answer is no, not possible, then the next-best solution would be one that minimizes the set of results that exceeds N, but still spans 1 to N inclusive. Bob Adams === Subject: Re: prime puzzle > I am trying to see if there is a solution to the following; I have many paper bags, each filled with a collection of wooden > squares with a prime number (or 1) written on each square. For each > experiment, I draw a prime (or a 1) from each bag, multiply the primes > together, and write down the resulting number. I then return the > primes to the bag they came from, and repeat the experiement over and > over again. I always draw from the same bags in the same order, for > each experiment. My question is this; is it possible to load each bag with specific > collections of primes such that my collection of results will span a > specific numeric range from 1 to N inclusive, but without exceeeding > N? N is allowed to be special; that is, I would be happy to find a > solution for a specific N, even if there is no general solution. If the answer is no, not possible, then the next-best solution would > be one that minimizes the set of results that exceeds N, but still > spans 1 to N inclusive. Bob Adams For a given N, if you have at least log(base 2) N bags, then it is possible, assuming you can pack the bags with specific primes as you described in your question. === Subject: Re: prime puzzle > I am trying to see if there is a solution to the following; > I have many paper bags, each filled with a collection of wooden > squares with a prime number (or 1) written on each square. For each > experiment, I draw a prime (or a 1) from each bag, multiply the primes > together, and write down the resulting number. I then return the > primes to the bag they came from, and repeat the experiement over and > over again. I always draw from the same bags in the same order, for > each experiment. Order's irrelevant, as multiplication's commutative. > My question is this; is it possible to load each bag with specific > collections of primes such that my collection of results will span a > specific numeric range from 1 to N inclusive, but without exceeeding > N? If you stick all primes<=N, and 1 in every bag, then clearly it's possible to achieve what you want. You just have to remember to draw 1s most of the time. As you've not specified how you are doing the drawing, I see no reason to presume that it's done randomly. Phil -- I tried the Vista speech recognition by running the tutorial. I was amazed, it was awesome, recognised every word I said. Then I said the wrong word ... and it typed the right one. It was actually just detecting a sound and printing the expected word! -- pbhj on /. === Subject: Re: prime puzzle Take, say, N = 5. If there's only one bag, then we can't produce the number 4, because it's neither prime nor equal to 1. So there are at least two bags, and at least two of them have blocks labeled 2 in them. Also, since we want to produce 5, there's a 5 in one of the bags. But then you could draw a 5 from one bag and a two from another and get 10 (or 10 times something larger, if there are more bags, but in any case something larger than 5). So the answer to your initial question is no. The situation will be just as bad in most cases; if p is the largest prime less than N, we will need to have p in one of the bags, and if m^2 is the largest square less than N, we will need m in at least two of the bags, so we will be producing numbers as large as mp. For large N, m and p will tend to be near N, so we will generally produce numbers near N^2. (And this is by no means a tight bound on how bad things will get.) Of course, since you said that you'd be happy with a special solution, I'll point out that we can handle things quite readily in the case N = 2 with a single bag holding a 1 and a 2. The question of generating the optimal set of bags such that you can generate all the numbers up to N (for some definition of optimal) might be a little more interesting. Can you explain why you're interested in this problem, though? > I am trying to see if there is a solution to the following; I have many paper bags, each filled with a collection of wooden > squares with a prime number (or 1) written on each square. For each > experiment, I draw a prime (or a 1) from each bag, multiply the primes > together, and write down the resulting number. I then return the > primes to the bag they came from, and repeat the experiement over and > over again. I always draw from the same bags in the same order, for > each experiment. My question is this; is it possible to load each bag with specific > collections of primes such that my collection of results will span a > specific numeric range from 1 to N inclusive, but without exceeeding > N? N is allowed to be special; that is, I would be happy to find a > solution for a specific N, even if there is no general solution. If the answer is no, not possible, then the next-best solution would > be one that minimizes the set of results that exceeds N, but still > spans 1 to N inclusive. Bob Adams === Subject: Re: Question for the Mathematicians > Suppose there is a four horse race with the odds of 2/10, 3/10, 4/10 and > 5/10 > and payments are awarded to the first three across the line. What amount > should > I bet on each horse to get the same profit no matter which horse comes 4th > and misses out on the payment? > I'm still working on this... x1 * .10 = y1 x2 * .20 = y2 x3 * .30 = y3 x4 * .40 = y4 y1 + x1 = z y2 + x2 = z y3 + x3 = z y4 + x4 = z y1 + (y1 / .10) = z y2 + (y2 / .20) = z y3 + (y3 / .30) = z y4 + (y4 / .40) = z Now take y1 + (y1 / .10) = z and set y1 equal to some value say 10 and that's 10 + (10 / .10) or z = 110 . Now we have y2 + (y2 / .20) = 110 (.2 * y2) + y2 = 110 * .2 1.2 * y2 = 22 y2 = 18.33 Now the first wage was (y1 / .10) or (10 / .10) or 100 . And the second wager is (y2 / .20) or (18.33 / .20) or 91.65. Next the percent change from the first wager to the second wager is -8.35% . So the third wager is 91.65 - (91.65 * .0835) or 84.00 . And the fourth wager is 84 - (84 * .0835) or 76.99 . So all wagers pay about 110 with the payout including the amount wagered. (And accuracy would be improved by working with more decimal places.) Of course I haven't yet scaled the sum of the wagers to some total bankroll amount...as the other poster mentioned doing. === Subject: Re: Question for the Mathematicians > Suppose there is a four horse race with the odds of 2/10, 3/10, 4/10 and > 5/10 > and payments are awarded to the first three across the line. What amount > should > I bet on each horse to get the same profit no matter which horse comes > 4th > and misses out on the payment? I'm still working on this... x1 * .10 = y1 > x2 * .20 = y2 > x3 * .30 = y3 > x4 * .40 = y4 y1 + x1 = z > y2 + x2 = z > y3 + x3 = z > y4 + x4 = z y1 + (y1 / .10) = z > y2 + (y2 / .20) = z > y3 + (y3 / .30) = z > y4 + (y4 / .40) = z Now take y1 + (y1 / .10) = z and set y1 equal to some value say 10 and that's 10 + (10 / .10) or z = 110 . Now we have y2 + (y2 / .20) = 110 (.2 * y2) + y2 = 110 * .2 1.2 * y2 = 22 y2 = 18.33 Now the first wage was (y1 / .10) or (10 / .10) or 100 . And the second wager is (y2 / .20) or (18.33 / .20) or 91.65. Next the percent change from the first wager to the second wager is -8.35% > . So the third wager is 91.65 - (91.65 * .0835) or 84.00 . And the fourth wager is 84 - (84 * .0835) or 76.99 . So all wagers pay about 110 with the payout including the amount wagered. > (And accuracy would be improved by working with more decimal places.) Of course I haven't yet scaled the sum of the wagers to some total > bankroll amount...as the other poster mentioned doing. > Okay the total wagers are 352.64 but should be 100 . That's 352.64 relates to 100 as the y1 value of 10 relates to an unknown. Then the new beginning y1 value is 2.8358... So repeat the process with the new beginning y1 value... === Subject: Re: Question for the Mathematicians > Suppose there is a four horse race with the odds of 2/10, 3/10, 4/10 and > 5/10 > and payments are awarded to the first three across the line. What amount > should > I bet on each horse to get the same profit no matter which horse comes > 4th > and misses out on the payment? > I'm still working on this... > x1 * .10 = y1 > x2 * .20 = y2 > x3 * .30 = y3 > x4 * .40 = y4 > y1 + x1 = z > y2 + x2 = z > y3 + x3 = z > y4 + x4 = z > y1 + (y1 / .10) = z > y2 + (y2 / .20) = z > y3 + (y3 / .30) = z > y4 + (y4 / .40) = z > Now take > y1 + (y1 / .10) = z > and set y1 equal to some value say 10 > and that's > 10 + (10 / .10) or z = 110 . > Now we have > y2 + (y2 / .20) = 110 > (.2 * y2) + y2 = 110 * .2 > 1.2 * y2 = 22 > y2 = 18.33 > Now the first wage was (y1 / .10) or (10 / .10) or 100 . > And the second wager is (y2 / .20) or (18.33 / .20) or 91.65. > Next the percent change from the first wager to the second wager > is -8.35% . > So the third wager is 91.65 - (91.65 * .0835) or 84.00 . > And the fourth wager is 84 - (84 * .0835) or 76.99 . > So all wagers pay about 110 with the payout including the amount wagered. > (And accuracy would be improved by working with more decimal places.) > Of course I haven't yet scaled the sum of the wagers to some total > bankroll amount...as the other poster mentioned doing. Okay the total wagers are 352.64 but should be 100 . That's 352.64 relates to 100 as the y1 value of 10 relates to an unknown. > Then the new beginning y1 value is 2.8358... So repeat the process with the new beginning y1 value... > Oh, the equations for y3 and y4 should be solved like the equation for y2 was solved...because the steps between the odds will not hold for all cases. === Subject: Re: Question for the Mathematicians > Suppose there is a four horse race with the odds of 2/10, 3/10, 4/10 > and 5/10 > and payments are awarded to the first three across the line. What > amount should > I bet on each horse to get the same profit no matter which horse comes > 4th > and misses out on the payment? > I'm still working on this... > x1 * .10 = y1 > x2 * .20 = y2 > x3 * .30 = y3 > x4 * .40 = y4 > y1 + x1 = z > y2 + x2 = z > y3 + x3 = z > y4 + x4 = z > y1 + (y1 / .10) = z > y2 + (y2 / .20) = z > y3 + (y3 / .30) = z > y4 + (y4 / .40) = z > Now take > y1 + (y1 / .10) = z > and set y1 equal to some value say 10 > and that's > 10 + (10 / .10) or z = 110 . > Now we have > y2 + (y2 / .20) = 110 > (.2 * y2) + y2 = 110 * .2 > 1.2 * y2 = 22 > y2 = 18.33 > Now the first wage was (y1 / .10) or (10 / .10) or 100 . > And the second wager is (y2 / .20) or (18.33 / .20) or 91.65. > Next the percent change from the first wager to the second wager > is -8.35% . > So the third wager is 91.65 - (91.65 * .0835) or 84.00 . > And the fourth wager is 84 - (84 * .0835) or 76.99 . > So all wagers pay about 110 with the payout including the amount > wagered. (And accuracy would be improved by working with more decimal > places.) > Of course I haven't yet scaled the sum of the wagers to some total > bankroll amount...as the other poster mentioned doing. > Okay the total wagers are 352.64 but should be 100 . > That's 352.64 relates to 100 as the y1 value of 10 relates to an unknown. > Then the new beginning y1 value is 2.8358... > So repeat the process with the new beginning y1 value... Oh, the equations for y3 and y4 should be solved like the equation for y2 > was solved...because the steps between the odds will not hold for all > cases. Gosh...but using the first calculation of x1 = 100 x2 = 91.65 x3 = 84.62 x4 = 78.57 The total wagers are 354.84... But each wager pays 110 including the amount wagered... So with one paying wager out there is 330 being returned to the player against 354.84 that was wagered...and that's a 7% loss. === Subject: Re: Question for the Mathematicians > Suppose there is a four horse race with the odds of 2/10, 3/10, >4/10 > and 5/10 > and payments are awarded to the first three across the line. >What > amount should > I bet on each horse to get the same profit no matter which horse >comes > 4th > and misses out on the payment? > I'm still working on this... > x1 * .10 = y1 > x2 * .20 = y2 > x3 * .30 = y3 > x4 * .40 = y4 > y1 + x1 = z > y2 + x2 = z > y3 + x3 = z > y4 + x4 = z > y1 + (y1 / .10) = z > y2 + (y2 / .20) = z > y3 + (y3 / .30) = z > y4 + (y4 / .40) = z > Now take > y1 + (y1 / .10) = z > and set y1 equal to some value say 10 > and that's > 10 + (10 / .10) or z = 110 . > Now we have > y2 + (y2 / .20) = 110 > (.2 * y2) + y2 = 110 * .2 > 1.2 * y2 = 22 > y2 = 18.33 > Now the first wage was (y1 / .10) or (10 / .10) or 100 . > And the second wager is (y2 / .20) or (18.33 / .20) or 91.65. > Next the percent change from the first wager to the second wager > is -8.35% . > So the third wager is 91.65 - (91.65 * .0835) or 84.00 . > And the fourth wager is 84 - (84 * .0835) or 76.99 . > So all wagers pay about 110 with the payout including the amount > wagered. (And accuracy would be improved by working with more >decimal > places.) > Of course I haven't yet scaled the sum of the wagers to some total > bankroll amount...as the other poster mentioned doing. > Okay the total wagers are 352.64 but should be 100 . > That's 352.64 relates to 100 as the y1 value of 10 relates to an >unknown. > Then the new beginning y1 value is 2.8358... > So repeat the process with the new beginning y1 value... > Oh, the equations for y3 and y4 should be solved like the equation >for y2 > was solved...because the steps between the odds will not hold for >all > cases. Gosh...but using the first calculation of x1 = 100 >x2 = 91.65 >x3 = 84.62 >x4 = 78.57 The total wagers are 354.84... But each wager pays 110 including the amount wagered... So with one paying wager out there is 330 being returned to the player against 354.84 that was wagered...and that's a 7% loss. Not sure if I've asked my question correctly. To unconfuse things a bit, I've simplified my question as follows: If the odds of the 4 horses are 1/5, 2/5, 2/5, 2/5 and the house pays on the first three across the line, then the percentage of your total bank to place on each to return the same profit is 28%, 24%, 24%, 24% respectively. (This was relatively easy to work out by trial and error). Similarly, 3/10, 2/5, 2/5, 2/5 would be 14.28%, 28.57%, 28.57%, 28.57% of your bank respectively to return the same profit no matter which three horses crossed the line first. Also, 3/10, 3/10, 2/5, 2/5 equates to 25.925925%, 25.925925%, 24.074074%, 24.074074% of your bank to return the same profit. So, is there a formula to work out these percentages from the 4 given odds (rather than my laborious trial and error system)? 'Onya === Subject: Re: Question for the Mathematicians > Not sure if I've asked my question correctly. To unconfuse things a bit, I've > simplified my question as follows: If the odds of the 4 horses are 1/5, 2/5, 2/5, 2/5 and the house pays on the > first three across the line, then the percentage of your total bank to place > on each to return the same profit is 28%, 24%, 24%, 24% respectively. (This > was relatively easy to work out by trial and error). Prehaps you could expand a bit on how you arrive at the payout values from a given bet and odds. === Subject: Re: Question for the Mathematicians > Not sure if I've asked my question correctly. To unconfuse things >a bit, >I've > simplified my question as follows: > If the odds of the 4 horses are 1/5, 2/5, 2/5, 2/5 and the house >pays on >the > first three across the line, then the percentage of your total bank >to >place > on each to return the same profit is 28%, 24%, 24%, 24% respectively. >(This > was relatively easy to work out by trial and error). Prehaps you could expand a bit on how you arrive at the payout values >from a given bet and odds. OK. If your bank was $4000 and you put $1000 each on the 1/5, 2/5, 2/5, 2/5 then if the 1/5 missed out you'd make a $200 profit. However, if one of the three 2/5's missed out, you'd make a $0 profit. Therefore (by trial and error *) I worked out if you add $166.67 to your bet on the 1/5 horse, you'd make a $33 profit no matter which horse missed out. (* eg. I added $50 first, then $100, $150 etc. until $166.67 gave me the same profit) Then I added $1166.67 + $1000 + $1000 + $1000 to get $4166.67. Then the first bet was 28% of the total, the other bets were each 24% of the total. Now, lets say my bank is $4000. Therefore I bet $1120 (28%) on the 1/5 and $960 (24%) on all the 2/5's. My total bet = $4000, the percentages total 100% and I'll now make a $32 profit no matter which of the three horses cross the line first. So, I'm thinking there must be a formula, given the four odds, to work out these percentages which I can then apply to the total bank to give me the amount for each bet? 'Onya === Subject: Re: Question for the Mathematicians > Not sure if I've asked my question correctly. To unconfuse things >a bit, >I've > simplified my question as follows: > If the odds of the 4 horses are 1/5, 2/5, 2/5, 2/5 and the house >pays on >the > first three across the line, then the percentage of your total bank >to >place > on each to return the same profit is 28%, 24%, 24%, 24% respectively. >(This > was relatively easy to work out by trial and error). >Prehaps you could expand a bit on how you arrive at the payout values >from a given bet and odds. OK. If your bank was $4000 and you put $1000 each on the 1/5, 2/5, 2/5, 2/5 > then if the 1/5 missed out you'd make a $200 profit. However, if one of the > three 2/5's missed out, you'd make a $0 profit. Therefore (by trial and error *) I worked out if you add $166.67 to your bet > on the 1/5 horse, you'd make a $33 profit no matter which horse missed out. > (* eg. I added $50 first, then $100, $150 etc. until $166.67 gave me the same > profit) Then I added $1166.67 + $1000 + $1000 + $1000 to get $4166.67. Then the first > bet was 28% of the total, the other bets were each 24% of the total. Now, lets say my bank is $4000. Therefore I bet $1120 (28%) on the 1/5 and > $960 (24%) on all the 2/5's. My total bet = $4000, the percentages total 100% > and I'll now make a $32 profit no matter which of the three horses cross the > line first. So, I'm thinking there must be a formula, given the four odds, to work out > these percentages which I can then apply to the total bank to give me the amount > for each bet? 'Onya- Hide quoted text - - Show quoted text - I thought this was answered in rec.puzzles. Distribute your bankroll to each horse in proportion to 1/(1+odds) for that horse. HTH, Mac. === Subject: Re: Question for the Mathematicians > Not sure if I've asked my question correctly. To unconfuse things >a bit, >I've > simplified my question as follows: > If the odds of the 4 horses are 1/5, 2/5, 2/5, 2/5 and the house >pays on >the > first three across the line, then the percentage of your total >bank >to >place > on each to return the same profit is 28%, 24%, 24%, 24% respectively. >(This > was relatively easy to work out by trial and error). >Prehaps you could expand a bit on how you arrive at the payout >values >from a given bet and odds. > OK. If your bank was $4000 and you put $1000 each on the 1/5, 2/5, >2/5, 2= >/5 > then if the 1/5 missed out you'd make a $200 profit. However, if >one of t= >he > three 2/5's missed out, you'd make a $0 profit. > Therefore (by trial and error *) I worked out if you add $166.67 >to your = >bet > on the 1/5 horse, you'd make a $33 profit no matter which horse >missed ou= >t. > (* eg. I added $50 first, then $100, $150 etc. until $166.67 gave >me the = >same > profit) > Then I added $1166.67 + $1000 + $1000 + $1000 to get $4166.67. Then >the f= >irst > bet was 28% of the total, the other bets were each 24% of the total. > Now, lets say my bank is $4000. Therefore I bet $1120 (28%) on the >1/5 an= >d > $960 (24%) on all the 2/5's. My total bet =3D $4000, the percentages >tota= >l 100% > and I'll now make a $32 profit no matter which of the three horses >cross = >the > line first. > So, I'm thinking there must be a formula, given the four odds, to >work ou= >t > these percentages which I can then apply to the total bank to give >me the= > amount > for each bet? > 'Onya- Hide quoted text - > - Show quoted text - I thought this was answered in rec.puzzles. Distribute your bankroll >to each horse in proportion to 1/(1+odds) for >that horse. HTH, >Mac. Sorry. I forgot to check rec.puzzles. Last time I asked a maths question there they told me to ask in a maths newsgroup hence my reposting the question here. Yes, your method allows me to easily calculate the percentages of the bank I'd need for each bet. You guys are geniuses. I've been trying to figure this out for weeks. Now it looks so simple! 'Onya === Subject: Re: Question for the Mathematicians > Not sure if I've asked my question correctly. To unconfuse things >a bit, >I've > simplified my question as follows: > If the odds of the 4 horses are 1/5, 2/5, 2/5, 2/5 and the house >pays on >the > first three across the line, then the percentage of your total >bank >to >place > on each to return the same profit is 28%, 24%, 24%, 24% respectively. >(This > was relatively easy to work out by trial and error). >Prehaps you could expand a bit on how you arrive at the payout >values >from a given bet and odds. > OK. If your bank was $4000 and you put $1000 each on the 1/5, 2/5, >2/5, 2= >/5 > then if the 1/5 missed out you'd make a $200 profit. However, if >one of t= >he > three 2/5's missed out, you'd make a $0 profit. > Therefore (by trial and error *) I worked out if you add $166.67 >to your = >bet > on the 1/5 horse, you'd make a $33 profit no matter which horse >missed ou= >t. > (* eg. I added $50 first, then $100, $150 etc. until $166.67 gave >me the = >same > profit) > Then I added $1166.67 + $1000 + $1000 + $1000 to get $4166.67. >Then >the f= >irst > bet was 28% of the total, the other bets were each 24% of the total. > Now, lets say my bank is $4000. Therefore I bet $1120 (28%) on >the >1/5 an= >d > $960 (24%) on all the 2/5's. My total bet =3D $4000, the percentages >tota= >l 100% > and I'll now make a $32 profit no matter which of the three horses >cross = >the > line first. > So, I'm thinking there must be a formula, given the four odds, >to >work ou= >t > these percentages which I can then apply to the total bank to give >me the= > amount > for each bet? > 'Onya- Hide quoted text - > - Show quoted text - >I thought this was answered in rec.puzzles. Distribute your bankroll >to each horse in proportion to 1/(1+odds) for >that horse. >HTH, >Mac. Sorry. I forgot to check rec.puzzles. Last time I asked a maths question >there >they told me to ask in a maths newsgroup hence my reposting the question >here. Yes, your method allows me to easily calculate the percentages of >the bank >I'd need for each bet. You guys are geniuses. I've been trying to figure this out for weeks. >Now it >looks so simple! >'Onya After the responses from Greg, KBH and Macavity, I've made a simple spreadsheet to give me the percentages of the bank I'd need for each bet. In cells A1 to A4 I type in the odds, eg. 0.2, 0.3, 0.4, 0.5 And in cells B1 to B4, I type in the following formulas: =(1/(1+A1))/((1/(1+A1))+(1/(1+A2))+(1/(1+A3))+(1/(1+A4))) =(1/(1+B1))/((1/(1+A1))+(1/(1+A2))+(1/(1+A3))+(1/(1+A4))) =(1/(1+C1))/((1/(1+A1))+(1/(1+A2))+(1/(1+A3))+(1/(1+A4))) =(1/(1+D1))/((1/(1+A1))+(1/(1+A2))+(1/(1+A3))+(1/(1+A4))) Now I can put in the odds of any four horses in cells A1 to A4 and cells B1 to B4 will display the percentage of the bank I'd need to bet to return the same profit or loss no matter which three horses cross the line first. You guys are legends. 'Onya === Subject: Re: Question for the Mathematicians > If the odds of the 4 horses are 1/5, 2/5, 2/5, 2/5 and the house pays on > the > first three across the line, then the percentage of your total bank to > place > on each to return the same profit is 28%, 24%, 24%, 24% respectively. > (This > was relatively easy to work out by trial and error). > Similarly, 3/10, 2/5, 2/5, 2/5 would be 14.28%, 28.57%, 28.57%, 28.57% of > your > bank respectively to return the same profit no matter which three horses > crossed > the line first. > Also, 3/10, 3/10, 2/5, 2/5 equates to 25.925925%, 25.925925%, 24.074074%, > 24.074074% > of your bank to return the same profit. > So, is there a formula to work out these percentages from the 4 given odds > (rather than my laborious trial and error system)? This has my attention so I am sharp on it at the moment... Given the odds .10, .20, .30, and .40 . Now y1 + (y1 / .10) = z y2 + (y2 / .20) = z y3 + (y3 / .30) = z y4 + (y4 / .40) = z Just set y1 = 1 and y1 + (y1 / .10) = z 1 + (1 / .10) = z z = 11 With z now equal to 11 solve for y2 y2 + (y2 / .20) = 11 y2 = 1.8333 Solve for y3 y3 + (y3 / .30) = 11 y3 = 2.5385 And solve for y4 y4 + (y4 / .40) = 11 y4 = 3.1429 Now with x1 = y1 / .10 x2 = y2 / .20 x3 = y3 / .30 x4 = y4 / .40 Calculate the wager x1 as x1 = y1 / .10 x1 = 1 / .10 x1 = 10 Calculate the wgaer x2 as x2 = y2 / .20 x2 = 1.8333 / .20 x2 = 9.1665 Calculate the wager x3 as x3 = y3 / .30 x3 = 2.5385 / .30 x3 = 8.4617 And calculate the wager x4 as x4 = y4 / .40 x4 = 3.1429 / .40 x4 = 7.8573 Now the total wagers are 35.4855. To make a total bankroll wager of 100... The new y1 is y1 = 100 / 35.4855 y1 = 2.8181 So just work the process a second time beginning with the new y1 value of 2.8181...to make the total wager equal to 100. And that works out to wagers of x1 = 28.18 x2 = 25.8335 x3 = 23.8460 x4 = 22.1428 However each payout is 31 which includes the amount wagered. So with one wager out there is 93 in payout but the total wager was 100. So that's a 7% loss regardless of which entry does not pay... === Subject: Re: Question for the Mathematicians > This has my attention so I am sharp on it at the moment... Given the odds .10, .20, .30, and .40 . Now y1 + (y1 / .10) = z > y2 + (y2 / .20) = z > y3 + (y3 / .30) = z > y4 + (y4 / .40) = z Just set y1 = 1 and y1 + (y1 / .10) = z > 1 + (1 / .10) = z > z = 11 With z now equal to 11 solve for y2 y2 + (y2 / .20) = 11 > y2 = 1.8333 Solve for y3 y3 + (y3 / .30) = 11 > y3 = 2.5385 And solve for y4 y4 + (y4 / .40) = 11 > y4 = 3.1429 Now with x1 = y1 / .10 > x2 = y2 / .20 > x3 = y3 / .30 > x4 = y4 / .40 Calculate the wager x1 as x1 = y1 / .10 > x1 = 1 / .10 > x1 = 10 Calculate the wgaer x2 as x2 = y2 / .20 > x2 = 1.8333 / .20 > x2 = 9.1665 Calculate the wager x3 as x3 = y3 / .30 > x3 = 2.5385 / .30 > x3 = 8.4617 And calculate the wager x4 as x4 = y4 / .40 > x4 = 3.1429 / .40 > x4 = 7.8573 Now the total wagers are 35.4855. To make a total bankroll wager of 100... The new y1 is y1 = 100 / 35.4855 > y1 = 2.8181 So just work the process a second time beginning with the new y1 value of > 2.8181...to make the total wager equal to 100. And that works out to > wagers of x1 = 28.18 > x2 = 25.8335 > x3 = 23.8460 > x4 = 22.1428 However each payout is 31 which includes the amount wagered. So with one > wager out there is 93 in payout but the total wager was 100. So that's a > 7% loss regardless of which entry does not pay... Oh, the percent difference between the beginning y1 and the new y1 can be calculated and then the first set of wagers can be adjusted by that percentage...and then no process is repeated. === Subject: Re: Question for the Mathematicians A little touch-up is included... > This has my attention so I am sharp on it at the moment... > Given the odds .10, .20, .30, and .40 . > Now > y1 + (y1 / .10) = z > y2 + (y2 / .20) = z > y3 + (y3 / .30) = z > y4 + (y4 / .40) = z > Just set y1 = 1 and > y1 + (y1 / .10) = z > 1 + (1 / .10) = z > z = 11 > With z now equal to 11 solve for y2 > y2 + (y2 / .20) = 11 > y2 = 1.8333 > Solve for y3 > y3 + (y3 / .30) = 11 > y3 = 2.5385 > And solve for y4 > y4 + (y4 / .40) = 11 > y4 = 3.1429 > Now with > x1 = y1 / .10 > x2 = y2 / .20 > x3 = y3 / .30 > x4 = y4 / .40 > Calculate the wager x1 as > x1 = y1 / .10 > x1 = 1 / .10 > x1 = 10 > Calculate the wgaer x2 as > x2 = y2 / .20 > x2 = 1.8333 / .20 > x2 = 9.1665 > Calculate the wager x3 as > x3 = y3 / .30 > x3 = 2.5385 / .30 > x3 = 8.4617 > And calculate the wager x4 as > x4 = y4 / .40 > x4 = 3.1429 / .40 > x4 = 7.8573 > Now the total wagers are 35.4855. To make a total bankroll wager of > 100... > ...just note that from 35.4855 of the total wager of the preliminary calculation to 100 of the desired total wager is +181.8052 percent-change. Then adjust the wager amounts of the preliminary calculation by +181.8052% to arrive at final wager amounts of... > x1 = 28.18 > x2 = 25.8335 > x3 = 23.8460 > x4 = 22.1428 > However each payout is 31 which includes the amount wagered. So with one > wager out there is 93 in payout but the total wager was 100. So that's a > 7% loss regardless of which entry does not pay... > === Subject: Re: Question for the Mathematicians > This has my attention so I am sharp on it at the moment... > Given the odds .10, .20, .30, and .40 . > Now > y1 + (y1 / .10) = z > y2 + (y2 / .20) = z > y3 + (y3 / .30) = z > y4 + (y4 / .40) = z > Just set y1 = 1 and > y1 + (y1 / .10) = z > 1 + (1 / .10) = z > z = 11 > With z now equal to 11 solve for y2 > y2 + (y2 / .20) = 11 > y2 = 1.8333 > Solve for y3 > y3 + (y3 / .30) = 11 > y3 = 2.5385 > And solve for y4 > y4 + (y4 / .40) = 11 > y4 = 3.1429 > Now with > x1 = y1 / .10 > x2 = y2 / .20 > x3 = y3 / .30 > x4 = y4 / .40 > Calculate the wager x1 as > x1 = y1 / .10 > x1 = 1 / .10 > x1 = 10 > Calculate the wgaer x2 as > x2 = y2 / .20 > x2 = 1.8333 / .20 > x2 = 9.1665 > Calculate the wager x3 as > x3 = y3 / .30 > x3 = 2.5385 / .30 > x3 = 8.4617 > And calculate the wager x4 as > x4 = y4 / .40 > x4 = 3.1429 / .40 > x4 = 7.8573 > Now the total wagers are 35.4855. To make a total bankroll wager >of 100... > The new y1 is > y1 = 100 / 35.4855 > y1 = 2.8181 > So just work the process a second time beginning with the new y1 >value of > 2.8181...to make the total wager equal to 100. And that works out >to > wagers of > x1 = 28.18 > x2 = 25.8335 > x3 = 23.8460 > x4 = 22.1428 > However each payout is 31 which includes the amount wagered. So >with one > wager out there is 93 in payout but the total wager was 100. So >that's a > 7% loss regardless of which entry does not pay... Oh, the percent difference between the beginning y1 and the new y1 >can be >calculated and then the first set of wagers can be adjusted by that percentage...and then no process is repeated. 2/10 thru 5/10 rather than 1/10 thru 4/10. Applying your formulas, I've worked out how to calculate the percentages. Now with a $4000 bank, I bet 1117 on the 2/10, 1031 on the 3/10, 958 on the 4/10 and 894 on the 5/10 and no matter which three horses cross the line first, I'll make a $22 profit each time. (Betting $1000 on each would return a P/L of either $200, $100, $0, -$100). Time to start putting your formulas into a spreadsheet. 'Onya === Subject: Re: Question for the Mathematicians > Actually, I haven't got any expressions. I'm just trialling and >erroring > figures > to get the best result. I've managed to get closer to the result >by > putting > 27.92% of my bank on the 2/10, 25.79% on the 3/10, 23.93% on the >4/10 > and 22.35% > on the 5/10. Like I said, trial and error. > However, I'm looking for the exact answer and a formula on how >to > do it for > these (and any other) four odds? > Having not done any maths for over 20 years, I need the help of >you > guys. > 'Onya > Also, I want to use my whole Bank in the bets. eg. If my Bank was >$100 and > my bets were (from lowest odds to highest) $27.92, $25.79, $23.93 >and >$22.36 > then my profit would be either 53,57,55 or 57 cents. Therefore I'm >trying >to > work out the amounts to bet (totalling my whole Bank) so the profit >is >*exactly* > the same no matter which horse misses out. More importantly, the >what is >the > 'Onya Let b1,b2,b3,b4 be the wagers on horses with odds h1,h2,h3,h4 In your example: b1 = $116, b2 = $108, b3 = $100, b4 = $92 > h1 = 2/10, h2 = 3/10, h3 = 4/10, h4 = 5/10 If all the horses 'came in', rather than just three of the four, >an expression representing your profit would be: (1 + h1)*b1 + (1 + h2)*b2 + (1 + h3)*b3 + (1 + h4)*b4 - B = P where B is the sum of your original bets, B = b1 + b2 + b3 + b4 For the four cases that present themselves for only three paying out, >take the above expression and eliminate the 'losing' term: (1 + h2)*b2 + (1 + h3)*b3 + (1 + h4)*b4 - B = P > (1 + h1)*b1 + (1 + h3)*b3 + (1 + h4)*b4 - B = P > (1 + h1)*b1 + (1 + h2)*b2 + (1 + h4)*b4 - B = P > (1 + h1)*b1 + (1 + h2)*b2 + (1 + h3)*b3 - B = P Expanding B and collecting terms we find: -1*b1 + h2*b2 + h3*b3 + h4*b4 = P > h1*b1 + -1*b2 + h3*b3 + h4*b4 = P > h1*b1 + h2*b2 + -1*b3 + h4*b4 = P > h1*b1 + h2*b2 + h3*b3 + -1*b4 = P Those are your four equations in four unknowns (b1..b4). Now, you *could* hammer away at it to solve for individual >expressions for each of the bets for a given profit P, but >the resulting expressions will be pretty long and cumbersome, >easy to make an error in the process. Instead, you might want to cast it in matrix form and >solve by determinants (Cramer's method). The matrix form is: > | -1 h2 h3 h4 || b1 | | P | > | h1 -1 h3 h4 || b2 | = | P | > | h1 h2 -1 h4 || b3 | | P | > | h1 h2 h3 -1 || b4 | | P | >The form is A*B = C, with A a square matrix, B and P column vectors. To solve for b1, form the adjoint matrix A1 by replacing column >one of A with the vector C. Then b1 is given by: b1 = det(A1)/det(A) Similarly, solve for b2, b3, and b4 by replacing the appropriate >columns in A to obtain the adjoint matrices A2, A3, A4 and solve >accordingly. Both determinants will be negative, but one divides the other >quotient. It will be convenient, therefore, to simply expand the >negative of each determinant: -det(A) = h1*h2 + h1*h3 + h1*h4 + h2*h3 + h2*h4 + h3*h4 > + 2*(h1*h2*h3 + h1*h2*h4 + h1*h3*h4 + H2*h3*h4) > + 3*(h1*h2*h3*h4) > - 1 and >-det(Ai) = 1 + h1 + h2 + h3 + h4 > + h1*h2 + h1*h3 + h1*h4 + h2*h3 + h2*h4 + h3*h4 > + h1*h2*h3 + h1*h2*h4 + h1*h3*h4 + h2*h3*h4 where hi is set to 0 (thus 'killing' the required terms) Using a math application (Mathcad) I solved for your given example >when the fixed profit is set to $1. The results were: b1 = $455/9, b2 = $140/3, b3 = $130/3, b4 = $364/9 You can scale these bets for any desired profit or total bet. again. 'Onya === Subject: Re: Property of uniform continuous function in metric spaces. > Let be given the metric spaces (X,d) and (Y,d') and a function f on X > into Y. > Prove (or deny) the following theorem: > The function f is uniform continuous on X if and only if each Cauchy > sequence in X is transformed by f into a Cauchy sequence in Y. > (It seems to me that only one part if ... then of this theorem can be > given) > If _f_ is uniformly continuous, then it maps Cauchy sequences into > Cauchy sequences. That is very easy to prove from the definitions > involved. > On the other hand, let _f_ be *any* continuous map from a complete > metric space into another complete metric space. Then, in both spaces, > a sequence is a Cauchy sequence if and only if it converges. Therefore, > the assertion _f_ maps Cauchy sequences into Cauchy sequences is > equivalent to _f_ maps convergent sequences into convergent sequences, > which is true, since _f_ is continuous. Are you aware of the fact that > there are continuous maps from complete metric spaces into complete > metric spaces which are not uniformly continuous? > The first part of the theorem is of course very easy to prove. > As for the second part,here it is not assumed that f is continuous nor > that X,d or Y,d' are complete metric spaces! We only consider f to be > a function from one metric space into another metric space whereby > Cauchy sequences remain Cauchy sequences by working of f. > Maybe Jose was not explicit enough for you. He pointed out that your > theorem is false. The fact that it is not assumed that ... does > not prevent us from producing a counterexample where f is continuous > and the metric spaces are complete. I don't quite understand the tone of Robert and Jose's responses. The > OP SAID (and I requote) > (It seems to me that only one part if ... then of this theorem can be > given) > and his mistake is to confuse the if...then part with the only if > part. Given his English, and that he's posting from Belgium, this > hardly registers with me as significant anymore. On the usual scale of > sci.math posts, I'm willing to believe he smelled something rotten in > Denmark. I fail to understand which tone you detected in my reply. The problem raised by the OP looked quite ordinary to me, he was wrong and I tried to make him reach the correct conclusion. My reply had nothing to do with his mistake (if... then instead of only if); I noticed it but I forgot to mention it. Jose Carlos Santos === Subject: Roots of quadratics posting-account=4W9t0woAAAB3dq7-fhllNhT3_mnzEKiC Gecko/2008120122 Firefox/3.0.5 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) Hi Evry1!!! I have a question asking me to find the values of m such that a quadratic has no real roots. Eventually I got down to m^2 < 36 And if it were m^2 = 36 I would write m = +/- 6 m^2 < +/- 6 when the answer is -6 < m < 6 ??? I reckon this answer to this question in my booklet is wrong: Find the values of m such that the quadratic y = x^2 + 2x - 5m has a real root greater than 5. m > 7 Am i right in saying m is not greater than 7? TIA Albert === Subject: Re: Roots of quadratics posting-account=AdyLXQoAAABgRay99CKv1O8Y_7jjivwq InfoPath.1),gzip(gfe),gzip(gfe) > I have a question asking me to find the values of > m such that a quadratic has no real roots. Eventually > I got down to m^2 < 36 And if it were m^2 = 36 I would write m = +/- 6 > m^2 < +/- 6 when the answer is -6 < m < 6 > ??? There are several standard ways of solving non-linear inequalities. I'll explain two methods. Incidentally, it's not expected that a student be able to come up with these methods on his/her own. To put the two methods in context, I'll show how the methods (or very similar methods, at any rate) can be used to solve the corresponding equality. One way of solving m^2 = 36 makes use of the so-called zero property for multiplication --> m^2 - 36 = 0 (m + 6)(m - 6) = 0 A product of two numbers is zero if and only if exactly one of the numbers is zero. Thus, we have m + 6 = 0 or m - 6 = 0 m = -6 or m = 6 m = -6, 6 Another way of solving m^2 = 36 makes use of absolute value considerations --> m^2 = 36 sqrt(m^2) = sqrt(36) |m| = 6 |m - 0| = 6 This last equality has a simple geometric interpretation: The distance between m and 0 on the number line is 6. Therefore, m can be -6 or 6, but no other number. m = -6, 6 These two methods can be reworked to give methods for solving certain inequalities, in particular, the inequality you have. Instead of the zero property for multiplication, we'll use something I'll call the sign property for multiplication. m^2 < 36 m^2 - 36 < 0 (m + 6)(m - 6) < 0 A product of two real numbers is negative if and only if exactly one of the numbers is negative. Thus, we have {m+6 negative and m-6 positive} or {m+6 positive and m-6 negative} {m+6 < 0 and m-6 > 0} or {m+6 > 0 and m-6 < 0} {m < -6 and m > 6} or {m > -6 and m < 6} 'empty set' or -6 < m < 6 -6 < m < 6 The corresponding absolute value method is: m^2 < 36 sqrt(m^2) < sqrt(36) |m| < 6 |m - 0| < 6 This last inequality has a simple geometric interpretation: The distance between m and 0 on the number line is less than 6. Therefore, m must be between -6 and 6, or -6 < m < 6. There are other ways to solve non-linear inequalities (sign charts for the factors being another way), but these two methods are usually good enough to easily solve quadratic inequalities. Dave L. Renfro === Subject: Re: Roots of quadratics >Hi Evry1!!! I have a question asking me to find the values of m such that a >quadratic has no real roots. Eventually I got down to m^2 < 36 And if it were m^2 = 36 I would write m = +/- 6 >m^2 < +/- 6 No. Take the positive square root of both sides of the equation m^2 < 36 giving | m | < 6 (remembering that sqrt(x^2) = |x|). which is satisfied for -6 < x < 6. >when the answer is -6 < m < 6 >??? I reckon this answer to this question in my booklet is wrong: >Find the values of m such that the quadratic y = x^2 + 2x - 5m has a >real root greater than 5. >m > 7 Am i right in saying m is not greater than 7? No. m > 7 is the correct answer to have a real root greater than 5. Take the positive sign in the quadratic formula and set that > 5 and solve the inequality for m. --Lynn http://math.asu.edu/~kurtz === Subject: Re: Roots of quadratics > I have a question asking me to find the values of m such that a > quadratic has no real roots. Eventually I got down to m^2 < 36 And if it were m^2 = 36 I would write m = +/- 6 > m^2 < +/- 6 when the answer is -6 < m < 6 > ??? I reckon this answer to this question in my booklet is wrong: > Find the values of m such that the quadratic y = x^2 + 2x - 5m has a > real root greater than 5. > m > 7 Am i right in saying m is not greater than 7? I don't understand what you write, but I understand the question. And the answer is correct: m > 7. This is so because the equation x^2 +2x - 5m = 0 has two roots, -1 + sqrt(1 + 5m) and -1 - sqrt(1 + 5m), of which the first one is the greatest of the two. So, the assertion the equation has a real root greater than 5 is equivalent to -1 + sqrt(1 + 5m) > 5 and this assertion is equivalent to m > 7. Jose Carlos Santos === Subject: Re: Roots of quadratics <6rt23lF34p6mU1@mid.individual.net> posting-account=4W9t0woAAAB3dq7-fhllNhT3_mnzEKiC Gecko/2008120122 Firefox/3.0.5 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > the equation > x^2 +2x - 5m = 0 has two roots, -1 + sqrt(1 + 5m) and -1 - sqrt(1 + 5m), > of which the first one is the greatest of the two. So, the assertion > the equation has a real root greater than 5 is equivalent to > -1 + sqrt(1 + 5m) > 5 and this assertion is equivalent to m > 7. Yep - I'm wrong. Let me rephrase the slightly more important question: do you just jump from writing m^2 < 36 to -6 < m < 6 ??? There are no additional steps in between?? TY === Subject: Re: number of sets in some standard set structures <49543162$0$195$e4fe514c@news.xs4all.nl> <4956152c$0$197$e4fe514c@news.xs4all.nl> posting-account=YftvUQoAAAD36OR-en6JDbmNKuS53Hzz Gecko/2008092417 Firefox/3.0.3,gzip(gfe),gzip(gfe) > 1.number of rings of sets: > ------------------------------------ > For example, there are 4 rings of sets on the n=2 element set X={x,y} > Not counting the empty set? I did indeed make an error here --- there are 5 rings of sets on X= {x,y}, as you indicated. Here are the five rings of sets on the set X={x,y}: R1 = { ?, } R2 = { ?, {x} } R3 = { ?, {y} } R4 = { ?, {x, y} } R5 = { ?, {x} , {y} , {x,y} } (I am not sure if ? will display correctly on all newsreaders/ browsers, but it is supposed to be the emptyset symbol.) R4 and R5 are also algebras of sets. > Oops. I meant to say the ring with only the empty set. > So while we should /not/ count R = {}, we /should/ count the trivial R = { {} } Yes, that one is a ring of sets. In fact, every ring of sets contains the empty set as an element. In universal algebra one would say that there are 7 standard set operations on X: union, intersection, difference, symmetric difference, complement, emptyset, and the universal set X (the first four are binary operations, the complement is a unary operation, and the last two are nullary operations). And of these 7 operations, rings of sets are closed under 5 of them --- union, intersection, difference, symmetric difference, and emptyset. > 15 rings of sets on the n=3 element set X={x,y,z}. > Counting the empty set this time? Here are the 15 rings of sets on the set X={x,y,z}: R1 = { ? } R2 = { ?, {x} } R3 = { ?, {y} } R4 = { ?, {z} } R5 = { ?, {x, y} } R6 = { ?, {x, z} } R7 = { ?, {y, z} } R8 = { ?, {x} , {y} , {x, y} } R9 = { ?, {x} , {z} , {x, z} } R10 = { ?, {y} , {z} , {y, z} } R11 = { ?, X } R12 = { ?, {x} , {y, z} , X } R13 = { ?, {y} , {x, z} , X } R14 = { ?, {z} , {x, y} , X } R15 = { ?, {x} , {y} , {z} , {x, y} , {x, z} , {y, z} , X } The last five, R11--R15, are also algebras of sets. > 2 algebras of sets on the n=2 element set X={x,y}, > 5 algebras of sets on the n=3 element set X={x,y,z}. Algebra of sets are closed under all 7 operations. Here are the two algebra of sets on X={x,y}: A1 = {?, X} A2 = {?, {x} , {y} , X} Here are the five algebra of sets on X={x,y,z}: A1 = { ?, X } A2 = { ?, {x} , {y, z} , X } A3 = { ?, {y} , {x, z} , X } A4 = { ?, {z} , {x, y} , X } A5 = { ?, {x} , {y} , {z} , {x, y} , {x, z} , {y, z} , X } > As far as I can see both the above are essentially Boolean algebras That is an interesting observation. In fact, it has been proven as far back as 1936 that every Boolean lattice is isomorphic to an algebra of sets: Stone (1936): Transactions of the American Mathematical Society 40 [1936] GrÂatzer (1971): Lattice Theory; first concepts and distributive lattices, page 76 GrÂatzer (1998): General Lattice Theory, page 85 > In the first case the minimal non-empty sets are an arbitrary partition of a subset of X > in which case f(n) = B(n+1), where B(n) is the nth Bell number; > http://www.research.att.com/~njas/sequences/A000110 > and in the second case they are an arbitrary partition of X > in which case f(n) = B(n). The Bell numbers by definition describe the number of partitions on a finite set X with n elements (or alternatively, the number of equivalence relations on X). Using the Bell numbers to describe the number of rings of sets as B(n+1) and the number of algebras of sets as B(n) is a very interesting suggestion and it would seem likely to this insight! Dan (original poster) > I have some questions about some standard set structures. 1.number of rings of sets: > ------------------------------------ > How many rings of sets are there on a finite set of with n labeled > elements? By ring of sets I mean any subset of the powerset of a set X that is > closed under set union and set difference. For example, there are > 4 rings of sets on the n=2 element set X={x,y}, and > 15 rings of sets on the n=3 element set X={x,y,z}. 2. number of algebras of sets: > ----------------------------------------- > How many algebras of sets are there on a finite set of with n labeled > elements? By algebra of sets I mean any subset of the powerset of a set X that > is closed under set complement set intersection. For example, there > are > 2 algebras of sets on the n=2 element set X={x,y}, and > 5 algebras of sets on the n=3 element set X={x,y,z}. -------------------------------- > For items 1 and 2 above, I am looking for something maybe similar to > what has been done for the number of topologies at > http://www.research.att.com/~njas/sequences/A000798 > or for the number of partitions at > http://www.research.att.com/~njas/sequences/A000110 > Here are references for the above definition of rings of sets: > * Berezansky, Sheftel and Us (1996): Functional Analysis: Volume > I. . . , page 4 > * Halmos (1950): Measure Theory, page 19 > * Hausdorff (1937): Set Theory (GrundzÂuge der Mengenlehre), page 90 Here are references for the above definition of algebra of sets: > * Aliprantis and Burkinshaw (1998): Principles of Real Analysis, page > 95 > * Halmos (1950): Measure Theory, page 21 > * Hausdorff (1937): Set Theory (GrundzÂuge der Mengenlehre), page 91 Note, some authors have used an alternative definition of rings of > sets that is incompatible with the one used in this post: > * Hausdorff (1937): Set Theory (GrundzÂuge der Mengenlehre), 90 > * Birkhoff (1937): Duke Math. J. 3 [1937], page 443 > * ErdÂos and Tarski (1943): Annals of Mathematics, page 315 > * MacLane and Birkhoff (1999): Algebra, page 485 Dan Greenhoe > I have some questions about some standard set structures. > 1.number of rings of sets: > ------------------------------------ > How many rings of sets are there on a finite set of with n labeled > elements? > By ring of sets I mean any subset of the powerset of a set X that is > closed under set union and set difference. For example, there are > 4 rings of sets on the n=2 element set X={x,y}, and Not counting the empty set? > 15 rings of sets on the n=3 element set X={x,y,z}. Counting the empty set this time? > 2. number of algebras of sets: > ----------------------------------------- > How many algebras of sets are there on a finite set of with n labeled > elements? > By algebra of sets I mean any subset of the powerset of a set X that > is closed under set complement set intersection. For example, there > are > 2 algebras of sets on the n=2 element set X={x,y}, and > 5 algebras of sets on the n=3 element set X={x,y,z}. 15, 52, 203, if I'm not mistaken. As far as I can see both the above are essentially Boolean algebras, at > least for finite X. > In the first case the minimal non-empty sets are an arbitrary partition > of a subset of X, and in the second case they are an arbitrary partition > of X. > That should make them relatively easy to count. -- > Niels Diepeveen > I have some questions about some standard set structures. > 1.number of rings of sets: > ------------------------------------ > How many rings of sets are there on a finite set of with n labeled > elements? > By ring of sets I mean any subset of the powerset of a set X that is > closed under set union and set difference. For example, there are > 4 rings of sets on the n=2 element set X={x,y}, and > Not counting the empty set? > 15 rings of sets on the n=3 element set X={x,y,z}. > Counting the empty set this time? > 2. number of algebras of sets: > ----------------------------------------- > How many algebras of sets are there on a finite set of with n labeled > elements? > By algebra of sets I mean any subset of the powerset of a set X that > is closed under set complement set intersection. For example, there > are > 2 algebras of sets on the n=2 element set X={x,y}, and > 5 algebras of sets on the n=3 element set X={x,y,z}. > 15, 52, 203, if I'm not mistaken. > As far as I can see both the above are essentially Boolean algebras, at > least for finite X. > In the first case the minimal non-empty sets are an arbitrary partition > of a subset of X, ... ... in which case f(n) = B(n+1), where B(n) is the nth Bell number; > see http://www.research.att.com/~njas/sequences/A000110 > and in the second case they are an arbitrary partition > of X... ... in which case f(n) = B(n). > That should make them relatively easy to count. Yep. > I have some questions about some standard set structures. > 1.number of rings of sets: > ------------------------------------ > How many rings of sets are there on a finite set of with n labeled > elements? > By ring of sets I mean any subset of the powerset of a set X that is > closed under set union and set difference. For example, there are > 4 rings of sets on the n=2 element set X={x,y}, and > Not counting the empty set? Oops. I meant to say the ring with only the empty set. > 15 rings of sets on the n=3 element set X={x,y,z}. > Counting the empty set this time? Same here. I didn't include the actual empty set anywhere, although it's > trivially closed under all operations. I think you meant to exclude > those as well, judging by the counts you came up with. I also seem to > remember that the last definition of algebra that I saw included > something to the effect of the empty set is an element of every algebra. > 2. number of algebras of sets: > ----------------------------------------- > How many algebras of sets are there on a finite set of with n labeled > elements? > By algebra of sets I mean any subset of the powerset of a set X that > is closed under set complement set intersection. For example, there > are > 2 algebras of sets on the n=2 element set X={x,y}, and > 5 algebras of sets on the n=3 element set X={x,y,z}. > 15, 52, 203, if I'm not mistaken. > As far as I can see both the above are essentially Boolean algebras, at > least for finite X. > In the first case the minimal non-empty sets are an arbitrary partition > of a subset of X, and in the second case they are an arbitrary partition > of X. > That should make them relatively easy to count. > I have some questions about some standard set structures. > 1.number of rings of sets: > ------------------------------------ > How many rings of sets are there on a finite set of with n labeled > elements? > By ring of sets I mean any subset of the powerset of a set X that is > closed under set union and set difference. For example, there are > 4 rings of sets on the n=2 element set X={x,y}, and > Not counting the empty set? > Oops. I meant to say the ring with only the empty set. > 15 rings of sets on the n=3 element set X={x,y,z}. > Counting the empty set this time? > Same here. I didn't include the actual empty set anywhere, although it's > trivially closed under all operations. I think you meant to exclude > those as well, judging by the counts you came up with. I also seem to > remember that the last definition of algebra that I saw included > something to the effect of the empty set is an element of every algebra. The definitions I looked at for both terms all have the condition R > is a ring of sets (or algebra) if R is non-empty and... (etc.). So while we should /not/ count R = {}, we /should/ count the trivial R > = { {} }, as it is a non-empty subset of the power-set, and satisfies > the axioms. This gives the Bell number sequences previously noted. Of > course, if the trivial ring (algebra) is to be excluded, just subtract > 1. > === Subject: Re: number of sets in some standard set structures > 1.number of rings of sets: > ------------------------------------ > For example, there are 4 rings of sets on the n=2 element set X={x,y} > Not counting the empty set? > I did indeed make an error here --- there are 5 rings of sets on X= > {x,y}, as you indicated. > Here are the five rings of sets on the set X={x,y}: > R1 = { ?, } > R2 = { ?, {x} } > R3 = { ?, {y} } > R4 = { ?, {x, y} } > R5 = { ?, {x} , {y} , {x,y} } > (I am not sure if ? will display correctly on all newsreaders/ > browsers, but it is supposed to be the emptyset symbol.) > R4 and R5 are also algebras of sets. Oops. I meant to say the ring with only the empty set. > So while we should /not/ count R = {}, we /should/ count the trivial R = { {} } > Yes, that one is a ring of sets. In fact, every ring of sets contains > the empty set as an element. In universal algebra one would say that > there are 7 standard set operations on X: union, intersection, > difference, symmetric difference, complement, emptyset, and the > universal set X (the first four are binary operations, the complement > is a unary operation, and the last two are nullary operations). And of > these 7 operations, rings of sets are closed under 5 of them --- > union, intersection, difference, symmetric difference, and emptyset. > 15 rings of sets on the n=3 element set X={x,y,z}. > Counting the empty set this time? > Here are the 15 rings of sets on the set X={x,y,z}: > R1 = { ? } > R2 = { ?, {x} } > R3 = { ?, {y} } > R4 = { ?, {z} } > R5 = { ?, {x, y} } > R6 = { ?, {x, z} } > R7 = { ?, {y, z} } > R8 = { ?, {x} , {y} , {x, y} } > R9 = { ?, {x} , {z} , {x, z} } > R10 = { ?, {y} , {z} , {y, z} } > R11 = { ?, X } > R12 = { ?, {x} , {y, z} , X } > R13 = { ?, {y} , {x, z} , X } > R14 = { ?, {z} , {x, y} , X } > R15 = { ?, {x} , {y} , {z} , {x, y} , {x, z} , {y, z} , X } > The last five, R11--R15, are also algebras of sets. > 2 algebras of sets on the n=2 element set X={x,y}, > 5 algebras of sets on the n=3 element set X={x,y,z}. > Algebra of sets are closed under all 7 operations. > Here are the two algebra of sets on X={x,y}: > A1 = {?, X} > A2 = {?, {x} , {y} , X} > Here are the five algebra of sets on X={x,y,z}: > A1 = { ?, X } > A2 = { ?, {x} , {y, z} , X } > A3 = { ?, {y} , {x, z} , X } > A4 = { ?, {z} , {x, y} , X } > A5 = { ?, {x} , {y} , {z} , {x, y} , {x, z} , {y, z} , X } As far as I can see both the above are essentially Boolean algebras > That is an interesting observation. In fact, it has been proven as far > back as 1936 that every Boolean lattice is isomorphic to an algebra of > sets: > Stone (1936): Transactions of the American Mathematical Society 40 > [1936] > GrÂatzer (1971): Lattice Theory; first concepts and distributive > lattices, page 76 > GrÂatzer (1998): General Lattice Theory, page 85 In the first case the minimal non-empty sets are an arbitrary partition of a subset of X > in which case f(n) = B(n+1), where B(n) is the nth Bell number; > http://www.research.att.com/~njas/sequences/A000110 > and in the second case they are an arbitrary partition of X > in which case f(n) = B(n). The Bell numbers by definition describe the number of partitions on a > finite set X with n elements (or alternatively, the number of > equivalence relations on X). Using the Bell numbers to describe the > number of rings of sets as B(n+1) and the number of algebras of sets > as B(n) is a very interesting suggestion and it would seem likely to > this insight! Dan (original poster) I have never seen a proof of this particular fact, but all the hard parts are well known facts, as far as I can see. Once you have the association with Boolean lattices, you can use the fact that the atoms (minimal nonzero elements) of the lattice correspond to minimal nonempty sets in the algebra. You also know that the maximum of the lattice is the supremum (union) of these atoms. Most importantly, you know that a finite Boolean lattice is completely determined by these atoms. In terms of an algebra of sets this boils down to a set is in the algebra if and only if it is the union of a combination of minimal nonempty sets. So what remains to be shown is that the minimal nonempty sets are a partition of X, which is easy. I have already noted that their union must be X. That they are pairwise disjoint follows from the fact that the intersection of two distinct sets is a proper subset of at least one of them. For rings of sets the story is pretty similar, except that there is no complement w.r.t. X, only w.r.t. the union of all sets in the ring, so that union can be an arbitrary subset of X. > I have some questions about some standard set structures. > 1.number of rings of sets: > ------------------------------------ > How many rings of sets are there on a finite set of with n labeled > elements? > By ring of sets I mean any subset of the powerset of a set X that is > closed under set union and set difference. For example, there are > 4 rings of sets on the n=2 element set X={x,y}, and > 15 rings of sets on the n=3 element set X={x,y,z}. > 2. number of algebras of sets: > ----------------------------------------- > How many algebras of sets are there on a finite set of with n labeled > elements? > By algebra of sets I mean any subset of the powerset of a set X that > is closed under set complement set intersection. For example, there > are > 2 algebras of sets on the n=2 element set X={x,y}, and > 5 algebras of sets on the n=3 element set X={x,y,z}. > -------------------------------- > For items 1 and 2 above, I am looking for something maybe similar to > what has been done for the number of topologies at > http://www.research.att.com/~njas/sequences/A000798 > or for the number of partitions at > http://www.research.att.com/~njas/sequences/A000110 > Here are references for the above definition of rings of sets: > * Berezansky, Sheftel and Us (1996): Functional Analysis: Volume > I. . . , page 4 > * Halmos (1950): Measure Theory, page 19 > * Hausdorff (1937): Set Theory (GrundzÂuge der Mengenlehre), page 90 > Here are references for the above definition of algebra of sets: > * Aliprantis and Burkinshaw (1998): Principles of Real Analysis, page > 95 > * Halmos (1950): Measure Theory, page 21 > * Hausdorff (1937): Set Theory (GrundzÂuge der Mengenlehre), page 91 > Note, some authors have used an alternative definition of rings of > sets that is incompatible with the one used in this post: > * Hausdorff (1937): Set Theory (GrundzÂuge der Mengenlehre), 90 > * Birkhoff (1937): Duke Math. J. 3 [1937], page 443 > * ErdÂos and Tarski (1943): Annals of Mathematics, page 315 > * MacLane and Birkhoff (1999): Algebra, page 485 > Dan Greenhoe I have some questions about some standard set structures. > 1.number of rings of sets: > ------------------------------------ > How many rings of sets are there on a finite set of with n labeled > elements? > By ring of sets I mean any subset of the powerset of a set X that is > closed under set union and set difference. For example, there are > 4 rings of sets on the n=2 element set X={x,y}, and > Not counting the empty set? > 15 rings of sets on the n=3 element set X={x,y,z}. > Counting the empty set this time? > 2. number of algebras of sets: > ----------------------------------------- > How many algebras of sets are there on a finite set of with n labeled > elements? > By algebra of sets I mean any subset of the powerset of a set X that > is closed under set complement set intersection. For example, there > are > 2 algebras of sets on the n=2 element set X={x,y}, and > 5 algebras of sets on the n=3 element set X={x,y,z}. > 15, 52, 203, if I'm not mistaken. > As far as I can see both the above are essentially Boolean algebras, at > least for finite X. > In the first case the minimal non-empty sets are an arbitrary partition > of a subset of X, and in the second case they are an arbitrary partition > of X. > That should make them relatively easy to count. > -- > Niels Diepeveen > I have some questions about some standard set structures. > 1.number of rings of sets: > ------------------------------------ > How many rings of sets are there on a finite set of with n labeled > elements? > By ring of sets I mean any subset of the powerset of a set X that is > closed under set union and set difference. For example, there are > 4 rings of sets on the n=2 element set X={x,y}, and > Not counting the empty set? > 15 rings of sets on the n=3 element set X={x,y,z}. > Counting the empty set this time? > 2. number of algebras of sets: > ----------------------------------------- > How many algebras of sets are there on a finite set of with n labeled > elements? > By algebra of sets I mean any subset of the powerset of a set X that > is closed under set complement set intersection. For example, there > are > 2 algebras of sets on the n=2 element set X={x,y}, and > 5 algebras of sets on the n=3 element set X={x,y,z}. > 15, 52, 203, if I'm not mistaken. > As far as I can see both the above are essentially Boolean algebras, at > least for finite X. > In the first case the minimal non-empty sets are an arbitrary partition > of a subset of X, ... > ... in which case f(n) = B(n+1), where B(n) is the nth Bell number; > see > http://www.research.att.com/~njas/sequences/A000110 > and in the second case they are an arbitrary partition > of X... > ... in which case f(n) = B(n). > That should make them relatively easy to count. > Yep. > I have some questions about some standard set structures. > 1.number of rings of sets: > ------------------------------------ > How many rings of sets are there on a finite set of with n labeled > elements? > By ring of sets I mean any subset of the powerset of a set X that is > closed under set union and set difference. For example, there are > 4 rings of sets on the n=2 element set X={x,y}, and > Not counting the empty set? > Oops. I meant to say the ring with only the empty set. > 15 rings of sets on the n=3 element set X={x,y,z}. > Counting the empty set this time? > Same here. I didn't include the actual empty set anywhere, although it's > trivially closed under all operations. I think you meant to exclude > those as well, judging by the counts you came up with. I also seem to > remember that the last definition of algebra that I saw included > something to the effect of the empty set is an element of every algebra. > 2. number of algebras of sets: > ----------------------------------------- > How many algebras of sets are there on a finite set of with n labeled > elements? > By algebra of sets I mean any subset of the powerset of a set X that > is closed under set complement set intersection. For example, there > are > 2 algebras of sets on the n=2 element set X={x,y}, and > 5 algebras of sets on the n=3 element set X={x,y,z}. > 15, 52, 203, if I'm not mistaken. > As far as I can see both the above are essentially Boolean algebras, at > least for finite X. > In the first case the minimal non-empty sets are an arbitrary partition > of a subset of X, and in the second case they are an arbitrary partition > of X. > That should make them relatively easy to count. I have some questions about some standard set structures. > 1.number of rings of sets: > ------------------------------------ > How many rings of sets are there on a finite set of with n labeled > elements? > By ring of sets I mean any subset of the powerset of a set X that is > closed under set union and set difference. For example, there are > 4 rings of sets on the n=2 element set X={x,y}, and > Not counting the empty set? > Oops. I meant to say the ring with only the empty set. > 15 rings of sets on the n=3 element set X={x,y,z}. > Counting the empty set this time? > Same here. I didn't include the actual empty set anywhere, although it's > trivially closed under all operations. I think you meant to exclude > those as well, judging by the counts you came up with. I also seem to > remember that the last definition of algebra that I saw included > something to the effect of the empty set is an element of every algebra. > The definitions I looked at for both terms all have the condition R > is a ring of sets (or algebra) if R is non-empty and... (etc.). > So while we should /not/ count R = {}, we /should/ count the trivial R > = { {} }, as it is a non-empty subset of the power-set, and satisfies > the axioms. This gives the Bell number sequences previously noted. Of > course, if the trivial ring (algebra) is to be excluded, just subtract > 1. > === Subject: Algorithms course posting-account=4dUGDAoAAABRfO7LkrSC6c7_KBACMyXw Gecko/2008120122 Firefox/3.0.5,gzip(gfe),gzip(gfe) I'm going to be taking a computer science course on algorithms next semester and wondered what math I should brush up on to prepare for the course? I had taken calculus I and II and discrete math about ten years ago, so I'm somewhat rusty. I don't know if this is the correct forum to post this question, any feedback is appreciated. Steve === Subject: Re: jmhbahciv is a dishonest scumbag <5a987$49553ba5$49e5dd2$7907@DIALUPUSA.NET> posting-account=p0JNqwkAAAChY16-5zbk2O2xWfBB6K-z Gecko/20061206 Firefox/1.5.0.9,gzip(gfe),gzip(gfe) > This is poor logic. That someone doesn't respond to your posts > doesn't mean your right. It may just mean that you're a fool, and > no one likes to argue with a fool. Q.E.D. You still have not answered the question. How > will _you_ make people obey? And you still haven't read the answer. But then you are one lying bitch ... Andrew Usher === Subject: Re: jmhbahciv is a dishonest scumbag This is poor logic. That someone doesn't respond to your posts > doesn't mean your right. It may just mean that you're a fool, and > no one likes to argue with a fool. > Q.E.D. You still have not answered the question. How > will _you_ make people obey? And you still haven't read the answer. But then you are one lying > bitch ... Andrew Usher All I read was some clumsy tap dancing with the obvious goal of not answering the question. Now, what will you do when people refuse to obey you? /BAH === Subject: Re: jmhbahciv is a dishonest scumbag > This is poor logic. That someone doesn't respond to your posts > doesn't mean your right. It may just mean that you're a fool, and > no one likes to argue with a fool. > Q.E.D. You still have not answered the question. How > will _you_ make people obey? > And you still haven't read the answer. But then you are one lying > bitch ... > Andrew Usher > All I read was some clumsy tap dancing with the obvious goal of > not answering the question. Now, what will you do when people > refuse to obey you? /BAH Lotsa luck. I'm now resigning from several newsgroups I expanded into (again) in the past few winter doldrum weeks. I know there are better things to do. Things were really bad when I shrank my .newsrc last time, but they've managed to get even worse, which came as a surprise, whoodathunk? I guess its partly because I have these gigantic killfiles where I normally read, and had none here. See ya if you accidentally stray into my neighborhood again. Trust me, making that trip just to say hello isn't worth wading through all the muck. There's just sooooo damn much of the stuff now. 1991, now that was a good year. === Subject: Reason and emotion posting-account=p0JNqwkAAAChY16-5zbk2O2xWfBB6K-z Gecko/20061206 Firefox/1.5.0.9,gzip(gfe),gzip(gfe) I wanted to post one more of my essays - actually, I've already shown this one place on the internet, but it's probably more appropriate here. After all, reason is a man's issue. Andrew Usher -------- Reason and Emotion Broadly speaking, it is surely correct that reason and emotion are the two forces that govern our minds. It is often stated or assumed that they are opposing forces; I do not believe that to be necessarily true. What is reason? One might say that it is logic, or the application of logic to practical problems. And as logic is absolute by definition, any reasoner given the same data will reach the same rational conclusion if any is possible. It is of great advantage to us that we can so predict what any person thinking rationally must do; it is the same as ourselves, thinking rationally, would do in the same situation. And one may find that any seeming exception is explained by a failure of reason to completely explain the action in question. What is emotion? Emotion may be defined as the part of our mental state that is not rational. This is very broad, and one might wish to differentiate physical needs such as 'I am hungry'. But I do not think it possible; an example that shows the point is the desire for a sexual relationship - does that have a physical or an emotional nature? I therefore subsume all under the word emotion. How well do we understand the emotions of others? It is a fundamental fact that we can never perfectly understand the emotional function of any other person; though most of us can do fairly well most of the time, we can all recall a time when it was otherwise. Do reason and emotion conflict? Not inherently, since they are separate processes. But we must be persuaded that where both apply, reason must correctly prevail over emotion, indeed by definition. For logic asserts not just that it useful, but that it is universal: where logic does apply, it must give the truth, or as near as possible with our knowledge. And those situations where logic does apply are precisely the domain of reason. But reason can't tell us everything; decisions from whether to prefer Coke or Pepsi to whom to be sexually attracted to can not be settled by reason. Those matters, then, are the domain of emotion. So we can rightly see that giving in to our emotions is not a contradiction of the supremacy of reason, but an extension of it. === Subject: Re: Reason and emotion > I wanted to post one more of my essays - actually, I've already shown > this one place on the internet, but it's probably more appropriate > here. After all, reason is a man's issue. Andrew Usher You're pretty brave, exposing your psychiatric problems like this in public. > Reason and Emotion Broadly speaking, it is surely correct that reason and emotion are the > two forces that govern our minds. By definition, emotion is an unrelenting driver that has nothing at all to do with mind, only with what are deemed impulsive actions. > It is often stated or assumed that > they are opposing forces; I do not believe that to be necessarily > true. You should listen rather than attempting to reinvent the wheel by using a bumpy one. > What is reason? One might say that it is logic, or the application of > logic to practical problems. Naive. > And as logic is absolute by definition, Find me someone published who agrees with this definition. > any reasoner given the same data will reach the same rational > conclusion if any is possible. Completely untrue. Reason is filtered through culture and personal experience. WWI veterans used to duck as a result of unexpected loud noises. And that was conditioning, not emotion. > It is of great advantage to us that we > can so predict what any person thinking rationally must do; it is the > same as ourselves, thinking rationally, would do in the same > situation. So you claim that's how Bill Gates and Donald Trump got so very rich, by doing what you would do in the same circumstances. Bwahahahahahaha!!!!!! > And one may find that any seeming exception is explained by > a failure of reason to completely explain the action in question. That's idiotic and it flys in the face of very logical value systems that are used by sane, logical people. snip === Subject: Re: Reason and emotion It's quite obvious that you're an idiot. I'm not going to bother responding to someone that makes (probably on purpose) so many elementary mistakes. Andrew Usher === Subject: Re: Reason and emotion You're pretty brave, exposing your psychiatric problems > like this in public. > Why is that? Are you not advertising your emotional fragility in this same sentence? Trust me, it's just letters on a screen, you don't have to be afraid. :-) === Subject: Re: Reason and emotion >You're pretty brave, exposing your psychiatric problems >like this in public. > Why is that? Are you not advertising your emotional fragility in this same > sentence? No. I was discussing you lack of rationality in interaction in a public forum. > Trust me, it's just letters on a screen, you don't have to be afraid. :-) Trust me, your irrationality is showing. === Subject: Re: Reason and emotion <58d50$49597c97$cdd08515$14531@DIALUPUSA.NET> posting-account=qHNgPQoAAAA40SLlrmjQxSJhnyKS76HY AppleWebKit/525.19 (KHTML, like Gecko) Chrome/1.0.154.36 Safari/525.19,gzip(gfe),gzip(gfe) >You're pretty brave, exposing your psychiatric problems >like this in public. > Why is that? > Are you not advertising your emotional fragility in this same > sentence? No. I was discussing you lack of rationality in > interaction in a public forum. I'd hate to correct you again and again but I'm not Andrew. > Trust me, it's just letters on a screen, you don't have to be afraid. > :-) Trust me, your irrationality is showing. Yeah, I know it looks that way to you. I'm still working at explaining things on your level. Wish me luck ok? :-) === Subject: Re: Reason and emotion >You're pretty brave, exposing your psychiatric problems >like this in public. >Why is that? >Are you not advertising your emotional fragility in this same >sentence? >No. I was discussing you lack of rationality in >interaction in a public forum. > I'd hate to correct you again and again but I'm not Andrew. >Trust me, it's just letters on a screen, you don't have to be afraid. >:-) >Trust me, your irrationality is showing. > Yeah, I know it looks that way to you. I'm still working at explaining things on your level. You ought to have recognized that for you this represents a glass ceiling no matter how you aspire to achieve that which is waaaaaaayyyyy above you. > Wish me luck ok? > :-) Hillary sends her condolences, she's in the same boat. === Subject: Re: Reason and emotion > I wanted to post one more of my essays - actually, I've already shown > this one place on the internet, but it's probably more appropriate > here. After all, reason is a man's issue. Andrew Usher -------- Reason and Emotion Broadly speaking, it is surely correct that reason and emotion are the > two forces that govern our minds. It is often stated or assumed that > they are opposing forces; I do not believe that to be necessarily > true. What is reason? One might say that it is logic, or the application of > logic to practical problems. And as logic is absolute by definition, > any reasoner given the same data will reach the same rational > conclusion if any is possible. It is of great advantage to us that we Not at all. No two people have the same data, nor the same algorithms for applying reason, nor for the weighting of data. > can so predict what any person thinking rationally must do; it is the > same as ourselves, thinking rationally, would do in the same > situation. And one may find that any seeming exception is explained by > a failure of reason to completely explain the action in question. What is emotion? Emotion may be defined as the part of our mental > state that is not rational. This is very broad, and one might wish to No. Emotion is what motivates. -- Dirk http://www.transcendence.me.uk/ - Transcendence UK http://www.theconsensus.org/ - A UK political party http://www.onetribe.me.uk/wordpress/?cat=5 - Our podcasts on weird stuff === Subject: Re: Reason and emotion <6rt47uF354vrU1@mid.individual.net> posting-account=p0JNqwkAAAChY16-5zbk2O2xWfBB6K-z Gecko/20061206 Firefox/1.5.0.9,gzip(gfe),gzip(gfe) On Dec 29, 5:19 pm, Dirk Bruere at NeoPax What is reason? One might say that it is logic, or the application of > logic to practical problems. And as logic is absolute by definition, > any reasoner given the same data will reach the same rational > conclusion if any is possible. It is of great advantage to us that we Not at all. > No two people have the same data, nor the same algorithms for applying > reason, nor for the weighting of data. I was referring to the perfect application of reason; they way real people use reason is of course imperfect. > can so predict what any person thinking rationally must do; it is the > same as ourselves, thinking rationally, would do in the same > situation. And one may find that any seeming exception is explained by > a failure of reason to completely explain the action in question. > What is emotion? Emotion may be defined as the part of our mental > state that is not rational. This is very broad, and one might wish to No. Emotion is what motivates. Etymological fallacy. And anyway, what you were criticising was a definition. Andrew Usher === Subject: Re: Reason and emotion > On Dec 29, 5:19 pm, Dirk Bruere at NeoPax What is reason? One might say that it is logic, or the application of > logic to practical problems. And as logic is absolute by definition, > any reasoner given the same data will reach the same rational > conclusion if any is possible. It is of great advantage to us that we > Not at all. > No two people have the same data, nor the same algorithms for applying > reason, nor for the weighting of data. I was referring to the perfect application of reason; they way real > people > use reason is of course imperfect. can so predict what any person thinking rationally must do; it is the > same as ourselves, thinking rationally, would do in the same > situation. And one may find that any seeming exception is explained by > a failure of reason to completely explain the action in question. > What is emotion? Emotion may be defined as the part of our mental > state that is not rational. This is very broad, and one might wish to > No. Emotion is what motivates. Etymological fallacy. And anyway, what you were criticising was a > definition. 1579, a (physical) moving, stirring, agitation, from M.Fr. emotion, from O.Fr. emouvoir stir up, from L. emovere move out, remove, agitate, from ex- out + movere to move (see move). Sense of strong feeling is first recorded 1660; extended to any feeling 1808. Emote is a 1917 back-formation. Emotional liable to emotion is from 1857. Dirk http://www.transcendence.me.uk/ - Transcendence UK http://www.theconsensus.org/ - A UK political party http://www.onetribe.me.uk/wordpress/?cat=5 - Our podcasts on weird stuff === Subject: Three consecutive primes conjecture posting-account=josrcgkAAABoiXs2WTgIH82zYbqHK43d 1.1.4322),gzip(gfe),gzip(gfe) Let p1, p2, and p3 be three consecutive primes. Let a1, a2, and a3 be integers with: (i) a1*p1+a2*p2+a3*p3=0 and (ii) |a1|+|a2|+|a3| as small as possible. Does this last sum divide p3-p1? Rich === Subject: Re: Three consecutive primes conjecture posting-account=sKfmEQkAAAC8kI3Pv6_U_nt9sVsxZ_ou 1.1.4322),gzip(gfe),gzip(gfe) > Let p1, p2, and p3 be three consecutive primes. Let a1, a2, and a3 be > integers with: (i) a1*p1+a2*p2+a3*p3=0 > and > (ii) |a1|+|a2|+|a3| as small as possible. Does this last sum divide p3-p1? a1 = a2 =a3 =0 gives |a1|+|a2|+|a3| =0 === Subject: Re: Three consecutive primes conjecture posting-account=josrcgkAAABoiXs2WTgIH82zYbqHK43d 1.1.4322),gzip(gfe),gzip(gfe) On Dec 29, 5:25pm, sttscitr...@tesco.net Let p1, p2, and p3 be three consecutive primes. Let a1, a2, and a3 be > integers with: > (i) a1*p1+a2*p2+a3*p3=0 > and > (ii) |a1|+|a2|+|a3| as small as possible. > Does this last sum divide p3-p1? a1 = a2 =a3 =0 gives > |a1|+|a2|+|a3| =0 My bad: (ii) |a1|+|a2|+|a3| is positive and as small as possible. Seems to be true if p1<500000, or so. Even more curious: If p1=2n+1, p2=p1+2*random(k), p3=2*random(k) then for every k there would seem to exist some n 0 such that (i) and (ii) both hold for all n>n 0. [random(k)=some random number >=0 and On Dec 29, 5:25pm, sttscitr...@tesco.net Let p1, p2, and p3 be three consecutive primes. Let a1, a2, and a3 be > integers with: > (i) a1*p1+a2*p2+a3*p3=0 > and > (ii) |a1|+|a2|+|a3| as small as possible. > Does this last sum divide p3-p1? > a1 = a2 =a3 =0 gives > |a1|+|a2|+|a3| =0 My bad: (ii) |a1|+|a2|+|a3| is positive and as small as possible. Seems to be true if p1<500000, or so. The fact that primes are involved may just be coincidence. pn + q(n+s) + r(n+t) =0, 0 qs'd + rt'd =0 => qs' + rt' =0 => q = t', r = -s', p = -t' +s' |p|+|q|+|r| = |t'|+|-s'|+|-t' +s'| |t'|+|s'|+|t'|-|s'| = 2t' t = t'd so if d is even 2t' divides t In your case |a1|+|a2|+|a3| divides p3-p1 which is always divisible by 2 I've checked a few small cases e.g. 21,33,49, 4,-7,3 For minimum solutions it seems that p+q+r =0. Have you found that a1 +a2 +a3 is always equal to 0 ? Is your |a1|+|a2|+|a3| always divisible by 2 ? I'm not sure if the above method always gives a minimal solution. Maybe the numbers do not have to be prime, but only co-prime. Even more curious: If p1=2n+1, p2=p1+2*random(k), p3=2*random(k) then for every k there > would seem to exist some n 0 such that (i) and (ii) both hold for all > n>n 0. [random(k)=some random number >=0 and It also seems as though (for the primes) lim inf (|a1|+|a2|+|a3|)/(p3- > p1) = 0, although this is just a guess. === Subject: Re: Three consecutive primes conjecture posting-account=josrcgkAAABoiXs2WTgIH82zYbqHK43d 1.1.4322),gzip(gfe),gzip(gfe) On Dec 30, 10:10am, sttscitr...@tesco.net On Dec 29, 5:25pm, sttscitr...@tesco.net Let p1, p2, and p3 be three consecutive primes. Let a1, a2, and a3 be > integers with: > (i) a1*p1+a2*p2+a3*p3=0 > and > (ii) |a1|+|a2|+|a3| as small as possible. > Does this last sum divide p3-p1? > a1 = a2 =a3 =0 gives > |a1|+|a2|+|a3| =0 > My bad: (ii) |a1|+|a2|+|a3| is positive and as small as possible. > Seems to be true if p1<500000, or so. The fact that primes are involved may just be coincidence. pn + q(n+s) + r(n+t) =0, 0 common factor from p,q,r (n = prime simplifies things) Let GCD(s,t) = d > => qs'd + rt'd =0 > => qs' + rt' =0 > => q = t', r = -s', p = -t' +s' |p|+|q|+|r| = |t'|+|-s'|+|-t' +s'| > |t'|+|s'|+|t'|-|s'| = 2t' t = t'd so if d is even 2t' divides t > In your case |a1|+|a2|+|a3| divides p3-p1 > which is always divisible by 2 I've checked a few small cases e.g. > 21,33,49, 4,-7,3 For minimum solutions it seems that > p+q+r =0. Have you found that a1 +a2 +a3 is > always equal to 0 ? Is your |a1|+|a2|+|a3| > always divisible by 2 ? I'm not sure if the above method always > gives a minimal solution. Maybe the numbers do not have to be prime, > but only co-prime. > Co-prime is not enough: [5,11,13] gives [3,1,-2], but 6 does not divide 8. > If p1=2n+1, p2=p1+2*random(k), p3=2*random(k) then for every k there > would seem to exist some n 0 such that (i) and (ii) both hold for all > n>n 0. [random(k)=some random number >=0 and I meant to write p3=p2+2*random(k), but seem to have completly mangled the rest of the sentence as well. Rich === Subject: Re: Three consecutive primes conjecture posting-account=josrcgkAAABoiXs2WTgIH82zYbqHK43d 1.1.4322),gzip(gfe),gzip(gfe) > On Dec 29, 5:25pm, sttscitr...@tesco.net Let p1, p2, and p3 be three consecutive primes. Let a1, a2, and a3 be > integers with: > (i) a1*p1+a2*p2+a3*p3=0 > and > (ii) |a1|+|a2|+|a3| as small as possible. > Does this last sum divide p3-p1? > a1 = a2 =a3 =0 gives > |a1|+|a2|+|a3| =0 My bad: (ii) |a1|+|a2|+|a3| is positive and as small as possible. Seems to be true if p1<500000, or so. Even more curious: If p1=2n+1, p2=p1+2*random(k), p3=2*random(k) then for every k there > would seem to exist some n 0 such that (i) and (ii) both hold for all > n>n 0. [random(k)=some random number >=0 and p1) = 0, although this is just a guess. > Even better: ? In the random model (|a1|+|a2|+|a3|)/(p3-p1) >= 1/ (k-1) ? Rich === Subject: Re: Three consecutive primes conjecture > On Dec 29, 5:25=A0pm, sttscitr...@tesco.net Let p1, p2, and p3 be three consecutive primes. =A0Let a1, a2, and > a3= > be > integers with: > > (i) =A0a1*p1+a2*p2+a3*p3=3D0 > and > (ii) |a1|+|a2|+|a3| as small as possible. > > Does this last sum divide p3-p1? > > a1 =3D a2 =3Da3 =3D0 gives > |a1|+|a2|+|a3| =3D0 > > My bad: =A0(ii) |a1|+|a2|+|a3| is positive and as small as possible. > > Seems to be true if p1<500000, or so. =A0Even more curious: > > If p1=3D2n+1, p2=3Dp1+2*random(k), p3=3D2*random(k) then for every k > ther= > e > would seem to exist some n_0 such that (i) and (ii) both hold for all > n>n_0. =A0[random(k)=3Dsome random number >=3D0 and > It also seems as though (for the primes) lim inf (|a1|+|a2|+|a3|)/(p3- > p1) =3D 0, although this is just a guess. > > Even better: ? In the random model (|a1|+|a2|+|a3|)/(p3-p1) >=3D 1/ > (k-1) ? Suppose p1 = p2 - 2 x and p3 = p2 + 2 y, and let g divide x and y. Then one solution to a1 p1 + a2 p2 + a3 p3 = 0 is a1 = y/g, a2 = -(x+y)/g, a3 = x/g, for which |a1| + |a2| + |a3| = 2 (x + y)/g = (p3 - p1)/g. Now we can write a1 p1 + a2 p2 + a3 p3 = 0 as (a1 + a2 + a3) p2 + 2 (a3 y - a1 x) = 0. If a1 + a2 + a3 = 0, then a3 y = a1 x, leading to the solutions above. On the other hand, if a1 + a2 + a3 <> 0, then |a3 y - a1 x| >= p2/2 and |a1| + |a2| + |a3| >= |a1| + |a3| >= p2/(2 max(x,y)) Now the gaps between primes get small as the primes get large, and we would expect p2/(2 max(x,y)) > 2(x+y) for large primes p2. This, and thus your conjecture, would follow from Cramer's conjecture . -- Robert Israel israel@math.MyUniversitysInitials.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada === Subject: New Mensa Clock: quick quizzes and tests while the coffee percolates ... . posting-account=rsfFvAoAAADqHCqmunbjtmaKjfuP-pwP .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; InfoPath.1; .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) > http://www.ng2000.com/blog/2008/11/10/mensa/ Clock, at 6.00 am: Wakey-wakey! Rise and shine! Dr. Gripper: What's this? What is going on? Clock: What is the height of Mount Everest? Cecila: It's that promo clock Mensa sent you ... . Clock: The following series omits three terms ... . Dr. Gripper: Out the window with it! Clock: Guys, don't do that to me: I know other stuff, too. Dr. Gripper: Like ... ? Clock: [ Sings Brahm's lullaby, and, listening, happily, they go back to sleep.] -- foolsrushin. PS: I remember toilet rolls with GK and IQ questions inscribed upon 'em! What next? -- foolsrushin. === Subject: Re: New Mensa Clock: quick quizzes and tests while the coffee percolates ... . Hey -- arsehole! Why do you continually vomit your symptoms on to cam.misc?? All your worthless mind-puke is *off topic* there. Will you please just off and die somewhere, and leave cam.misc alone...? M. > http://www.ng2000.com/blog/2008/11/10/mensa/ Clock, at 6.00 am: > Wakey-wakey! Rise and shine! Dr. Gripper: > What's this? What is going on? Clock: > What is the height of Mount Everest? Cecila: > It's that promo clock Mensa sent you ... . Clock: > The following series omits three terms ... . Dr. Gripper: > Out the window with it! Clock: > Guys, don't do that to me: I know other stuff, too. Dr. Gripper: > Like ... ? Clock: > [ Sings Brahm's lullaby, and, listening, happily, they go back to > sleep.] > -- > foolsrushin. PS: I remember toilet rolls with GK and IQ questions inscribed upon > 'em! What next? > -- > foolsrushin. > === Subject: Re: New Mensa Clock: quick quizzes and tests while the coffee percolates ... . > Hey -- arsehole! Why do you continually vomit your symptoms on to cam.misc?? > All your worthless mind-puke is *off topic* there. Will you please just > off and die somewhere, and leave cam.misc alone...? M. He likes you. He recommended you lot as a good place to have discussions with better minds. I visited briefly and while there are a few people with the characteristics foolsrushin mentioned, I most of what goes on insipid and boring. Considering their level of participation I immediately recognized that they have a life elsewhere. Do you do anything other than yell at folks who are having a good time? http://www.ng2000.com/blog/2008/11/10/mensa/ >Clock, at 6.00 am: >Wakey-wakey! Rise and shine! >Dr. Gripper: >What's this? What is going on? >Clock: >What is the height of Mount Everest? >Cecila: >It's that promo clock Mensa sent you ... . >Clock: >The following series omits three terms ... . >Dr. Gripper: >Out the window with it! >Clock: >Guys, don't do that to me: I know other stuff, too. >Dr. Gripper: >Like ... ? >Clock: >[ Sings Brahm's lullaby, and, listening, happily, they go back to >sleep.] >-- >foolsrushin. >PS: I remember toilet rolls with GK and IQ questions inscribed upon >'em! What next? >-- >foolsrushin. === Subject: Re: New Mensa Clock: quick quizzes and tests while the coffee percolates ... . posting-account=rsfFvAoAAADqHCqmunbjtmaKjfuP-pwP .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; InfoPath.1; .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) > Hey -- arsehole! Why do you continually vomit your symptoms on to cam.misc?? > All your worthless mind-puke is *off topic* there. Will you please just > off and die somewhere, and leave cam.misc alone...? M. >http://www.ng2000.com/blog/2008/11/10/mensa/ > Clock, at 6.00 am: > Wakey-wakey! Rise and shine! > Dr. Gripper: > What's this? What is going on? > Clock: > What is the height of Mount Everest? > Cecila: > It's that promo clock Mensa sent you ... . > Clock: > The following series omits three terms ... . > Dr. Gripper: > Out the window with it! > Clock: > Guys, don't do that to me: I know other stuff, too. > Dr. Gripper: > Like ... ? > Clock: > [ Sings Brahm's lullaby, and, listening, happily, they go back to > sleep.] > -- > foolsrushin. > PS: I remember toilet rolls with GK and IQ questions inscribed upon > 'em! What next? > -- > foolsrushin.- Hide quoted text - - Show quoted text - > Hey -- arsehole! Why do you continually vomit your symptoms on to cam.misc?? > All your worthless mind-puke is *off topic* [What topic, Nunns?] there [?]. 'Sapient Fridge'? Just a guess, else an equivalent mediocre person. If it's you, Sapient Fridge, you will ever be a sow's ear! I'd prefer not: stoopid persons make life even tougher. You are so unsubtle! 'There'? Think about that! -- foolsrushin. === Subject: Re: New Mensa Clock: quick quizzes and tests while the coffee percolates ... . posting-account=rsfFvAoAAADqHCqmunbjtmaKjfuP-pwP .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; InfoPath.1; .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) > Hey -- arsehole! Why do you continually vomit your symptoms on to cam.misc?? > All your worthless mind-puke is *off topic* [What topic, Nunns?] there [?]. 'Sapient Fridge'? Just a guess, else an equivalent mediocre person. If it's you, Sapient Fridge, you will ever be a sow's ear! I'd prefer not: stoopid persons make life even tougher. You are just so unsubtle! 'There'? Think about that! [ snip.] >http://www.ng2000.com/blog/2008/11/10/mensa/ > Clock, at 6.00 am: > Wakey-wakey! Rise and shine! > Dr. Gripper: > What's this? What is going on? > Clock: > What is the height of Mount Everest? > Cecila: > It's that promo clock Mensa sent you ... . > Clock: > The following series omits three terms ... . > Dr. Gripper: > Out the window with it! > Clock: > Guys, don't do that to me: I know other stuff, too. > Dr. Gripper: > Like ... ? > Clock: > [ Sings Brahm's lullaby, and, listening, happily, they go back to > sleep.] > -- > foolsrushin. > PS: I remember toilet rolls with GK and IQ questions inscribed upon > 'em! What next? > -- > foolsrushin. -- foolsrushin.' === Subject: Re: opposing newtonian flawed laws of motion posting-account=_m9LngoAAAAtlhPgHQ2dCa-Pag64iiXh 1.1.4322),gzip(gfe),gzip(gfe) When a snail crossed the road, he was run over by a turtle. Regaining consciousness in the emergency room, he was asked what caused the accident. I really can't remember, the snail replied. You see, it all happened so fast. Q: Does light have mass? A: Of course not. It's not even Catholic!!! Ivan Ivanovich, the great Russian scientist does an experiment. He wants to know how fast a thermometer falls down. He takes a thermometer and a light, a candle light. He drops both from the 3rd floor and recognizes that they are reaching the ground at the same A thermometer falls with the speed of light. A neutron walks into a bar. I'd like a beer he says. The bartender promptly serves up a beer. How much will that be? asks the neutron. For you? replies the bartender, no charge === Subject: Re: opposing newtonian flawed laws of motion posting-account=_m9LngoAAAAtlhPgHQ2dCa-Pag64iiXh Gecko/2008120122 Firefox/3.0.5,gzip(gfe),gzip(gfe) I took another look at your document and it is written well. As for how true it is I don't know yet. > When a snail crossed the road, he was run over by a turtle. Regaining > consciousness in the emergency room, he was asked what caused the > accident. I really can't remember, the snail replied. You see, it > all happened so fast. Q: Does light have mass? > A: Of course not. It's not even Catholic!!! Ivan Ivanovich, the great Russian scientist does an experiment. He > wants to know how fast a thermometer falls down. He takes a > thermometer and a light, a candle light. He drops both from the 3rd > floor and recognizes that they are reaching the ground at the same > A thermometer falls with the speed of light. A neutron walks into a bar. I'd like a beer he says. The bartender > promptly serves up a beer. How much will that be? asks the neutron. > For you? replies the bartender, no charge === Subject: Joint Mathematics Meetings in Washington, D.C. (EurekAlert!) Mail-To-News-Contact: abuse@dizum.com http://www.ng2000.com/blog/2008/11/04/mathematics/ === Subject: Re: kung fu mereotopology ) > but others claiming to know mereology > including wit and moeblee I said I am familiar with Lesniewski's contribution to mereology but that I am not expert in it. I don't know what you mean otherwise by a claim by me to know mereology. MoeBlee === Subject: Re: kung fu mereotopology posting-account=EL3hgwoAAABtyRFrR2z7EBO1tnJeMiO7 Gecko/2008120122 Firefox/3.0.5,gzip(gfe),gzip(gfe) > The last time I > checked, in ZFC, set is a undefined primitive . (Of > course, in class theories such as NBG, class is the > undefined primitive object, and a set is a class that > is an element of another class.) In either ZFC or NBG, we don't need to take 'set' or 'class' as primitives; 'is a member' is the only primitive we need. (However, to ensure that urelements are not precluded, we would need to take something other than 'is a member' as primitive, whether that something is 'is a set', 'is a class', 'is an urelement', '0' or other). > So if tommy1729 has decided that the basic objects of > his theory are sets, then no one, neither galathaea > nor MoeBlee, can give a definition to the primitive > concept of a set. I made no assumption what the basic objects (whatever that means) of his theory are. Rather, from his axioms, we derive a contaradiction, NO MATTER WHAT the basic objects (whatever that means). Since you (Tonio) directed me to reread galathaea's > post as well, let me do so: but your current tactic > moeblee > of focusing down on the word set > well > it's just showing off more of what you do not know > because > from the polish logicians to modern computer science > lesniewski to scott and beyond > mereologies have been used as foundations of set theories > the use is very common What's going on here? Clearly galathaea and MoeBlee > disagree on what a set is. Since we can't define the primitive set, let me take > something which can be defined, empty set -- especially > since MoeBlee used an empty set in his proposed proof that > TST is inconsistent. To MoeBlee, an empty set cannot have any element, not > even itself. This is, of course, how empty sets work in > standard set theories such as ZFC. That's how it works when one states the empty set axiom. If one means something OTHER than the ordinary empty set axiom, then one needs to SAY what that is. > In MoeBlee's proof, he > shows that tommy1729's x = [x] implies that the empty set > does contain itself, [] = [[]], hence a contradiction. > Then galathaea argued that in tommy1729's proposed theory, > that's not how [] works in the flattened mereology. So > MoeBlee countered that tommy1729 insisted that his was a > set theory, which allegedly precludes it from having the > flattened mereology. No, I didn't say anything about precluding flattened mereology. Rather, tommy1729's stated context of set theory is more indicative that the axioms he mentioned are the ordinary set theoretic axioms than that they are some other special variant that he DIDN'T EVEN MENTION. > Then galathaea disagreed. So MoeBlee then accused her of > redefining set to satisfy her own argument, WHAT? WHERE? Where did I say that galathaea had redefined 'set'? > and then Tonio > compared her redefinition of set to 1+1 = 3. To galathaea, every set theory has a mereology -- even ZFC, > but ZFC's mereology is not the flattened one. To MoeBlee, > Tonio, and others, set theory and mereology are distinct > concepts, and being a set theory precluding a theory from > having mereology, and vice versa. After about six months of you INCORRECTLY putting words in my mouth, I've really had it at this point. Now I'm just saying you are LYING. I NEVER posted that set theory precludes mereology or vice versa. I NEVER posted that there is not a consistent theory that may qualify as both a set theory and a mereology. I simply never posted ONE WAY OR ANOTHER on that question. Stop LYING about my postings. > To galathaea and tommy1729, the objects of a theory having > flattened mereology may be called sets. To MoeBlee, Tonio, > and others, the objects may be called something else, like > fusions or heaps, but not sets -- and calling them > sets is an arbitrary redefinition akin to 1+1 = 3. YOU'RE LYING. I NEVER POSTED ANY SUCH THING. STOP FABRICATING ABOUT MY POSTS. > To galathaea and tommy1729, an empty object can contain > itself (as a part). To MoeBlee, Tonio, and others, the empty > set cannot contain itself (as an element), and anyone saying > otherwise is an arbitratry redefinition akin to 1+1 = 3. YOU'RE LYING. I NEVER POSTED ANY SUCH THING. STOP FABRICATING ABOUT MY POSTS. Specifically, I never posted about arbitrariness of redefinition making anything akin (or cognate of it) to '1+1=3'. And I never even mentioned any arbitrariness about redefining 'empty set'. > I can go on and on. Yes, it is clear now that you can go on and on lying about my posts. > The Stanford Encyclopedia of Philosophy, > which MoeBlee has suggested that I read earlier, does use > different symbols and terms for the flattened mereology, > such as fusion for set, part for element, bottom > for empty set, top for universal set, and so on. So what? tommy1729 gave no indication that he meant anything other than the ordinary empty set axiom, even when he qualified to say perhaps he needs to drop the empty set axiom in favor of the empty set exists. That one is free to intend the empty set exists to mean something other than the ordinary empty set axiom is not at issue. Byt the empty set exists one may mean Tokyo hot dogs are the yummiest in the world for all I care. But if that is what one means means, then one needs to SAY SO, and no other person is unreasonable to think rather meant is just the plain empty set axiom otherwise. > To galathaea, these changes are merely cosmetic, and one can > call them sets, elements, and empty set if one chooses > to do so. To MoeBlee, Tonio, and others, these changes are > necessarily to distinguish set theory from mereology. I made no mention that one needs to change terminology. Rather, just that one needs to include in one's formulations whatever variation one intends; otherwise others are reasonable to think that the ordinary axiom of the empty set is intended. > My own opinion? To me, galathaea is more of an expert on > mereology than MoeBlee or Tonio, and so if she argues that > the changes are cosmetic, than who am I to disagree? Who am *I* to disagree? I made NO argument about what is cosmetic. > Still, > I would use the Stanford notation, in order to avoid confusing > posters like MoeBlee or Tonio who find the change in notation > and terminology to be necessary. If by axiom of the empty set you don't mean the ordinary empty set axiom, then just say what axiom you do mean. I don't have a huge problem with that. But that doesn't make me incorrect for taking tommy1729 to be asserting that there is a set that has no members when he states the axiom of the empty set and the empty set exists. And if HE wishes NOW to revise his statement of his axioms so that the ordinary empty set axiom is not among them, then he's quite welcome, but that does not entail that I or anybody else was the least bit unreasonable to take the axiom of the empty set and the empty set exists as the ordinary empty set axiom. > Notice that even tommy1729 made a cosmetic change -- replacing > the braces {} of standard set theory to the [] of the > flattened mereology. This could have alerted MoeBlee that > tommy1729 doesn't intend [] to be an object such that no other > object, not even [] itself, is part of it And it DID. I ASKED him about that, as did Jesse. And HE said: [x] = is the set that contains x ( only ) however x may be a set itself. > -- and if that did > not, then galathaea's argument should have. If galathaea and tommy1729 had called [] Bottom, and if > they had called it TMT (M = mereology) rather than TST, then > MoeBlee might not have proposed what he had written as a proof > of its inconsistency. No, I didn't base on what he CALLS things. Rather, I just took his axioms and his statement: [x] = is the set that contains x ( only ) however x may be a set itself. But, now I, in retrospect, I realize that by the above he could have meant anything from the fundamental theorem of algebra to Barcelona girls really know how to swing it all about. > To galathaea, tommy1729 can still call his theory a set theory > despite having the flattened mereology. To me, maybe it would > be less confusing if he didn't -- but nonetheless, I don't > consider it a redefinition of set theory akin to 1+1 = 3. And if I havent' made clear enough already, I am asking you to stop lying about my posts. MoeBlee === Subject: Re: kung fu mereotopology posting-account=euF15goAAACbw3KIqEWxZHCIPUc2KPmU .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) > If galathaea and tommy1729 had called [] Bottom, and if > they had called it TMT (M = mereology) rather than TST, then > MoeBlee might not have proposed what he had written as a proof > of its inconsistency. > No, I didn't base on what he CALLS things. Rather, I just took his > axioms and his statement: > [x] = is the set that contains x ( only ) > however x may be a set itself. > But, now I, in retrospect, I realize that by the above he could have > meant anything from the fundamental theorem of algebra to Barcelona > girls really know how to swing it all about. There's an easier way to determine exactly what tommy1729, or anyone using the flattened mereology, means, and there's a way to approximate his meaning to someone who's unfamiliar with mereology and more familiar with ZFC. And it's not as arbitrary a redefinition as MoeBlee seems to think it is, based on his comments regarding FTA and Barcelona girls. [x] = is the set that contains x ( only ) however x may be a set itself. The word contains means contains as a part, and is more like contains as a subset , not like contains as an element at all! So we can interpret tommy1729's statement as: [x] = is the set that contains x [as a subset] ( only ) however x may be a set itself. And the word only implies that [x] has no elements that aren't elements of x. It is the smallest set that has x as a subset. In other words, [x] is actually what ZFC set theorists think of as U({x}), where U is unary union. And of course, now x = [x] becomes a tautology , just as Ax (x = U({x}) becomes a tautology in ZFC. Notice that the last line, x may be a set itself, emphasizes the fact that x need not even be a singleton (an atom). If x = [a,b], then this is akin to writing x = U({a,b}) in ZFC. ZFC set theorist should think of it as U({}) notation instead, to gain an intuitive grasp of it. Those claiming TST to be trivially inconsistent keep missing the point. They keep thinking that galathaea's and tommy1729's definitions are arbitrary , random redefinitions that could be used to prove anything at all. > To galathaea, tommy1729 can still call his theory a set theory > despite having the flattened mereology. To me, maybe it would > be less confusing if he didn't -- but nonetheless, I don't > consider it a redefinition of set theory akin to 1+1 = 3. > And if I havent' made clear enough already, I am asking you to stop > lying about my posts. No, MoeBlee didn't write 1+1 = 3 (actually Tonio did), but his remarks about Tokyo hot dogs and Barcelona girls are similar, and imply that these are arbitrary redefinitions. I disagree. These are 100% systematic definitions, not arbitrary redefinitions. I see absolutely nothing wrong with systematically defining something, as long as one is consistent about the definition. Considering contains to mean contains as a subset rather than contains as an element, as tommy1729 did, isn't arbitrary at all. And tommy1729 did define the notation. The lines MoeBlee often repeats: [x] = is the set that contains x ( only ) however x may be a set itself. is a definition of [x]. If the context of this line were ZFC, then [x] would equal U({x}), exactly by the above definition . In particular, it's not really a re definition of anything -- since the brackets had no previous meaning until tommy1729 defined it. That MoeBlee would assume that [x] means {x} is a reasonable assumption to make at first, until galathaea showed otherwise. Once galathaea made the clarification, then assuming that [x] means {x} and treating [x] in a proof the same way one would treat {x} in a ZFC proof is unwarranted. There is absolutely no reason that [x] must mean {x}. In TST, [x] has at least two parts -- x and [], just as U({x}) has at least two subsets in ZFC -- x and 0. To assume that the lines: [x] = is the set that contains x ( only ) however x may be a set itself. means that x is the only part of [x] is just as erroneous as assuming that x is the only subset of U({x}) in ZFC -- especially once galathaea explained how flattened mereology actually works. then everything he's written should end up being theorems of ZFC. So tommy1729's definition: [x] = is the set that contains x ( only ) however x may be a set itself. is 100% systematic, 100% logical, and once we introduce the parthood primitive, 100% rigorous. It's nothing like 1+1 = 3, Tokyo hot dogs, or Barcelona girls. We can make progress on TST as soon as everyone realizes that tommy1729's definitions aren't arbitrary. === Subject: Re: kung fu mereotopology posting-account=EL3hgwoAAABtyRFrR2z7EBO1tnJeMiO7 Gecko/2008120122 Firefox/3.0.5,gzip(gfe),gzip(gfe) > There's an easier way to determine exactly what > tommy1729, or anyone using the flattened > mereology, means, You keep saying tommy1729 used a flattened mereology. That is YOUR stipulation. tommy1729 just gave axioms and descriptions of axioms and some comments. He didn't specify with the kind of definititeness you invoke, or even specify at all, a flattened mereology. > and there's a way to approximate > his meaning to someone who's unfamiliar with > mereology and more familiar with ZFC. And it's not > as arbitrary a redefinition as MoeBlee seems to > think it is, based on his comments regarding FTA > and Barcelona girls. > [x] = is the set that contains x ( only ) > however x may be a set itself. The word contains means contains as a part, and > is more like contains as a subset , not like > contains as an element at all! First your objection regarded the empty set axiom. You didn't object to understanding of the word 'contains'. Your objection about the empty set axiom didn't hold, so now you're on to a DIFFERENT objection. Now, as to 'contains', I have no objection (in general) to stipulating now that it means 'subset' not 'element'. But the fact that two mathematician/logicians (Ullrich and Hughes) and one fairly informed beginner (me) read as 'element' (while other people may have read as 'subset') signals not that these people were unreasonable or shortsighted but rather that tommy1729 was careless not to articulate himself. And this is in context of these people asking and suggesting that he more fully and carefully articulate what he means. So, again, the matter is not whether we can bend backwards to reconstitue tommy1729's formulations into a semblance of a coherent and consistent theory. That was not disputed. But your argument still does not make sense: > So we can interpret tommy1729's statement as: [x] = is the set that contains x [as a subset] ( only ) > however x may be a set itself. And the word only implies that [x] has no elements > that aren't elements of x. It is the smallest set that > has x as a subset. To say [x] is the set that has x as a subset and only x as a subset Is not a DEFINITION of '[x]' unless we can prove: E!y(x subset of y & only x subset of y), But suppose only x is a subset of y. Then y has only one subset. But only the empty set has only one subset. So y is the empty set. So [x] = the empty set. But, since x subset of y = 0, then x = 0. So the operation is only well defined for x = 0. So all we have left is [0] = 0, and [x] undefined for x not= 0. And if that is what tommy1729 really did mean, then so be it, but one could hardly expect that a reader would take that trivial alternative over the more ordinary reading of 'contains' as in the sense of elementhood. > In other words, [x] is actually what ZFC set theorists > think of as U({x}), where U is unary union. Prove it. And U{x} = x. So this reduces to taking tommy1729 to mean that [x] = x not just as a theorem, but as a defintion, thus that '[ ]' is merely superfluous notation to introduce the identity operation. Again, if that is what tommy1729 really did mean, then so be it, but one could hardly expect that a reader would take that trivial alternative over the more ordinary reading of 'contains' as in the sense of elementhood. > And of > course, now x = [x] becomes a tautology , just as > Ax (x = U({x}) becomes a tautology in ZFC. It's a theorem of ZFC. > Notice that the last line, x may be a set itself, > emphasizes the fact that x need not even be a singleton > (an atom). A singleton is not ordinarily taken to be an atom. A singelton is a set y such that there exists an x such that y = {x}. Anyway, no prejudice as to what x is or is not has been used in my reasoning. The clause and x may be a set itself is superfluous. > If x = [a,b], then this is akin to writing > x = U({a,b}) in ZFC. ZFC set theorist should think of it as U({}) notation > instead, to gain an intuitive grasp of it. Those claiming TST to be trivially inconsistent keep > missing the point. They keep thinking that galathaea's > and tommy1729's definitions are arbitrary , random > redefinitions that could be used to prove anything at all. No claim was made that they are random. > To galathaea, tommy1729 can still call his theory a set theory > despite having the flattened mereology. To me, maybe it would > be less confusing if he didn't -- but nonetheless, I don't > consider it a redefinition of set theory akin to 1+1 = 3. > And if I havent' made clear enough already, I am asking you to stop > lying about my posts. No, MoeBlee didn't write 1+1 = 3 (actually Tonio did), but his > remarks about Tokyo hot dogs and Barcelona girls are similar, > and imply that these are arbitrary redefinitions. No, you COMPLETELY missed the point. *I* don't claim that tommy1729's terminology should be allowed to be understood any random way, but rather that YOU impose YOUR redefinitions. The part about Tokyo hot method. And you OMITTED the heart of what is your lie about me (it's not the 1*1=3 part: > To MoeBlee, Tonio, > and others, the objects may be called something else, like > fusions or heaps, but not sets -- and calling them > sets is an arbitrary redefinition akin to 1+1 = 3. I never said anything about the objects being called 'fusions' or 'heaps' but not 'sets'. > I disagree. These are 100% systematic definitions, not > arbitrary redefinitions. I see absolutely nothing wrong > with systematically defining something, as long as one is > consistent about the definition. Considering contains to > mean contains as a subset rather than contains as an > element, as tommy1729 did, isn't arbitrary at all. And I never claimed that one is wrong to redefine. Rather that one needs to make clear definitions (even if redefinitions) and that people are not to be faulted for taking an ordinary sense of terminology that has NOT been stipulated by tommy1729 or whomever to be different from ordinary. And that ex post fact redefinining or reconstituting or whatever is fine, but it is not a basis of criticism of people who commented on the original writeup as it was given. I've said this over and over. Why can't you understand this? Why do you instead post that I've claimed all kinds of bizarre stuff I never even HINTED at? > And tommy1729 did define the notation. The lines MoeBlee > often repeats: [x] = is the set that contains x ( only ) > however x may be a set itself. is a definition of [x]. If the context of this line > were ZFC, then [x] would equal U({x}), exactly by the > above definition . In particular, it's not really a > re definition of anything -- since the brackets had > no previous meaning until tommy1729 defined it. All that is answered in my remarks earlier in this post. > That MoeBlee would assume that [x] means {x} is a > reasonable assumption to make at first, until > galathaea showed otherwise. Once galathaea made the > clarification, then assuming that [x] means {x} and > treating [x] in a proof the same way one would treat > {x} in a ZFC proof is unwarranted. There is absolutely > no reason that [x] must mean {x}. (1) galathaea did not SHOW otherwise. (2) I just took tommy1720 to mean 'contains' in the sense of elementhood since the alternative makes no sense and leaves [x] without a correctly stated definition. > In TST, [x] has at least two parts -- x and [], just > as U({x}) has at least two subsets in ZFC -- x and 0. To > assume that the lines: [x] = is the set that contains x ( only ) > however x may be a set itself. means that x is the only part of [x] is just as erroneous > as assuming that x is the only subset of U({x}) in ZFC -- > especially once galathaea explained how flattened mereology > actually works. How flattened mereology really works. tommy1729 did not specify the axioms for this and did not specify such a context by general rubric 'mereology' either. tommy1729 mentioned NOTHING about part and whole or eschewing the elementhood relation in favor of some other part and whole relation with axioms regarding such a relation. He simply called his a 'set theory' then rattled off a few ordinary set theory axioms and some other stuff that does not vitiate the reasonableness of taking his named set theory axioms to be the ordinary ones along with taking 'contains' in the sense of elementhood since otherwise reduces to the notation still undefined. > then everything he's written should end up being theorems > of ZFC. But he DIDN'T write U{x}, did he? You simply NOW stipulate this. And it is otiose anyway. If [x] = U{x}, then '[]' is just a superfluous introduction of notation for the identity operation. > So tommy1729's definition: [x] = is the set that contains x ( only ) > however x may be a set itself. is 100% systematic, 100% logical, and once we introduce > the parthood primitive, 100% rigorous. ONCE we introduce. But he DIDN'T introduce it, did he? He introduced his set theory and mentioned set theory axioms and other notations, but he did NOT introduce any parthood primitive and he did NOT stipulate [x]= U{x}. Rather, you only NOW stipulate that. MOREOVER [x] = U{x} is NOT consistent with [x] = the set y such that x subset of y and only x subset of y. > It's nothing > like 1+1 = 3, Tokyo hot dogs, or Barcelona girls. We can > make progress on TST as soon as everyone realizes that > tommy1729's definitions aren't arbitrary. We can make progress once you understand the arrow of time: FIRST he introduces a set theory iterating ordinary set theory axioms plus some other muddled notaton and statments. THEN you utterly revamp his presentation to the extent of EX POST FACTO introducing a parthood primitive NEVER mentioned by him in his formulations. AGAIN, you're welcome to do that. But you are NOT correct to fault others for first taking his presentation on its own terms that DO NOT include any parthood primitives and mentions of U{x} etc. Sheesh! MoeBlee === Subject: Re: kung fu mereotopology posting-account=EL3hgwoAAABtyRFrR2z7EBO1tnJeMiO7 Gecko/2008120122 Firefox/3.0.5,gzip(gfe),gzip(gfe) > I ASKED him about that, as did Jesse. And HE said: [x] = is the set that contains x ( only ) > however x may be a set itself. By 'HE' I meant tommy1729 not Jesse. MoeBlee === Subject: Re: kung fu mereotopology posting-account=EL3hgwoAAABtyRFrR2z7EBO1tnJeMiO7 Gecko/2008120122 Firefox/3.0.5,gzip(gfe),gzip(gfe) > MoeBlee seems to imply that because the word SET theory > is used, tommy1729's proposed theory must a priori prove > certain properties, and he uses those assumed properties > in his proposed proof that TST is inconsistent. No I don't seem to imply that AT ALL. I make no such implication about a priori or even that a set theory must prove certain properties. Rather, I said that when tommy1729 presents the axiom of the empty set and the empty set exists then, unless he specifies some other sense, I take him to mean the ordinary empty set axiom - that there is a set that has no members - and I mentioned that he calls his theory a 'set theory' in contrast as additional context that IS present as opposed to 'mereology' which was NOT mentioned by him. > For example, MoeBlee assumed that because tommy1729 used > the word SET theory and stated that it has an Empty Set > Axiom, said axiom must be of the form: Ex (Ay (y not-in x)). (1) I don't claim that one can't have a variant of the empty set axiom. But he didn't specify any variance. (2) And I mentioned that he was in the context of set theory in response to the claim that he was in the context of mereology. (And I did not even claim that there is NECESSARILY not a theory that combines set theory and mereology, but only that tommy1729 gave the names of ordinary set theoretic axioms in context of his self-described set theory.) > And thus Tonio implied that galathaea, in her defense of > tommy1729, must have redefined SET theory (or maybe > Empty Set Axiom) to avoid MoeBlee's inconsistency proof, > in the same way that one must redefine 1 to get 1+1 = 3. I'm not sure whether galathaea's definition, or MoeBlee's > implied definition, of SET theory is the correct one. I didn't even imply a definition of 'set theory'. > But > I disagree that a theory that is reasonably sound, such as > the theory of flattened mereology, can become inconsistent > just because one attached the name SET theory to it. Oh, come on! Now you are waxing VERY silly. tommmy1729 didn't specify a flattened mereology. And I didn't try to make a flattened mereology inconsistent just because it is named a 'set theory'. Rather, he specified that there is a set that has no members and that x in [x] while [x] has x as its only member, which is inconsistent. MoeBlee === Subject: Re: [order theory] maximized sets > [...] > The original non-simplified problem I'm dealing with is the following. > Let (D,<=) be a complete lattice. Let Y be a generating subset of D in > the sense that each element of D is the supremum of some subset of Y. > Moreover, let Y be closed under suprema of chains. > A set M is called _maximized_ if M is a subset of Y and whenever y in Y > and y <= sup(M), there is some y' in M with y<=y'. > Now how do you call these maximized sets? I do not know. Also observe that the notion is not independent > of the generating subset Y. Take the ordered set with Hasse diagram 1 > / | > / | > m e n > / / / > a b c d and adjoin a smallest element 0. Take the generating sets > Y = {0, a, b, c, d} and Y' = {0, a, b, c, d, e}. > Then the set M = {m, n} has the property with respect to Y > but not with respect to Y'. > I don't agree. M is neither a subset of Y, nor a subset of Y', so M is neither Y-maximized, nor Y'-maximized. > So the terminology cannot really omit the generating set. I agree. By the way, at least for questions of terminology, it is enough > to consider M with sup(M) = sup(D) = 1 by replacing > D with D' = { x in D | d <= sup(M) } and > Y with Y' = { y in Y | y <= sup(M) }. > I agree. > Marc Sasha. === Subject: Re: [order theory] maximized sets > [...] > The original non-simplified problem I'm dealing with is the following. > Let (D,<=) be a complete lattice. Let Y be a generating subset of D in > the sense that each element of D is the supremum of some subset of Y. > Moreover, let Y be closed under suprema of chains. > A set M is called _maximized_ if M is a subset of Y and whenever y in Y > and y <= sup(M), there is some y' in M with y<=y'. > Now how do you call these maximized sets? I do not know. Also observe that the notion is not independent > of the generating subset Y. Take the ordered set with Hasse diagram 1 > / | > / | > m e n > / / / > a b c d and adjoin a smallest element 0. Take the generating sets > Y = {0, a, b, c, d} and Y' = {0, a, b, c, d, e}. > Then the set M = {m, n} has the property with respect to Y > but not with respect to Y'. I don't agree. M is neither a subset of Y, nor a subset of Y', so M is > neither Y-maximized, nor Y'-maximized. Oh sorry, you are right. I had missed the condition M subset of Y in your above description. But then just consider instead Y = {0, a, b, c, d, m, n} and Y' = {0, a, b, c, d, m, n, e} to obtain a similar situation. Marc === Subject: Re: counting ... posting-account=hEsTJAoAAABBB9neOo9d5YFd2CC8eBZx Gecko/20061205 Iceweasel/2.0.0.1 (Debian-2.0.0.1+dfsg-1),gzip(gfe),gzip(gfe) I found a few typos and conceptual lapses in my brain dump ~ ... you have one way or the other found -yourself- wondering ... I meant ~ ... the sum of the entities constituting a whole other one is -less- than that new organically integrated being, even though the combined properties are richer than the sum of the parts ~ lbrtchx === Subject: Some help vector spaces posting-account=gc2kDQoAAADMsLO9kJjQL9hCJkI0D8qJ .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) Let U be the space generated by the following vectors: { (0,5,0,4,4) , (1,1,1,0,0), (1,2,1,1,1), (2,4,2,1,1)}. Now let V be the space generated by the following vectors: { (0,1,0,2,1), (0,3,0,0,1), (0,1,0,0,1), (0,2,0,0,1)}. Now the vectors that span U are linearly dependent since (2,4,2,1) = (0,5,0,4,4) + 5(1,1,1,0,0) - 3(1,2,1,1,1). Therefore U = < (0,5,0,4,4) , (1,1,1,0,0), (1,2,1,1,1), (2,4,2,1,1) > = < (0,5,0,4,4) , (1,1,1,0,0), (1,2,1,1,1,)>. where <,> denotes span. The latter set , is linearly independent so dimension(U) = 3. Similarly for V (0,2,0,0,1) is a linear combination of the other vectors and { (0,1,0,2,1) , (0,3,0,0,1) , (0,1,0,0,1)} is a linearly independent set so dimension(V) = 3 and this set is a basis for V. Questions: 1. I'm trying to find a basis for U + V. Can I simply take the union of the above two basis I just found and then exclude the linearly dependent vectors? What I mean is this, let X be the union of the vectors that span U and V respectively. Then exclude those vectors from X which are linearly dependent. Would this give a basis of U + V? 2. Can you please give a hint on how to find a basis of U intersection V. === Subject: Re: Some help vector spaces > Let U be the space generated by the following vectors: > { (0,5,0,4,4) , (1,1,1,0,0), (1,2,1,1,1), (2,4,2,1,1)}. > Now let V be the space generated by the following vectors: > { (0,1,0,2,1), (0,3,0,0,1), (0,1,0,0,1), (0,2,0,0,1)}. Now the vectors that span U are linearly dependent since > (2,4,2,1) = (0,5,0,4,4) + 5(1,1,1,0,0) - 3(1,2,1,1,1). Therefore U = < (0,5,0,4,4) , (1,1,1,0,0), (1,2,1,1,1), (2,4,2,1,1) = < (0,5,0,4,4) , (1,1,1,0,0), (1,2,1,1,1,)>. > where <,> denotes span. > The latter set , is linearly independent so dimension(U) = 3. Similarly for V (0,2,0,0,1) is a linear combination of the other > vectors and { (0,1,0,2,1) , (0,3,0,0,1) , (0,1,0,0,1)} is > a linearly independent set so dimension(V) = 3 and this set is a basis > for V. Questions: 1. I'm trying to find a basis for U + V. > Can I simply take the union of the above two basis I just found and > then exclude the linearly dependent vectors? > What I mean is this, let X be the union of the vectors that span U and > V respectively. Then exclude those vectors > from X which are linearly dependent. Would this give a basis of U + V? 2. Can you please give a hint on how to find a basis of U intersection > V. Determine explicitly U / V solving the system a*(0,5,0,4,4) + b*(1,1,1,0,0) + c*(1,2,1,1,1) = = d*(0,1,0,2,1) + e*(0,3,0,0,1) + f*(0,1,0,0,1). You will see that U / V is 2-dimensional. Then find a basis. Jose Carlos Santos === Subject: Re: Some help vector spaces > Let U be the space generated by the following vectors: > { (0,5,0,4,4) , (1,1,1,0,0), (1,2,1,1,1), (2,4,2,1,1)}. > Now let V be the space generated by the following vectors: > { (0,1,0,2,1), (0,3,0,0,1), (0,1,0,0,1), (0,2,0,0,1)}. Now the vectors that span U are linearly dependent since > (2,4,2,1) = (0,5,0,4,4) + 5(1,1,1,0,0) - 3(1,2,1,1,1). Therefore U = < (0,5,0,4,4) , (1,1,1,0,0), (1,2,1,1,1), (2,4,2,1,1) = < (0,5,0,4,4) , (1,1,1,0,0), (1,2,1,1,1,)>. > where <,> denotes span. > The latter set , is linearly independent so dimension(U) = 3. Similarly for V (0,2,0,0,1) is a linear combination of the other > vectors and { (0,1,0,2,1) , (0,3,0,0,1) , (0,1,0,0,1)} is > a linearly independent set so dimension(V) = 3 and this set is a basis > for V. Questions: 1. I'm trying to find a basis for U + V. > Can I simply take the union of the above two basis I just found and > then exclude the linearly dependent vectors? Yes. One way to find a basis for U + V is to make a matrix of the basis vectors of U and V as rows, then row-reduce it as far as possible. The non-zero rows remaining will form a basis for U + V. === Subject: Re: L-3 space anyone > Its quite well known that fourier series converges to their functions almost everywhere if that function is periodic and L-2 integrable. but what about L-3 spaces ? what typical series are used for them ? i havent seen this subject in sci.math before , how come ? I need to learn more about this. no book references plz. You might be interested in an animation illustrating how the first few terms in the Fourier series (a sum ...) for a square-wave function approach the square-wave function. It's the Synthesis_square.gif from: http://en.wikipedia.org/wiki/File:Synthesis_square.gif For the formulas, cf.: http://en.wikipedia.org/wiki/Square_wave David Bernier === Subject: Re: L-3 space anyone Its quite well known that fourier series converges > to their functions almost everywhere if that function > is periodic and L-2 integrable. > but what about L-3 spaces ? > what typical series are used for them ? > i havent seen this subject in sci.math before , how > come ? > I need to learn more about this. > no book references plz. > You might be interested in an animation illustrating > how the first few > terms in the Fourier series (a sum ...) for a > square-wave > function approach the square-wave function. > It's the Synthesis_square.gif from: > http://en.wikipedia.org/wiki/File:Synthesis_square.gif > For the formulas, > cf.: > http://en.wikipedia.org/wiki/Square_wave > David Bernier no , im not intrested in that. thats not what i asked. Well, suit yourself then. BTW, my name is not Berbnier ... David Bernier === Subject: Re: L-3 space anyone > Its quite well known that fourier series converges to their functions > almost everywhere if that function is periodic and L-2 integrable. Yes, but do you know what that means? Do you know how to find the fourier series of a non-integrable L-2 function? Can you give an example of such a function? but what about L-3 spaces ? Good exercise: What's an important difference between L-2 and L-3 (or even L-2 and L-1)? what typical series are used for them ? i havent seen this subject in sci.math before , how come ? I need to learn more about this. What is your motivation? no book references plz. What have you got against books? A most essential skill in math is to be able to learn what you need on your own. You should arrive here with your key questions at hand--not when you first start thinking about something. You'll find people may try to even be more helpful. You can (and I can) probably learn a great deal from browsing wikipedia.org. Have fun and best wishes with your learning, Bill tommy1729 === Subject: Re: L-3 space anyone > Its quite well known that fourier series converges to their functions > almost everywhere if that function is periodic and L-2 integrable. but what about L-3 spaces ? On a space of finite measure, L_3 is contained in L_2. Actually, Carleson's theorem is true in L_p for any p > 1. > I need to learn more about this. no book references plz. It might do you good to read a book once in a while. -- Robert Israel israel@math.MyUniversitysInitials.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada === Subject: Re: L-3 space anyone posting-account=iyXB5AkAAABPCtkDKhRJOsNWmafzHSRE Gecko/2008120122 Firefox/3.0.5,gzip(gfe),gzip(gfe) On 30 joulu, 03:25, Robert Israel > Its quite well known that fourier series converges to their functions > almost everywhere if that function is periodic and L-2 integrable. > but what about L-3 spaces ? On a space of finite measure, L 3 is contained in L 2. Or is it the other way? > Actually, Carleson's theorem is true in L p for any p > 1. It wasn`t trivial to extend the Carleson theorem for greater p:s, it was done by Hunt. The general version is known as Carleson-Hunt theorem. There is also extension to non-integer p:s, and there is a race how close to p=1 you can go keeping the theorem valid. > I need to learn more about this. > no book references plz. It might do you good to read a book once in a while. > -- > Robert Israel isr...@math.MyUniversitysInitials.ca > Department of Mathematics http://www.math.ubc.ca/~israel > University of British Columbia Vancouver, BC, Canada === Subject: Re: L-3 space anyone <3h9kl4hq1li7qiqe2pdkrkuq8v60fbo1kg@4ax.com> posting-account=iyXB5AkAAABPCtkDKhRJOsNWmafzHSRE Gecko/2008120122 Firefox/3.0.5,gzip(gfe),gzip(gfe) >On 30 joulu, 03:25, Robert Israel > Its quite well known that fourier series converges to their functions > almost everywhere if that function is periodic and L-2 integrable. > but what about L-3 spaces ? > On a space of finite measure, L 3 is contained in L 2. >Or is it the other way? No, it's the way he stated it. I don`t still understand, because in my Rudin 1966, I have this question 5 on page 70. 'Suppose f is a complex measurable function on X, m is a positive measure on X, and m(X) = 1. 5,a) prove that norm(f) r =< norm(F) s, if 0 < r < s < oo. Doensn`t this mean that L r is contained in L s? Also I would think that when the exponent s is more bigger than 1 than r , more bigger the integral is when the values of f are bigger than 1. > An easy way to keep this straight: On a space of > finite measure it's clear that a bounded (measurable) > function is integrable. So L^infinity is contained > in L^1. > Actually, Carleson's theorem is true in L p for any p > 1. >It wasn`t trivial to extend the Carleson theorem for greater p:s, it >was done by Hunt. If greater ps means values of p greater than 2 then yes, this > was trivial, in fact it's not an extension at all. The not quite so > trivial part was 1 < p < 2. >The general version is known as Carleson-Hunt >theorem. There is also extension to non-integer p:s, and there is a >race how close to p=1 you can go keeping the theorem valid. ??? Maybe you mean there was a race? > I need to learn more about this. > no book references plz. > It might do you good to read a book once in a while. > -- > Robert Israel isr...@math.MyUniversitysInitials.ca > Department of Mathematics http://www.math.ubc.ca/~israel > University of British Columbia Vancouver, BC, Canada David C. Ullrich Understanding Godel isn't about following his formal proof. > That would make a mockery of everything Godel was up to. > (John Jones, My talk about Godel to the post-grads. > in sci.logic.) === Subject: Re: L-3 space anyone > On 30 joulu, 03:25, Robert Israel > Its quite well known that fourier series converges to their functions > almost everywhere if that function is periodic and L-2 integrable. > but what about L-3 spaces ? > On a space of finite measure, L_3 is contained in L_2. Or is it the other way? Suppose f:[0,1] -> R f(x) = x^(-2/5) if x> 0, f(0) = 0. f(x)^3 = x^(-6/5), x>0 but f(x)^2 = x^(-4/5), x>0. So f is not in L_3, but f is in L_2. For a finite measure space, if a function f is not square-summable, it won't be cube-summable. But for infinite measure, one has ell_1 strictly contained in ell_oo , for instance. > Actually, Carleson's theorem is true in L_p for any p > 1. It wasn`t trivial to extend the Carleson theorem for greater p:s, it > was done by Hunt. The general version is known as Carleson-Hunt > theorem. There is also extension to non-integer p:s, and there is a > race how close to p=1 you can go keeping the theorem valid. So perhaps the a.e. convergence property has been shown for Banach spaces that contain strictly all L_p , p>1 for the space [0, 1] , or [0, 2pi] ? (not that the space matters... ) David Bernier > I need to learn more about this. > no book references plz. > It might do you good to read a book once in a while. > -- > Robert Israel isr...@math.MyUniversitysInitials.ca > Department of Mathematics http://www.math.ubc.ca/~israel > University of British Columbia Vancouver, BC, Canada > === Subject: Re: L-3 space anyone posting-account=iyXB5AkAAABPCtkDKhRJOsNWmafzHSRE Gecko/2008120122 Firefox/3.0.5,gzip(gfe),gzip(gfe) > On 30 joulu, 03:25, Robert Israel > Its quite well known that fourier series converges to their functions > almost everywhere if that function is periodic and L-2 integrable. > but what about L-3 spaces ? > On a space of finite measure, L 3 is contained in L 2. > Or is it the other way? Suppose f:[0,1] -> R f(x) = x^(-2/5) if x> 0, f(0) = 0. f(x)^3 = x^(-6/5), x>0 but f(x)^2 = x^(-4/5), x>0. So f is not in L 3, but f is in L 2. For a finite measure space, > if a function f is not square-summable, it won't be cube-summable. I don`t understand. I must be missing something. You are saying that f (x)^3 = x^(-6/5) is not integrable over [0,1] ??? > But for infinite measure, one has ell 1 strictly contained in ell oo , > for instance. > Actually, Carleson's theorem is true in L p for any p > 1. > It wasn`t trivial to extend the Carleson theorem for greater p:s, it > was done by Hunt. The general version is known as Carleson-Hunt > theorem. There is also extension to non-integer p:s, and there is a > race how close to p=1 you can go keeping the theorem valid. So perhaps the a.e. convergence property has been shown for > Banach spaces that contain strictly all L p , p>1 for the > space [0, 1] , or [0, 2pi] ? (not that the space matters... ) David Bernier > I need to learn more about this. > no book references plz. > It might do you good to read a book once in a while. > -- > Robert Israel isr...@math.MyUniversitysInitials.ca > Department of Mathematics http://www.math.ubc.ca/~israel > University of British Columbia Vancouver, BC, Canada === Subject: Re: L-3 space anyone posting-account=iyXB5AkAAABPCtkDKhRJOsNWmafzHSRE Gecko/2008120122 Firefox/3.0.5,gzip(gfe),gzip(gfe) > On 30 joulu, 03:25, Robert Israel > Its quite well known that fourier series converges to their functions > almost everywhere if that function is periodic and L-2 integrable. > but what about L-3 spaces ? > On a space of finite measure, L_3 is contained in L_2. > Or is it the other way? > Suppose f:[0,1] -> R f(x) = x^(-2/5) if x> 0, f(0) = 0. > f(x)^3 = x^(-6/5), x>0 but f(x)^2 = x^(-4/5), x>0. > So f is not in L_3, but f is in L_2. For a finite measure space, > if a function f is not square-summable, it won't be cube-summable. >I don`t understand. I must be missing something. You are saying that f >(x)^3 = x^(-6/5) is not integrable over [0,1] ??? Find a calculus book! OK :) It is in other city :) But to me is not trivial that f(x)^2 = x^ (-4/5) is integrable over [0,1] can someone more wiser prove that to me? === Subject: Re: L-3 space anyone > On 30 joulu, 03:25, Robert Israel > Its quite well known that fourier series converges to their > functions > almost everywhere if that function is periodic and L-2 integrable. > but what about L-3 spaces ? > On a space of finite measure, L_3 is contained in L_2. > Or is it the other way? > Suppose f:[0,1] -> R f(x) = x^(-2/5) if x> 0, f(0) = 0. > f(x)^3 = x^(-6/5), x>0 but f(x)^2 = x^(-4/5), x>0. > So f is not in L_3, but f is in L_2. For a finite measure space, > if a function f is not square-summable, it won't be cube-summable. >I don`t understand. I must be missing something. You are saying that f >(x)^3 = x^(-6/5) is not integrable over [0,1] ??? > Find a calculus book! OK :) It is in other city :) But to me is not trivial that f(x)^2 = x^ > (-4/5) is integrable over [0,1] can someone more wiser prove that to > me? This is a standard Calc I problem. === Subject: Re: L-3 space anyone posting-account=iyXB5AkAAABPCtkDKhRJOsNWmafzHSRE Gecko/2008120122 Firefox/3.0.5,gzip(gfe),gzip(gfe) > On 30 joulu, 03:25, Robert Israel > Its quite well known that fourier series converges to their > functions > almost everywhere if that function is periodic and L-2 integrable. > but what about L-3 spaces ? > On a space of finite measure, L 3 is contained in L 2. > Or is it the other way? > Suppose f:[0,1] -> R f(x) = x^(-2/5) if x> 0, f(0) = 0. > f(x)^3 = x^(-6/5), x>0 but f(x)^2 = x^(-4/5), x>0. > So f is not in L 3, but f is in L 2. For a finite measure space, > if a function f is not square-summable, it won't be cube-summable. >I don`t understand. I must be missing something. You are saying that f >(x)^3 = x^(-6/5) is not integrable over [0,1] ??? > Find a calculus book! > OK :) It is in other city :) But to me is not trivial that f(x)^2 = x^ > (-4/5) is integrable over [0,1] can someone more wiser prove that to > me? This is a standard Calc I problem. come then f(x) = 1/x^(4/5) is integrable over [0,1] to me it seems lim (x--->0+) 1/x^(4/5) = oo and the function f(x) is continuous 0 on (0,1].... === Subject: Re: L-3 space anyone <85ckl4tgkvrjb3n2amolighjn9s0jvul0t@4ax.com> posting-account=9QOSvAoAAACEOWJVSDuswW7dB_0wApQO Gecko/20070530 Fedora/1.5.0.12-1.fc5 Firefox/1.5.0.12,gzip(gfe),gzip(gfe) > On 30 joulu, 03:25, Robert Israel > Its quite well known that fourier series > converges to their functions > almost everywhere if that function is periodic > and L-2 integrable. > but what about L-3 spaces ? > On a space of finite measure, L_3 is contained in > L_2. > Or is it the other way? > Suppose f:[0,1] -> R f(x) = x^(-2/5) if x> 0, f(0) > = 0. > f(x)^3 = x^(-6/5), x>0 but f(x)^2 = x^(-4/5), x>0. > So f is not in L_3, but f is in L_2. For a finite > measure space, > if a function f is not square-summable, it won't be > cube-summable. >so , L_2 is contained in L_3 ! Wow. You need to know about topics that many > pros in the field don't understand because they're just > too hard. You're not interested in books on the topic. > And when someone says something extremely simple > here on sci.math, something very elementary, and > states it very clearly, you can't get it straight when > you _read_ it. He didn't say L^2 is contained in L^3. He said > just the opposite. >and not : L_3 is contained in L_2 !? >the set of cube-integrables contains the set of square-integrables : L_2 is contained in L_3. He _gave_ a _counterexample_ to this. > But for infinite measure, one has ell_1 strictly > contained in ell_oo , > for instance. > Actually, Carleson's theorem is true in L_p for > any p > 1. > It wasn`t trivial to extend the Carleson theorem >so people should stop pretending i ask trivial questions. The question you asked was trivial. No pretending needed. >and , yes this might be my weak spot ( L_3 ) but some of you complain i refuse to learn , well here im willing to learn ... >but then i guess they will refuse too teach ? It's not possible to teach you about extremely advanced material > in a few sci.math posts. If you really want to understand this > stuff you're going to have to study analysis for many years. You _say_ you're willing to learn. But you're not interested in > actually doing the work that's _needed_ to learn about this > stuff. Ironclad proof of that in another post from you in this > thread, where someone gives a place you might start and you > say you're not interested. >or dont they understand themselves ? I couldn't say for certain, but I wouldn't be surprised to learn > that none of the regular posters here has ever gone through > a proof of the ae convergence of L^2 Fourier series. So > what? It is quite a trip ;-) -- m === Subject: Re: A MOD B NO MATH HAHAHAHA !! Nntp-Posting-Host: hera.cwi.nl ... > Indeed, your (Ullrich's) post correcting the first error was > far superior to Winter's, which informed him that a mod b > was nonstandard but not why Why should I inform *why* a mod b was non-standard in mathematics? Two questions: (1) Do you know *why*? (2) Why should I tell him *again* that that is the case when I told him already a few years ago? -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: A MOD B NO MATH HAHAHAHA !! posting-account=euF15goAAACbw3KIqEWxZHCIPUc2KPmU .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) > ... > Indeed, your (Ullrich's) post correcting the first error was > far superior to Winter's, which informed him that a mod b > was nonstandard but not why > Why should I inform *why* a mod b was non-standard in mathematics? > Two questions: > (1) Do you know *why*? You've already told me -- it's because (a == b) mod m is the only standard use of mod, and because a mod b doesn't work in rings such as Q(sqrt(2)) that you mentioned -- despite the fact that more than 99% of the time, the person wanting to use a mod b has both a and b as positive natural numbers and couldn't care less about Q(sqrt(2)) -- despite the fact that in the cases where more than 99% of the users of the notation a mod b, including computer scientists and those who didn't study algebra past secondary school, find the notation a mod b to be very convenient and don't care that it doesn't work in Q(sqrt(2)), and wouldn't even consider using a mod b for nontrivial elements of Q(sqrt(2)) -- despite the fact that in the cases where the layperson wants to use a mod b -- namely for positive natural numbers, a mod b can be given a 100& rigorous, 100% unambiguous definition via the Division Algorithm. > (2) Why should I tell him *again* that that is the case when I told him > already a few years ago? It's because tommy1729 concluded from your post that mod isn't defined in math at all. Since he, like most people, have only seen mod in the form a mod b if at all, and have never seen a == b (mod m) at all, and so he reached the only reasonable conclusion that's possible to someone in that situation -- namely that if a mod b isn't defined, then mod isn't defined at all. It's the only reasonable conclusion one can make, until someone has introduced to tommy1729 the notation a == b (mod m). And that someone was Ullrich, not Winter. === Subject: Re: A MOD B NO MATH HAHAHAHA !! ... > Why should I inform *why* a mod b was non-standard in mathematics? > Two questions: > (1) Do you know *why*? > > You've already told me -- it's because (a == b) mod m is the > only standard use of mod, and because a mod b doesn't work > in rings such as Q(sqrt(2)) that you mentioned -- despite > the fact that more than 99% of the time, the person wanting > to use a mod b has both a and b as positive natural numbers > and couldn't care less about Q(sqrt(2)) -- despite the fact > that in the cases where more than 99% of the users of the > notation a mod b, including computer scientists and those > who didn't study algebra past secondary school, find the > notation a mod b to be _very_ convenient and don't care > that it doesn't work in Q(sqrt(2)), and wouldn't even consider > using a mod b for nontrivial elements of Q(sqrt(2)) -- > despite the fact that in the cases where the layperson wants > to use a mod b -- namely for positive natural numbers, > a mod b can be given a 100& rigorous, 100% unambiguous > definition via the Division Algorithm. Right. And so? It is has still nog standard definition in mathematics, regardless what the layperson thinks about it. And as I already did write, I use it a lot (althout it is spelled % when I use it). Mathematics, and especially number theory, is far more than considering only the natural numbers, or the integers. Even when factoring integers with NSF the calculations go beyond the integers. > (2) Why should I tell him *again* that that is the case when I told him > already a few years ago? > > It's because tommy1729 concluded from your post that mod > isn't defined in math at all. The first time that I told it, he did not conclude that at all, so why does he conclude it now? And how do you know that? > Since he, like most people, > have only seen mod in the form a mod b if at all, and > have never seen a == b (mod m) at all, and so he reached > the only reasonable conclusion that's possible to someone > in that situation -- namely that if a mod b isn't > defined, then mod isn't defined at all. It's the only > reasonable conclusion one can make, until someone has > introduced to tommy1729 the notation a == b (mod m). And > that someone was Ullrich, not Winter. How do you know that I did not introduce him to that the first time I told him? But whatever, mod is *not* defined as an operation in mathematics. In mathematics mod is an equivalence relation, and that is very basic mathematics. That some programming languages did usurp the notation for remaindering is something quite different. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: A MOD B NO MATH HAHAHAHA !! posting-account=suWj4AkAAADE1IvGmj55Nmq3f98qb17e .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; InfoPath.2; .NET CLR 3.5.21022; Tablet PC 2.0),gzip(gfe),gzip(gfe) > ... > Indeed, your (Ullrich's) post correcting the first error was > far superior to Winter's, which informed him that a mod b > was nonstandard but not why > Why should I inform *why* a mod b was non-standard in mathematics? > Two questions: > (1) Do you know *why*? You've already told me -- it's because (a == b) mod m is the > only standard use of mod, and because a mod b doesn't work > in rings such as Q(sqrt(2)) that you mentioned -- despite > the fact that more than 99% of the time, the person wanting > to use a mod b has both a and b as positive natural numbers > and couldn't care less about Q(sqrt(2)) -- despite the fact > that in the cases where more than 99% of the users of the > notation a mod b, including computer scientists and those > who didn't study algebra past secondary school, find the > notation a mod b to be very convenient and don't care > that it doesn't work in Q(sqrt(2)), and wouldn't even consider > using a mod b for nontrivial elements of Q(sqrt(2)) -- > despite the fact that in the cases where the layperson wants > to use a mod b -- namely for positive natural numbers, > a mod b can be given a 100& rigorous, 100% unambiguous > definition via the Division Algorithm. > (2) Why should I tell him *again* that that is the case when I told him > already a few years ago? It's because tommy1729 concluded from your post that mod > isn't defined in math at all. Since he, like most people, > have only seen mod in the form a mod b if at all, and > have never seen a == b (mod m) at all, and so he reached > the only reasonable conclusion that's possible to someone > in that situation -- namely that if a mod b isn't > defined, then mod isn't defined at all. It's the only > reasonable conclusion one can make, until someone has > introduced to tommy1729 the notation a == b (mod m). And > that someone was Ullrich, not Winter. **************************************************************************** *** It's really touching to realize how exactly you know what Tommy knows, what he understand and understood, what conclusions he reached, why and how... If this isn't love then I don't know what is. Tonio === Subject: Re: A MOD B NO MATH HAHAHAHA !! Nntp-Posting-Host: hera.cwi.nl > > And your explanation does not explain, for instance: > 1 == 5 mod (98763 + 3989.sqrt(613)) > > Using a mod b is perfectly defined, justified and useable in a given > situation. Right. In a given situtation. The response was to somebody who said that I could see remaindering in a == b mod c. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: JSH: Was never a factor argument > [David Bernier] > ... > For now, my working assumption is that James can > manipulate algebraic symbols, but he > hasn't mastered some fundamental concepts in > high school algebra. Maybe this includes > the conceptual difference between parameters > or coefficients and an indeterminate or unknown quantity, > as the x is in ax^2 + bx + c. agree also I agree that's part of the truth. James is a symbol pusher, endlessly > manipulating equations /as/ equations, with a spectacular lack of > /insight/. It's typical that he complicates the set of equations he > works with until it's such a mess he can talk himself into believing > there's a revolutionary breakthrough hiding in the parts of that mess > that have grown so complicated he can no longer understand them at all. disagree, he has failed to learn higher levels algebra, high school algebra, he does not know complex numbers at all. to save his ego he attacks, driven by NPD to its ultimate end, living in the woods alone, in a small plywood room, chasing rabbits in the snow, supreme and the God of all around him, and they all worship him. (whoever they are) In this respect, this JSH post from 2006 was revealing: http://mathforum.org/kb/message.jspa?messageID=4773926 ... As a hobby when I was a kid I was fascinated with parabolas. > I'd draw them, play with the equations for them. Trace out > tangent lines, and marvel over their properties--and I liked > to rotate them into hyperbolas. Just for fun. He later admitted this (rotating parabolas into hyperbolas) wasn't > not just a simple mistake, it reveals a mind with /no understanding > whatsover/ of plane geometry. It's an extreme symbol-pusher's brain, > prone to accepting /obviously/ wrong conclusions based on mistakes made > while manipulating equations mindlessly. That's our Jimmy ;-) === Subject: Re: Tutte's theorem made easy? <4958eaaa$0$306$b45e6eb0@senator-bedfellow.mit.edu> posting-account=mMlFNwkAAAB4mlUHsL9lydZIKUPXmAkO Gecko/2008120122 Firefox/3.0.5,gzip(gfe),gzip(gfe) > I'm looking for a proof as elementary as possible of Tutte's theorem > stating that any vertically 4-connected planar graph is Hamiltonian. I > have tried to read Tutte's paper (the 1977 version of the proof) but > find it very dry. Maybe its wording doesn't help... > [...] >Sorry for my ignorance, what is a *vertically* 4-connected planar >graph? He means 4-vertex-connected, as opposed to 4-edge-connected. I haven't ever studied this result in detail myself, but there's a proof > at the end of Chapter 5 in Ore's book The Four-Color Problem. I'm > guessing that it's more readable than Tutte's proof, simply because Tutte > is almost always hard to read. > -- > Tim Chow tchow-at-alum-dot-mit-dot-edu > The range of our projectiles---even ... the artillery---however great, will > never exceed four of those miles of which as many thousand separate us from > the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences grab a copy of Ore's book. === Subject: how much? 1+1 in binary ? === Subject: Math, the language of physics posting-account=tCEoyAoAAAAkltU5zxOoI8uJ4lyz5-kv .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; .NET CLR 3.5.21022; Tablet PC 2.0),gzip(gfe),gzip(gfe) I really see no reason whatsoever that mathematics should be considered the end-all be-all modelling tool for physics and the other hard sciences. If my Doctrine of Existential Indeterminacy can be used to construct scientific models in these areas, then it should be just as valid science as any other findings which are modellable based on math. As stated elsewhere, the Doctrine of Existential Indeterminacy cannot be called mathematics. In my opinion it is indeterminate as to whether it is math or not. And as such, it cannot be said that it is math. Likewise, it cannot be said that it is not math. It is quite simply indeterminate. But this leaves you with a tool which is radicically different from standard math in certain ways. My claims is just this: that this Doctrine of Existential Indeterminacy might be regarded as a tool for modelling in science just as mathematics is, and if it models nature accurately then you may not have good math, but you do have some good science. Because guess what - Mathematics is not Science. Neither is the Doctrine of Existential Indeterminacy. If one can model Physics using conjectural methods instead of mathematics.....if the models make accurate Predictions.........then the Science is just as valid as if you had used math to do it. === Subject: Re: Math, the language of physics posting-account=beI85QkAAACAAUTQbCemu04CsboPXCD4 > I really see no reason whatsoever that mathematics should be > considered the end-all be-all modelling tool for physics and the other > hard sciences. If my Doctrine of Existential Indeterminacy can be used to construct > scientific models in these areas, then it should be just as valid > science as any other findings which are modellable based on math. As stated elsewhere, the Doctrine of Existential Indeterminacy > cannot be called mathematics. In my opinion it is indeterminate as to > whether it is math or not. And as such, it cannot be said that it is > math. Likewise, it cannot be said that it is not math. It is quite > simply indeterminate. But this leaves you with a tool which is radicically different from > standard math in certain ways. My claims is just this: that this Doctrine of Existential > Indeterminacy might be regarded as a tool for modelling in science > just as mathematics is, and if it models nature accurately then you > may not have good math, but you do have some good science. Because guess what - Mathematics is not Science. Neither is the > Doctrine of Existential Indeterminacy. If one can model Physics using conjectural methods instead of > mathematics.....if the models make accurate Predictions.........then > the Science is just as valid as if you had used math to do it. i've used my mind to understand wisdom and knowledge as well as madness and stupidity. [Now] I know that this is [like] trying to catch the wind. With a lot of wisdom [comes] a lot of heartache. The greater [your] knowledge, the greater [your] pain. There is nothing better for people to do than to eat, drink, and find satisfaction in their work. I saw that even this comes from the hand of God. is not what you are trying to do just more vanity? is not what is not seen more important than what is seen? i think i have had my fill of posting to news groups for at least a little while. blaaaaaaaaaah if you or anyone you know still has doubts: http://tinyurl.com/isJesusChristGod HAPPY, CHRIST CENTERED LIFE IN THE FUTURE WISHES FOR YOU!!!!!!! PEACE AND LOVE, AND, LOVE AND PEACE, KIRK KIRK GREGORY CZUHAI http://kirkgregoryczuhai.ws http://kirkgregoryczuhai.here.ws http://kirk.here.ws http://czuhai.ws PASTOR/OWNER/CEO/TECHNICAL SUPPORT, HEAVEN SENSE http://HeavenSense.ws THE FOR PROFIT CHURCH OF: FATHER GOD, HIS ONLY BEGOTTEN SON, JESUS CHRIST, AND THE HOLY SPIRIT !!!!!!! === Subject: Re: Math, the language of physics > I really see no reason whatsoever that mathematics should be > considered the end-all be-all modelling tool for physics and the other > hard sciences. > If my Doctrine of Existential Indeterminacy can be used to construct > scientific models in these areas, then it should be just as valid > science as any other findings which are modellable based on math. > As stated elsewhere, the Doctrine of Existential Indeterminacy > cannot be called mathematics. In my opinion it is indeterminate as to > whether it is math or not. And as such, it cannot be said that it is > math. Likewise, it cannot be said that it is not math. It is quite > simply indeterminate. > But this leaves you with a tool which is radicically different from > standard math in certain ways. > My claims is just this: that this Doctrine of Existential > Indeterminacy might be regarded as a tool for modelling in science > just as mathematics is, and if it models nature accurately then you > may not have good math, but you do have some good science. > Because guess what - Mathematics is not Science. Neither is the > Doctrine of Existential Indeterminacy. > If one can model Physics using conjectural methods instead of > mathematics.....if the models make accurate Predictions.........then > the Science is just as valid as if you had used math to do it. i've used my mind to understand wisdom and knowledge as well as > madness and stupidity. I've got plenty of all 4. Madness is a special kind of wisdom. Stupidity, a special kind of knowledge. > [Now] I know that this is [like] trying to > catch the wind. > With a lot of wisdom [comes] a lot of heartache. The greater [your] > knowledge, the greater [your] pain. > There is nothing better for people to do than to eat, drink, and find > satisfaction in their work. I saw that even this comes from the hand > of God. > is not what you are trying to do just more vanity? It can hardly be vanity if I am posting anonymously. Im just a person who has a great love of science, but also has a very open mind. Im so open minded that I would even consider modelling in physics not with mathematics, but a doctrine of conjecture. A tool as vast as math, but it is not math. Perhaps mathematics is not the only tool which can effect the accurate modelling of nature. That is what I believe. Interestingly, all of the regular PHYSICISTS in here are suddenly silent when you present them with the truth. I dont know why. They are all CHICKENS. > is not what is not seen more important than what is seen? > i think i have had my fill of posting to news groups for at least a > little while. > blaaaaaaaaaah > if you or anyone you know > still has doubts: http://tinyurl.com/isJesusChristGod HAPPY, CHRIST CENTERED LIFE > IN THE FUTURE WISHES FOR YOU!!!!!!! > PEACE AND LOVE, > AND, > LOVE AND PEACE, Christmas/Hannukah/Kwanza back at ya. === Subject: Re: Math, the language of physics posting-account=tCEoyAoAAAAkltU5zxOoI8uJ4lyz5-kv .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; .NET CLR 3.5.21022; Tablet PC 2.0),gzip(gfe),gzip(gfe) There is no formal proof that mathematics is the best, most accurate tool for modelling physics or any other physical science. One would have great difficulty building a tool which compares to mathematics in this regard, but there is no proof that it is the most valid tool, or even the only valid tool which would serve the purpose. Curently, there is probably _nobody_ on the entire planet looking for tools which lie outside of the realm of math, but that does not mean that it is not a valid thing to think about. Math is based on logic. Are there other such structures, similar in construction to mathematics, but based on other considerations ? I would argue that there may be. I may not be doing standard mathematics on this forum, but I dont think that I can be accused of voodoo. If you have a model that predicts physical phenomena then you are doing science and it does not matter what the actual nature of your model is or if people dont like it or if they think it's wacky. If a model predicts physical phenomena, then you do have science. You might not have mathematics, but you do have science. === Subject: Re: Square zero-one-matrix with equal number of ones in each row and each column. > I would find it very helpful to know > under what name/technical term > more can be found about the following object: > An n by n matrix, each entry either 1 or 0, such > that the number of ones in every row and in every > columns is the same. > This must be a very common topic in Design Theory, > for instance, and there must be a standard > terminology for this. 0-1 semi-magic squares, perhaps. > In particular, it is surely known for which values of n > such matrices exist. Does anyone know more about > this? As hagman remarked, they always exist. Moreover, you can think >of them this way. Fix integer k, 0 < k < n, and consider the >convex polytope in R^(n^2) defined by the equations sum_{i=1}^n x_{ij} = k for each j=1..n >sum_{j=1}^n x_{ij} = k for each i=1..n >0 <= x_{ij} <= 1 for each i,j In linear programming terminology, these constitute the constraints for a >transportation problem where each source and sink has capacity k >and each arc has upper bound 1. The extreme points of this polytope >correspond to your matrices. It's easy to see that such matrices correspond to extreme points. I'm having trouble seeing is why the converse is true. Why must an extreme point of the polytope have coordinates with only 0s and 1s? >Also perhaps of interest: each such matrix can be written (not necessarily >uniquely) as a sum of k disjoint permutation matrices (disjoint in the sense >that their 1's never coincide). That's a cool observation. Again, one direction is obvious, namely, a sum of disjoint permutations yields a matrix of the required type. For the converse, the case k = 1 is immediate. For k > 1, one can show that it's possible, for a given such matrix, to find a permutation which is fully covered by the given matrix. One can then remove that permutation (actually subtract it), and the modified matrix also satisfies the conditions but with k decremented by 1, hence the result is clinched by induction. However, at first glance, I didn't see immediately see how to solve the problem of finding such a removable permutation. Analyzing the case k = 2, though a little tricky, resolves nicely, leading immediately to a general resolution. It was fun to think through. quasi === Subject: Re: Square zero-one-matrix with equal number of ones in each row and each column. > I would find it very helpful to know > under what name/technical term > more can be found about the following object: > An n by n matrix, each entry either 1 or 0, such > that the number of ones in every row and in every > columns is the same. > This must be a very common topic in Design Theory, > for instance, and there must be a standard > terminology for this. > >0-1 semi-magic squares, perhaps. > > In particular, it is surely known for which values of n > such matrices exist. Does anyone know more about > this? > >As hagman remarked, they always exist. Moreover, you can think >of them this way. Fix integer k, 0 < k < n, and consider the >convex polytope in R^(n^2) defined by the equations > >sum_{i=1}^n x_{ij} = k for each j=1..n >sum_{j=1}^n x_{ij} = k for each i=1..n >0 <= x_{ij} <= 1 for each i,j > >In linear programming terminology, these constitute the constraints for a >transportation problem where each source and sink has capacity k >and each arc has upper bound 1. The extreme points of this polytope >correspond to your matrices. It's easy to see that such matrices correspond to extreme points. I'm > having trouble seeing is why the converse is true. Why must an extreme > point of the polytope have coordinates with only 0s and 1s? Because of the Integrality Theorem for network flows. See e.g. . Or more directly: suppose you have x in the polytope with some 0 < x_{ij} < 1. Consider the bipartite graph consisting of sources s_1 .. s_n and sinks t_1 .. t_n, with an edge (s_i, t_j) whenever 0 < x_{ij} < 1. Since sum_i x_{ij} is an integer for each j and sum_j x_{ij} is an integer for each i, for any set A of vertices sum_{s_i in A, t_j in A^c} x_{ij} - sum_{s_i in A^c, t_j in A} x_{ij} must be an integer. Taking A to be the connected component of t_{j_0} in the graph with one edge (s_{i_0}, t_{j_0}) removed, we find that s_i must be in that connected component, and thus there must be a path (t_{j_0}, s_{i_1}, t_{j_1},..., s_{i_0}) in the graph. Given such a path, for some epsilon > 0 both x' and x'' = 2 x - x' are in the polytope, where we get x' from x by increasing x_{ij} by epsilon whenever (s_i, t_j) is in the path and decreasing it by epsilon whenever (t_j, s_i) is in the path. -- Robert Israel israel@math.MyUniversitysInitials.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada === Subject: Re: Square zero-one-matrix with equal number of ones in each row and each column. > I would find it very helpful to know > under what name/technical term > more can be found about the following object: > An n by n matrix, each entry either 1 or 0, such > that the number of ones in every row and in every > columns is the same. > This must be a very common topic in Design Theory, > for instance, and there must be a standard > terminology for this. >0-1 semi-magic squares, perhaps. > In particular, it is surely known for which values of n > such matrices exist. Does anyone know more about > this? >As hagman remarked, they always exist. Moreover, you can think >of them this way. Fix integer k, 0 < k < n, and consider the >convex polytope in R^(n^2) defined by the equations >sum_{i=1}^n x_{ij} = k for each j=1..n >sum_{j=1}^n x_{ij} = k for each i=1..n >0 <= x_{ij} <= 1 for each i,j >In linear programming terminology, these constitute the constraints for a >transportation problem where each source and sink has capacity k >and each arc has upper bound 1. The extreme points of this polytope >correspond to your matrices. > It's easy to see that such matrices correspond to extreme points. I'm > having trouble seeing is why the converse is true. Why must an extreme > point of the polytope have coordinates with only 0s and 1s? Because of the Integrality Theorem for network flows. See e.g. >. >Or more directly: suppose you have x in the polytope with some >0 < x_{ij} < 1. Consider the bipartite graph consisting of sources >s_1 .. s_n and sinks t_1 .. t_n, with an edge (s_i, t_j) whenever >0 < x_{ij} < 1. Since sum_i x_{ij} is an integer for each j and >sum_j x_{ij} is an integer for each i, for any set A of vertices >sum_{s_i in A, t_j in A^c} x_{ij} - sum_{s_i in A^c, t_j in A} x_{ij} >must be an integer. Taking A to be the connected component of t_{j_0} >in the graph with one edge (s_{i_0}, t_{j_0}) removed, we find that s_i must >be in that connected component, and thus there must be a path >(t_{j_0}, s_{i_1}, t_{j_1},..., s_{i_0}) in the graph. Given such >a path, for some epsilon > 0 both x' and x'' = 2 x - x' are in the >polytope, where we get x' from x by increasing x_{ij} by epsilon whenever >(s_i, t_j) is in the path and decreasing it by epsilon whenever (t_j, s_i) is >in the path. may need a little time to work through it). quasi === Subject: Re: Square zero-one-matrix with equal number of ones in each row and each column. > I would find it very helpful to know > under what name/technical term > more can be found about the following object: > An n by n matrix, each entry either 1 or 0, such > that the number of ones in every row and in every > columns is the same. > This must be a very common topic in Design Theory, > for instance, and there must be a standard > terminology for this. >0-1 semi-magic squares, perhaps. > In particular, it is surely known for which values of n > such matrices exist. Does anyone know more about > this? >As hagman remarked, they always exist. Moreover, you can think >of them this way. Fix integer k, 0 < k < n, and consider the >convex polytope in R^(n^2) defined by the equations >sum_{i=1}^n x_{ij} = k for each j=1..n >sum_{j=1}^n x_{ij} = k for each i=1..n >0 <= x_{ij} <= 1 for each i,j >In linear programming terminology, these constitute the constraints for a >transportation problem where each source and sink has capacity k >and each arc has upper bound 1. The extreme points of this polytope >correspond to your matrices. >It's easy to see that such matrices correspond to extreme points. I'm >having trouble seeing is why the converse is true. Why must an extreme >point of the polytope have coordinates with only 0s and 1s? Because if 0 < a < 1 then there exist b and c in (0,1) such that >a is a convex combination of b and c _and_ b and c are different from >a. Sure, that's obvious. But it's not obvious to me that you can replace a component a of one of the _qualifying_ matrices (one of the matrices of the convex polytope) with components b and c (separate replacements, of course) as you suggest above, while staying in (or on the boundary) the polytope. >In other words, because the extreme points of the interval [0,1] >are precisely 0 and 1. But now the feasible region is no longer an interval. Nor is it a higher dimensional rectangular solid. The polytope can be visualized as the intersection of an (n^2-2n)-dimensional flat with a 2n-dimensional cubic region in R^(2n). It's clear that the extreme points of the resulting polytope will be on the boundary of the cube. But they need not be at the vertices of the cube. Perhaps in this case, the nature of the defining equations forces all extreme points. to be at vertices of the cube? If so, I don't see it. quasi === Subject: Re: Square zero-one-matrix with equal number of ones in each row and each column. <9v5jl4t6aopfcjiikfso5ddnh87d16kcs3@4ax.com> <339kl4lmu1ie2m0gt9uvd7n436o69ikk13@4ax.com> posting-account=9QOSvAoAAACEOWJVSDuswW7dB_0wApQO Gecko/20070530 Fedora/1.5.0.12-1.fc5 Firefox/1.5.0.12,gzip(gfe),gzip(gfe) > I would find it very helpful to know > under what name/technical term > more can be found about the following object: > An n by n matrix, each entry either 1 or 0, such > that the number of ones in every row and in every > columns is the same. > This must be a very common topic in Design Theory, > for instance, and there must be a standard > terminology for this. >0-1 semi-magic squares, perhaps. > In particular, it is surely known for which values of n > such matrices exist. Does anyone know more about > this? >As hagman remarked, they always exist. Moreover, you can think >of them this way. Fix integer k, 0 < k < n, and consider the >convex polytope in R^(n^2) defined by the equations >sum_{i=1}^n x_{ij} = k for each j=1..n >sum_{j=1}^n x_{ij} = k for each i=1..n >0 <= x_{ij} <= 1 for each i,j >In linear programming terminology, these constitute the constraints for a >transportation problem where each source and sink has capacity k >and each arc has upper bound 1. The extreme points of this polytope >correspond to your matrices. >It's easy to see that such matrices correspond to extreme points. I'm >having trouble seeing is why the converse is true. Why must an extreme >point of the polytope have coordinates with only 0s and 1s? >Because if 0 < a < 1 then there exist b and c in (0,1) such that >a is a convex combination of b and c _and_ b and c are different from >a. >Sure, that's obvious. >But it's not obvious to me that you can replace a component a of one >of the _qualifying_ matrices (one of the matrices of the convex >polytope) with components b and c (separate replacements, of course) >as you suggest above, while staying in (or on the boundary) the >polytope. It's not so clear to me either, sorry. Missed a bit this morning. The matrix of coefficients in the system of equations sum_{i=1}^n x_{ij} = k for each j=1..n sum_{j=1}^n x_{ij} = k for each i=1..n (for some ordering of the variables x_{ij}...) is a totally unimodular matrix, so the polyhedron considered by Robert indeed has integral vertices. -- m === Subject: Re: Square zero-one-matrix with equal number of ones in each row and each column. <9v5jl4t6aopfcjiikfso5ddnh87d16kcs3@4ax.com> <339kl4lmu1ie2m0gt9uvd7n436o69ikk13@4ax.com> posting-account=9QOSvAoAAACEOWJVSDuswW7dB_0wApQO Gecko/20070530 Fedora/1.5.0.12-1.fc5 Firefox/1.5.0.12,gzip(gfe),gzip(gfe) On Dec 30, 6:36 pm, Mariano Su.87rez-Alvarez > I would find it very helpful to know > under what name/technical term > more can be found about the following object: > An n by n matrix, each entry either 1 or 0, such > that the number of ones in every row and in every > columns is the same. > This must be a very common topic in Design Theory, > for instance, and there must be a standard > terminology for this. >0-1 semi-magic squares, perhaps. > In particular, it is surely known for which values of n > such matrices exist. Does anyone know more about > this? >As hagman remarked, they always exist. Moreover, you can think >of them this way. Fix integer k, 0 < k < n, and consider the >convex polytope in R^(n^2) defined by the equations >sum {i=1}^n x {ij} = k for each j=1..n >sum {j=1}^n x {ij} = k for each i=1..n >0 <= x {ij} <= 1 for each i,j >In linear programming terminology, these constitute the constraints for a >transportation problem where each source and sink has capacity k >and each arc has upper bound 1. The extreme points of this polytope >correspond to your matrices. >It's easy to see that such matrices correspond to extreme points. I'm >having trouble seeing is why the converse is true. Why must an extreme >point of the polytope have coordinates with only 0s and 1s? >Because if 0 < a < 1 then there exist b and c in (0,1) such that >a is a convex combination of b and c and b and c are different from >a. >Sure, that's obvious. >But it's not obvious to me that you can replace a component a of one >of the qualifying matrices (one of the matrices of the convex >polytope) with components b and c (separate replacements, of course) >as you suggest above, while staying in (or on the boundary) the >polytope. > It's not so clear to me either, sorry. Missed a bit this morning. The matrix of coefficients in the system of equations sum {i=1}^n x {ij} = k for each j=1..n > sum {j=1}^n x {ij} = k for each i=1..n (for some ordering of the variables x {ij}...) is > a totally unimodular matrix, so the polyhedron > considered by Robert indeed has integral vertices. Indeed: this is the edge-vertex incidence matrix for a complex bipartite graph on (n,n) vertices, which is easily seen to be totally unimodular. The integrality of the polytope follows then using the Hoffman-Kruskal theorem. -- m === Subject: Re: Square zero-one-matrix with equal number of ones in each row and each column. >On Dec 30, 6:36 pm, Mariano Su.87rez-Alvarez > I would find it very helpful to know > under what name/technical term > more can be found about the following object: > An n by n matrix, each entry either 1 or 0, such > that the number of ones in every row and in every > columns is the same. > This must be a very common topic in Design Theory, > for instance, and there must be a standard > terminology for this. >0-1 semi-magic squares, perhaps. > In particular, it is surely known for which values of n > such matrices exist. Does anyone know more about > this? >As hagman remarked, they always exist. Moreover, you can think >of them this way. Fix integer k, 0 < k < n, and consider the >convex polytope in R^(n^2) defined by the equations >sum_{i=1}^n x_{ij} = k for each j=1..n >sum_{j=1}^n x_{ij} = k for each i=1..n >0 <= x_{ij} <= 1 for each i,j >In linear programming terminology, these constitute the constraints for a >transportation problem where each source and sink has capacity k >and each arc has upper bound 1. The extreme points of this polytope >correspond to your matrices. >It's easy to see that such matrices correspond to extreme points. I'm >having trouble seeing is why the converse is true. Why must an extreme >point of the polytope have coordinates with only 0s and 1s? >Because if 0 < a < 1 then there exist b and c in (0,1) such that >a is a convex combination of b and c _and_ b and c are different from >a. >Sure, that's obvious. >But it's not obvious to me that you can replace a component a of one >of the _qualifying_ matrices (one of the matrices of the convex >polytope) with components b and c (separate replacements, of course) >as you suggest above, while staying in (or on the boundary) the >polytope. > It's not so clear to me either, sorry. Missed a bit this morning. > The matrix of coefficients in the system of equations > sum_{i=1}^n x_{ij} = k for each j=1..n > sum_{j=1}^n x_{ij} = k for each i=1..n > (for some ordering of the variables x_{ij}...) is > a totally unimodular matrix, so the polyhedron > considered by Robert indeed has integral vertices. Indeed: this is the edge-vertex incidence matrix for >a complex bipartite graph on (n,n) vertices, which is >easily seen to be totally unimodular. The integrality >of the polytope follows then using the Hoffman-Kruskal >theorem. To follow up, I'll definitely take a look at the the Hoffman-Kruskal theorem. quasi === Subject: Re: Square zero-one-matrix with equal number of ones in each row and each column. I would find it very helpful to know > under what name/technical term > more can be found about the following object: An n by n matrix, each entry either 1 or 0, such > that the number of ones in every row and in every > columns is the same. This must be a very common topic in Design Theory, > for instance, and there must be a standard > terminology for this. >0-1 semi-magic squares, perhaps. > In particular, it is surely known for which values of n > such matrices exist. Does anyone know more about > this? >As hagman remarked, they always exist. Moreover, you can think >of them this way. Fix integer k, 0 < k < n, and consider the >convex polytope in R^(n^2) defined by the equations >sum_{i=1}^n x_{ij} = k for each j=1..n >sum_{j=1}^n x_{ij} = k for each i=1..n >0 <= x_{ij} <= 1 for each i,j >In linear programming terminology, these constitute the constraints for a >transportation problem where each source and sink has capacity k >and each arc has upper bound 1. The extreme points of this polytope >correspond to your matrices. >It's easy to see that such matrices correspond to extreme points. I'm >having trouble seeing is why the converse is true. Why must an extreme >point of the polytope have coordinates with only 0s and 1s? >Because if 0 < a < 1 then there exist b and c in (0,1) such that >a is a convex combination of b and c _and_ b and c are different from >a. Sure, that's obvious. But it's not obvious to me that you can replace a component a of one >of the _qualifying_ matrices (one of the matrices of the convex >polytope) with components b and c (separate replacements, of course) >as you suggest above, while staying in (or on the boundary) the >polytope. >In other words, because the extreme points of the interval [0,1] >are precisely 0 and 1. But now the feasible region is no longer an interval. Nor is it a >higher dimensional rectangular solid. The polytope can be visualized >as the intersection of an (n^2-2n)-dimensional flat with a Correction: In the above line, (n^2-2n) should be (n^2 - 2n + 1) or (n - 1)^2. >2n-dimensional cubic region in R^(2n). It's clear that the extreme >points of the resulting polytope will be on the boundary of the cube. >But they need not be at the vertices of the cube. Perhaps in this >case, the nature of the defining equations forces all extreme points. >to be at vertices of the cube? If so, I don't see it. quasi === Subject: Re: Square zero-one-matrix with equal number of ones in each row and each column. > I would find it very helpful to know > under what name/technical term > more can be found about the following object: > An n by n matrix, each entry either 1 or 0, such > that the number of ones in every row and in every > columns is the same. > This must be a very common topic in Design Theory, > for instance, and there must be a standard > terminology for this. >0-1 semi-magic squares, perhaps. > In particular, it is surely known for which values of n > such matrices exist. Does anyone know more about > this? >As hagman remarked, they always exist. Moreover, you can think >of them this way. Fix integer k, 0 < k < n, and consider the >convex polytope in R^(n^2) defined by the equations >sum_{i=1}^n x_{ij} = k for each j=1..n >sum_{j=1}^n x_{ij} = k for each i=1..n >0 <= x_{ij} <= 1 for each i,j >In linear programming terminology, these constitute the constraints for a >transportation problem where each source and sink has capacity k >and each arc has upper bound 1. The extreme points of this polytope >correspond to your matrices. >It's easy to see that such matrices correspond to extreme points. I'm >having trouble seeing is why the converse is true. Why must an extreme >point of the polytope have coordinates with only 0s and 1s? >Because if 0 < a < 1 then there exist b and c in (0,1) such that >a is a convex combination of b and c _and_ b and c are different from >a. >Sure, that's obvious. >But it's not obvious to me that you can replace a component a of one >of the _qualifying_ matrices (one of the matrices of the convex >polytope) with components b and c (separate replacements, of course) >as you suggest above, while staying in (or on the boundary) the >polytope. >In other words, because the extreme points of the interval [0,1] >are precisely 0 and 1. >But now the feasible region is no longer an interval. Nor is it a >higher dimensional rectangular solid. The polytope can be visualized >as the intersection of an (n^2-2n)-dimensional flat with a Correction: In the above line, (n^2-2n) should be (n^2 - 2n + 1) or (n - 1)^2. >2n-dimensional cubic region in R^(2n). Ugh -- I was being careless. Here are the correct dimensions (I'm fairly sure). I'll replace the entire previous paragraph. But now the feasible region is no longer an interval. Nor is it a higher dimensional rectangular solid. The polytope can be visualized as the intersection of an ((n-1)^2)-dimensional flat with an (n^2)-dimensional cubic region in R^(n^2). >It's clear that the extreme >points of the resulting polytope will be on the boundary of the cube. >But they need not be at the vertices of the cube. Perhaps in this >case, the nature of the defining equations forces all extreme points. >to be at vertices of the cube? If so, I don't see it. quasi === Subject: Re: Galileo canonized by Pope posting-account=jPnQ2goAAAA461y3QD0lbyw0oKeThma1 AppleWebKit/525.18 (KHTML, like Gecko) Version/3.1.2 Safari/525.20.1 FOH:R051,gzip(gfe),gzip(gfe) glad & frightened to read about the lack of sunspots, and the correlation with the Little Ice Age, I hadn't known of. the Face and Genitals on Mars people, with their hyper-D crap, do find interesting anamolies that need explanation -- just not theirs!... for instance, the whole hidden NASA life story is silly, since it is very clear that water implies the likelihood of past life, or remnants of that. after all, Mars is much snaller than Earth, so its life would've been much shorter, all other things being equal, a thorough bodyshave with Ockham's razor -- going to Cydonia Temple? > http://www.enterprisemission.com/ thus: that was more-or-less what I said, two; Russel's paradoxes were simply pidgen -- I yam lying what I bean; not, I yam lying what I yam! the same applies to Korzybski (sp.?) and his E' (and probably his whole general semantics, unless the first was a purposeful joke). thus: that is an interesting inference of yours; had not someone proven the case for n=3 (and, of course, the very special case of n=4) ?? > life, Fermat, in a letter, raised the question of proving that no fifth > power is a sum of two fifth powers. So, by this time, he didn't even thus: on Nondystributive Geometry. yeah; if you can't put into constructive geometrical terms, you can't do ****. yeah; you had the definitive 2-week course in Geometry from an Advanced/Remedial Viewpoint in some Mice.Space at Vanderbilt! http://wlym.com/~boston/cartoons/slides/Mice%20Space.htm thus: here is an example of the Skeptics (current Calif. or USA mag.) being unable to come-up with a rational explanation of: sodium-vapor streetlights going off, as you walk underneath them; they think it to be either a hoax or psycho/visual. also, cropcircles. also, http://www.svpvril.com/svpweb14.html. thus: even Ockham'd slice through that apple & orange, with one wild Yahoo! (tm); western astrology is the same as Ptolemy's epicyclic hoax, over 2000yo. > some have been even making into popular news. > that astrological signs may have some meaning thus: I yam lying what I bean!... of what possible use is the set of all sets, whether or not it can eventually include itself, at the end of the list of elements -- shades of AP-adics? so, perhaps we can blame Russell for the Bourbaki New Math, based upon set theory, but see what Whitehead had to say about him, not to say Godel. thus: shouldn't it be clear that photons are an artifact of the idea that actually were zero-dimensional points, but, since they are waves, as shown by Young, Huyghens et al, there is really no need for them, except in the Pauli matrix formalism of statistical bosons; eh? Schroedinger's cat is dead -- long-live Schoredinger's cat! --only 24 hours to impeach Trickier Dick from the N.Admin, metaphorically typing, or Cheeny & Zbiggy, fo'mo' years; Good Morning, Afghanistan! ... Good Afternoon, Sudan! http://tarpley.net/bush12.htm http://wlym.com/campaigner/8011.pdf -- Brits hate Shakes, Why? http://www.wlym.com/~seattle/dynamis/ http://www.21stcenturysciencetech.com/current.html http://www.rwgrayprojects.com/synergetics/plates/plates.html http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=3163 http://wlym.com/campaigner/8011.pdf -- English, not! === Subject: Re: Comprehensive Solution Manual for Textbooks posting-account=rLOz6QoAAAAmvEIbrGZd27QhtZqovu5R rv:1.9.0.5) Gecko/2008120121 Firefox/3.0.5,gzip(gfe),gzip(gfe) continued...Updated list per December 30, 2008 I have the comprehensive SOLUTIONS MANUAL for ALL of the following textbooks and TEST BANKS for MOST of them in electronic format (PDF/ Word). The solutions manual are comprehensive with answers to both even & odd problems in the text. The price for the solution manual is US$35 for each. The price for the test bank is also $35. The methods of payment is through PAYPAL (It is easy, safe, and you can use debit or credit card to pay even if you don't have an account). Email me at sbooks4sale[at]hotmail[dot]com if you are interested. If you could not find the book you are looking for, please let me know, I -------------------------- Chemistry - John E McMurry (Test Bank only) (5th ed) (ISBN 0131993232) Chemistry : An Introduction to General, Organic, Biological Chemistry - Karen Timberlake (9th ed) (ISBN 0805330151) Chemistry: An Introduction to General, Organic, & Biological Chemistry - Karen C Timberlake (10th ed) (ISBN 0136019706) ed) (ISBN 0534408966) CMOS Circuit Design, Layout, and Simulation - David E. Boyce et al (1st ed) (ISBN 0780334167) College Accounting 1-12 - Jeffrey Slater (9th ed) (ISBN 0131071696) College Accounting 1-25 - Jeffrey Slater (10th ed) (ISBN 0132286386) College Accounting Chapters 1-15 - James Heintz (19th ed) (ISBN 0324382499) College Accounting Chapters 1-27 - James Heintz (19th ed) (ISBN 0324376162) College Accounting Chapters 1-9 - James Heintz (19th ed) (ISBN 0324382480) College Algebra - J. S. Ratti (1st ed) (ISBN 0321296443) College Algebra - Judith A. Beecher (3rd ed) (ISBN 0321466071) College Algebra - Margaret L. Lial (10th ed) (ISBN 0321499131) College Algebra - Mark Dugopolski (4th ed) (ISBN 0321356918) College Algebra - Michael Sullivan (8th ed) (ISBN 0132402866) College Algebra and Trigonometry - J. S. Ratti (1st ed) (ISBN 0321296427) College Algebra and Trigonometry - Margaret L. Lial (4th ed) (ISBN 0321497449) College Algebra Enhanced with Graphing Utilities - Michael Sullivan (5th ed) (ISBN 0136004911) College Algebra Essentials - Michael Sullivan (8th ed) (ISBN 0136154344) College Algebra: Graphs and Models with Graphing Calculator Manual Package - Marvin L. Bittinger (4th ed) (ISBN 0321531922) College Geometry - David C. Kay (2nd ed) (ISBN 0321046242) College Geometry: A Problem Solving Approach with Applications - Gary L. Musser (2nd ed) (ISBN 0131879693) College Math for Business, Economics, Life Sciences & Social Sciences - Raymond Barnett (11th ed) (ISBN 0131572253) College Physics - Jerry D Wilson (6th ed) (ISBN 0131495798) College Physics with Mastering Physics - Hugh Young (8th ed) (ISBN 0805390707) Communication Systems Engineering - John G. Proakis (2nd ed) (ISBN 0130617938) Comparative International Accounting - Christopher Nobes (9th ed) (ISBN 0273703579) Complex Variables With Applications - A. David Wunsch (3rd ed) (ISBN 0201756099) Computer Algorithms - Allen Van Gelder, Sara Baase (3rd ed) (ISBN 0201612445) Computer Networking Complete Package - James F. Kurose (3rd ed) (ISBN 0321418492) Computer Networking with Internet Protocols - William Stallings (1st ed) (ISBN 0131410989) Computer Networking: A Top-Down Approach - James F. Kurose (4th ed) (ISBN 0321497708) Computer Networking: A Top-Down Approach Featuring the Internet - James F. Kurose (3rd ed) (ISBN 0321227352) Computer Organization and Architecture - William Stallings (7th ed) (ISBN 0130351199) Computer Organization and Architecture: Designing for Performance - William Stallings (7th ed) (ISBN 0131856448) Computer Science: An Overview - J. Glenn Brookshear (10th ed) (ISBN 0321524039) Computer Security: Principles and Practice - William Stallings (1st ed) (ISBN 0136004245) Computer Systems Organization & Architecture - John D. Carpinelli (1st ed) (ISBN 0201612534) Concepts in Federal Taxation 2007 - Kevin Murphy (14th ed) (ISBN 0324313527) Concepts in Federal Taxation 2008 - Kevin Murphy (15th ed) (ISBN 0324640153) Concepts in Federal Taxation 2009 - Kevin Murphy (16th ed) (ISBN 0324659377) Concepts In Systems and Signals - John D. Sherrick (2nd ed) (ISBN 0131782711) Concepts of Calculus with Applications - Martha Goshaw (1st ed) (ISBN 0321320786) Concepts of Calculus With Applications-Updated Edition - Martha Goshaw (2nd ed) (ISBN 0321577442) Concepts of Programming Languages - Robert W. Sebesta (8th ed) (ISBN 0321493621) Conceptual Physical Science - Paul G. Hewitt (4th ed) (ISBN 0321516958) Conceptual Physics Fundamentals - Paul G. Hewitt (1st ed) (ISBN 0321501365) Conceptual Physics Media Update - Paul G. Hewitt (10th ed) (ISBN 0321548094) Concrete Structures - Mehdi Setareh (1st ed) (ISBN 0131988271) Construction Accounting & Financial Management - Stephen Peterson (2nd ed) (ISBN 0135017114) Construction Methods and Management - Stephens W. Nunnally (7th ed) (ISBN 0131716859) Construction Project Management - Fred Gould (3rd ed) (ISBN 0131996231) Consumer Behavior - Michael Solomon (8th ed) (ISBN 0136015964) Contemporary Business and Online Commerce Law - Henry R. Cheeseman (6th ed) (ISBN 013601500X) Contemporary Engineering Economics - Chan S. Park (4th ed) (ISBN 0131876287) Contemporary Financial Management - Charles Moyer (10th ed) (ISBN 0324289081) Contemporary Financial Management - R. Charles Moyer, James R. McGuigan (11th ed) (ISBN 0324653506) Contemporary Logistics - Paul R. Murphy (9th ed) (ISBN 013156207X) Contemporary Marketing 2009 Update - Louis E. Boone (13th ed) (ISBN 0324580215) Cornerstones of Managerial Accounting - Maryanne M. Mowen (2nd ed) (ISBN 0324379609) Corporate Finance - Jonathan Berk (1st ed) (ISBN 0321415116) Corporate Finance - Michael C. Ehrhardt, Eugene F. Brigham (3rd ed) (ISBN 0324655681) Corporate Finance: The Core plus MyFinanceLab Student Access Kit - Jonathan Berk (1st ed) (ISBN 032155759X) Corporate Financial Management - Douglas R. Emery (3rd ed) (ISBN 0132278723) Cost Accounting - Charles T. Horngren, George Foster, Srikant M. Datar (12th ed) (ISBN 0131495380) Cost Accounting - Charles T. Horngren, George Foster, Srikant M. Datar (13th ed) (ISBN 0136126634) Cost Accounting: Traditions & Innovations - Jesse Barfield (5th ed) (ISBN 032418090X) Cost Benefit Analysis: Concepts and Practice - Anthony Boardman (3rd ed) (ISBN 0131435833) Cost Management: Accounting and Control - Don R. Hansen, Maryanne M. Mowen (6th ed) (ISBN 0324559674) Course in Probability - Neil Weiss (1st ed) (ISBN 0201774712) Criminology: A Global Perspective - Robert W. Winslow (1st ed) (ISBN 0131839020) Cryptography and Network Security - William Stallings (4th ed) (ISBN 0131873164) Customer Service: Career Success Through Customer Loyalty - Paul R. Timm (4th ed) (ISBN 0132236583) Data Abstraction & Problem Solving with C++ - Frank M. Carrano (5th ed) (ISBN 0321433327) Data and Computer Communications - William Stallings (8th ed) (ISBN 0132433109) Data Structures and Algorithm Analysis in C++ - Mark Allen Weiss (3rd ed) (ISBN 032144146X) Data Structures and Algorithm Analysis in Java - Mark Allen Weiss (2nd ed) (ISBN 0321370139) Database Systems: A Practical Approach - Thomas M. Connolly (4th ed) (ISBN 0321294017) Derivatives Markets - Robert L. McDonald (2nd ed) (ISBN 032128030X) Detection and Estimation:Theory and Its Applications - Thomas Schonhoff (1st ed) (ISBN 0130894990) Developmental Mathematics - Marvin L. Bittinger (7th ed) (ISBN 0321331915) Developmental Mathematics: Basic Mathematics and Algebra - Margaret L. Lial (1st ed) (ISBN 0321506421) Differential Equations - John Polking (2nd ed) (ISBN 0131437380) Differential Equations and Boundary Value Problems: Computing and Modeling - Henry Edwards (4th ed) (ISBN 0131561073) Differential Equations and Linear Algebra - Henry Edwards, David E. Penney (2nd ed) (ISBN 0131481460) Differential Equations and Linear Algebra - Jerry Farlow (2nd ed) (ISBN 0131860615) Differential Equations and Linear Algebra - Stephen W. Goode (3rd ed) (ISBN 0130457949) Differential Equations Computing and Modeling - Henry Edwards (4th ed) (ISBN 0136004385) Differential Equations With Boundary Value Problems - John C. Polking (2nd ed) (ISBN 0130911062) Digital & Analog Communication Systems - Leon Couch (7th ed) (ISBN 0131424920) Digital Communications - John Proakis (4th ed) (ISBN 0072321113) Digital Design - Morris Mano (4th ed) (ISBN 0131989243) Digital Electronics: A Practical Approach - William Kleitz (8th ed) (ISBN 0132435780) Digital Signal Processing - John Proakis (4th ed) (ISBN 0131873741) Digital Signal Processing Using MATLAB -Vinay K. Ingle, John G. Proakis (2nd ed) (ISBN 0495073113) Digital Systems Design Using VHDL - Charles H. Roth (2nd ed) (ISBN 0534384625) Digital Systems: Principles and Applications - Ronald Tocci et al (10th ed) (ISBN 0131725793) Discrete and Combinatorial Mathematics - Ralph P. Grimaldi (5th ed) (ISBN 0201726343) Discrete Mathematics - Edgar G. Goodaire, Michael M Parmenter (3rd ed) (ISBN 0131679953) Discrete Mathematics - Otto, Eynden, Dossey, Spence (4th ed) (ISBN 0321079124) Discrete Mathematics - Otto, Eynden, Dossey, Spence (5th ed) (ISBN 0321305159) Discrete Mathematics - Richard Johnsonbaugh (6th ed) (ISBN 0131176862) Drugs & the Human Body - Ken Liska (8th ed) (ISBN 0132447134) === Subject: Re: Comprehensive Solution Manual for Textbooks posting-account=rLOz6QoAAAAmvEIbrGZd27QhtZqovu5R rv:1.9.0.5) Gecko/2008120121 Firefox/3.0.5,gzip(gfe),gzip(gfe) continued...Updated list per December 30, 2008 I have the comprehensive SOLUTIONS MANUAL for ALL of the following textbooks and TEST BANKS for MOST of them in electronic format (PDF/ Word). The solutions manual are comprehensive with answers to both even & odd problems in the text. The price for the solution manual is US$35 for each. The price for the test bank is also $35. The methods of payment is through PAYPAL (It is easy, safe, and you can use debit or credit card to pay even if you don't have an account). Email me at sbooks4sale[at]hotmail[dot]com if you are interested. If you could not find the book you are looking for, please let me know, I -------------------------- Financial Markets and Institutions - Frederic S. Mishkin (5th ed) (ISBN 0321280296) Financial Markets and Institutions - Frederic S. Mishkin (6th ed) (ISBN 0321374215) Financial Markets and Institutions - Jeff Madura (8th ed) (ISBN 0324568215) Financial Reporting and Analysis - Lawrence Revsine (3rd ed) (ISBN 0131430211) Financial Reporting and Analysis Using Financial Accounting Information - Charles Gibson (10th ed) (ISBN 0324304455) Financial Reporting, Financial Statement Analysis, and Valuation - Clyde P. Stickney (6th ed) (ISBN 0324302959) Financial/Managerial Accounting - Walter T. Harrison (1st ed) (ISBN 0131568779) Finite Element Analysis Theory and Application with ANSYS - Saeed Moaveni (3rd ed) (ISBN 0131890808) Finite Math and Its Application - Larry Goldstein (9th ed) (ISBN 0131873644) Finite Mathematics - Margaret L. Lial et al (8th ed) (ISBN 032122826X) Finite Mathematics and Calculus with Applications - Margaret Lial (8th ed) (ISBN 0321426517) Finite Mathematics for Business, Economics, Life Sciences & Social Sciences - Raymond Barnett (11th ed) (ISBN 0132255707) Finite Mathematics with Applications - Margaret L. Lial (9th ed) (ISBN 0321386728) First Course in Abstract Algebra - John Fraleigh (7th ed) (ISBN 0201763907) First Course in Abstract Algebra - Joseph Rotman (3rd ed) (ISBN 0131862677) First Course In Probability - Sheldon M. Ross (7th ed) (ISBN 0131856626) First Course in Statistics, A - James T. McClave (10th ed) (ISBN 0136152597) Fluency with Information Technology: Skills, Concepts, and Capabilities - Lawrence Snyder (3rd ed) (ISBN 0321512391) Foundations of Economics - Robin Bade (4th ed) (ISBN 0321522362) Foundations of Finance - Arthur Keown, William Petty, John Martin, David Scott (5th ed) (ISBN 0131856057) Foundations of Finance: Logic and Practice of Financial Mangement - Arthur J. Keown (6th ed) (ISBN 0135048168) Foundations of Finance: The Logic and Practice of Financial Management - Arthur Keown (6th ed) (ISBN 0132339226) Foundations of Geometry - Gerard Venema (5th ed) (ISBN 0131437003) Foundations of Macroeconomics - Robin Bade (4th ed) (ISBN 0321522370) Foundations of MEMS - Chang Liu (1st ed) (ISBN 0131472860) Foundations of Microeconomics - Robin Bade (3rd ed) (ISBN 0321415957) Foundations of Microeconomics - Robin Bade (4th ed) (ISBN 0321522389) Framework for Human Resource Management, A - Gary Dessler (5th ed) (ISBN 0136041531) Framework for Marketing Management, A - Philip Kotler (4th ed) (ISBN 0136026605) Fraud Examination - Steve Albrecht (2nd ed) (ISBN 0324651155) Friendly Introduction to Analysis - Witold A.J. Kosmala (2nd ed) (ISBN 0130457965) Fundamental Cornerstones of Managerial Accounting - Dan L. Heitger, Maryanne M. Mowen (1st ed) (ISBN 0324378068) Fundamental Mathematics through Applications - Geoffrey Akst (4th ed) (ISBN 0321496906) Fundamentals of Advanced Accounting - Paul M. Fischer (Test Bank) (1st ed) (ISBN 0324378904) Fundamentals of Applied Electromagnetics - Fawwaz T. Ulaby (5th ed) (ISBN 0132413264) Fundamentals of Business Law Summarized Cases - Roger LeRoy Miller (7th ed) (ISBN 0324381689) Fundamentals of Communication Systems - John G. Proakis (1st ed) (ISBN 013147135X) Fundamentals of Complex Analysis - Edward Saff (3rd ed) (ISBN 0139078746) Fundamentals of Derivatives Markets - Robert L. McDonald (1st ed) (ISBN 0321357175) Fundamentals of Differential Equations - Kent Nagle, Edward Saff (6th ed) (ISBN 0321145720) Fundamentals of Differential Equations - R. Kent Nagle (7th ed) (ISBN 0321410483) Fundamentals of Differential Equations with Boundary Value Problems - R. Kent Nagle (5th ed) (ISBN 0321419219) Fundamentals of Electromagnetics for Electrical and Computer Engineering - Nannapaneni Narayana Rao (1st ed) (ISBN 0136013333) Fundamentals of Engineering Economics - Chan S. Park (2nd ed) (ISBN 0132209608) Fundamentals of Financial Management - Eugene Brigham (11th ed) (ISBN 0324319800) Fundamentals of Investing - Lawrence J. Gitman (10th ed) (ISBN 0321489381) Fundamentals of Management: Essential Concepts and Applications - Stephen P. Robbins (Test Bank) (5th ed) (ISBN 0131487361) Fundamentals of Multinational Finance - Michael Moffett (3rd ed) (ISBN 0321541642) Fundamentals of Organic Chemistry - John McMurry (Test Bank only) (5th ed) (ISBN 0534395732) Fundamentals of Probability, with Stochastic Processes - Saeed Ghahramani (3rd ed) (ISBN 0131453408) Fundamentals of Signals and Systems - Edward Kamen (3rd ed) (ISBN 0131687379) Fundamentals of Statistics - Michael Sullivan (2nd ed) (ISBN 0131569872) Further Mathematics for Economic Analysis - Knut Sydsaeter et al (1st ed) (ISBN 0273655760) Geometry: Theorems and Constructions - Allan Berele (1st ed) (ISBN 0130871214) Global Investments - Bruno Solnik (6th ed) (ISBN 0321527704) Governmental and Nonprofit Accounting: Theory and Practice - Robert J. Freeman (9th ed) (ISBN 0136029515) High-Speed Networks and Internets: Performance and Quality of Service - William Stallings (2nd ed) (ISBN 0130322210) Human Anatomy & Physiology - Elaine N. Marieb (7th ed) (ISBN 0805359095) Human Anatomy and Physiology Lab Manual - Elaine N. Marieb (9th ed) (ISBN 0805372652) Human Relations for Career and Personal Success: Concepts, Applications, and Skills - Andrew J. DuBrin (8th ed) (ISBN 0131791796) Human Relations: Interpersonal Job-Oriented Skills - Andrew J. DuBrin (10th ed) (ISBN 0135019443) Human Resource Management - Gary Dessler (11th ed) (ISBN 0131746170) Human Resource Management - Wayne Mondy (10th ed) (ISBN 0132225956) Human Side of Organizations - Michael Drafke (10th ed) (ISBN 0135139740) Hydrology and Floodplain Analysis - Philip B. Bedient (4th ed) (ISBN 0131745891) Income Tax Fundamentals 2006 - Gerald E. Whittenburg (24th ed) (ISBN 0324399022) Income Tax Fundamentals 2007 - Gerald E. Whittenburg (25th ed) (ISBN 032439926X) Information Systems Today: Managing in the Digital World - Leonard Jessup (3rd ed) (ISBN 0132335069) Information Technology Auditing and Assurance - James Hall (2nd ed) (ISBN 0324191987) Inquiry into Physics - Vern J. Ostdiek (6th ed) (ISBN 0495119431) Integrated Arithmetic and Basic Algebra - Bill E. Jordan (4th ed) (ISBN 0321442555) Intel Micro 8086 - Barry B. Brey (8th ed) (ISBN 0135026458) Intel Microprocessors - Barry B. Brey (7th ed) (ISBN 0131195069) Intel Microprocessors - Barry B. Brey (8th ed) (ISBN 0135026458) Interactive Computer Graphics: A Top-Down Approach Using OpenGL - Edward Angel (5th ed) (ISBN 0321535863) Interactive Statistics - Martha Aliaga, Brenda Gunderson (3rd ed) (ISBN 0131497561) Intermediate Accounting - James D. Stice (16th ed) (ISBN 0324312148) Intermediate Accounting - Loren A. Nikolai (10th ed) (ISBN 0324651929) Intermediate Accounting (Revised) - David Spiceland (4th ed) (ISBN 0073215422) Intermediate Algebra - Elayn El Martin-Gay (5th ed) (ISBN 0136007295) Intermediate Algebra - Margaret L. Lial (10th ed) (ISBN 0321443624) Intermediate Algebra - Marvin L. Bittinger (10th ed) (ISBN 0321319087) Intermediate Algebra for College Students - Allen R. Angel (7th ed) (ISBN 0132383578) Intermediate Algebra for College Students - Robert F. Blitzer (5th ed) (ISBN 0136007627) Intermediate Algebra with Applications & Visualization - Gary K. Rockswold (3rd ed) (ISBN 0321500032) Intermediate Algebra: Functions & Authentic Applications - Jay Lehmann (3rd ed) (ISBN 0131953338) Intermediate Algebra: Graphs & Models - Marvin L. Bittinger (3rd ed) (ISBN 0321416163) International Accounting - Frederick Choi (5th ed) (ISBN 0131480979) International Accounting - Frederick D. Choi (6th ed) (ISBN 0131588141) International Business - John Daniels (12th ed) (ISBN 0136029655) International Business Law - Ray A. August (5th ed) (ISBN 013600864X) International Business: Environments and Operations - John Daniels (11th ed) (ISBN 0131869426) International Business: Strategy, Management, and the New Realities - Tamer Cavusgil (1st ed) (ISBN 0131738607) International Business: The Challenges of Globalization - John J. Wild (4th ed) (ISBN 0131747436) International Economics - Charles Sawyer, Richard Sprinkle (2nd ed) (ISBN 0131704168) International Economics - James Gerber (3rd ed) (ISBN 032123796X) International Economics - James Gerber (4th ed) (ISBN 0321415558) International Economics - Robert Carbaugh (11th ed) (ISBN 032442194X) International Economics - W. Charles Sawyer (3rd ed) (ISBN 0136054692) International Economics: Theory And Policy - Paul Krugman, Maurice Obstfeld (7th ed) (ISBN 0321293835) International Economics: Theory and Policy - Paul R. Krugman (8th ed) (ISBN 0321488830) International Financial Management - Geert Bekaert (1st ed) (ISBN 0131163604) International Financial Management - Jeff Madura (9th ed) (ISBN 0324568193) International Financial Management, Abridged Edition - Jeff Madura (8th ed) (ISBN 0324365632) === Subject: Re: Comprehensive Solution Manual for Textbooks posting-account=rLOz6QoAAAAmvEIbrGZd27QhtZqovu5R rv:1.9.0.5) Gecko/2008120121 Firefox/3.0.5,gzip(gfe),gzip(gfe) continued...Updated list per December 30, 2008 I have the comprehensive SOLUTIONS MANUAL for ALL of the following textbooks and TEST BANKS for MOST of them in electronic format (PDF/ Word). The solutions manual are comprehensive with answers to both even & odd problems in the text. The price for the solution manual is US$35 for each. The price for the test bank is also $35. The methods of payment is through PAYPAL (It is easy, safe, and you can use debit or credit card to pay even if you don't have an account). Email me at sbooks4sale[at]hotmail[dot]com if you are interested. If you could not find the book you are looking for, please let me know, I -------------------------- Managerial Economics - Mark Hirschey (12th ed) (ISBN 0324584849) Managerial Economics: A Problem Solving Approach - Luke M. Froeb (1st ed) (ISBN 0324359810) Managerial Economics: Applications, Strategies, and Tactics - James R. McGuigan (11th ed) (ISBN 0324421605) Managerial Economics: Economic Tools for Today's Decision Makers - Paul G. Keat (5th ed) (ISBN 0131860151) Managerial Statistics A Case-Based Approach - Peter Klibanoff (1st ed) (ISBN 0324226454) Managing Human Resources - Luis Gomez-Mejia (5th ed) (ISBN 013187067X) Managing in a Global Economy: Demystifying International Macroeconomics - John E. Marthinsen (1st ed) (ISBN 0324395507) Managing Information Technology - Carol V Brown (6th ed) (ISBN 0131789546) Managing the Law: The Legal Aspects of Doing Business - Mitchell McInnes (2nd ed) (ISBN 0132042762) Manual Auditing and Assurance Practice Set: CAST - Frank A. Buckless (1st ed) (ISBN 0130464716) Manufacturing Processes for Engineering Materials - Serope Kalpakjian (5th ed) (ISBN 0132272717) Manufacturing, Engineering & Technology - Serope Kalpakjian (5th ed) (ISBN 0131489658) Market Regulation - Roger Sherman (1st ed) (ISBN 0321322320) Market-Based Management - Roger Best (5th ed) (ISBN 0132336537) Marketing Management - Philip Kotler (13th ed) (ISBN 0136009980) Materials Science and Engineering: An Introduction - William Callister (6th ed) (ISBN 0471135763) Mathematical Economics - Jeffrey Baldani (2nd ed) (ISBN 0324183321) Mathematical Ideas - Charles D. Miller (11th ed) (ISBN 0321361466) Mathematical Ideas - Charles D. Miller (11th ed) (ISBN 0321361482) Mathematical Methods for Economics - Michael Klein (2nd ed) (ISBN 0201726262) Mathematical Proofs: A Transition to Advanced Mathematics - Gary Chartrand (2nd ed) (ISBN 0321390539) Mathematical Proofs: A Transition to Advanced Mathematics - Gary Chartrand (1st ed) (ISBN 0201710900) Mathematical Reasoning for Elementary Teachers - Calvin T. Long (5th ed) (ISBN 0321460847) Mathematics for Business - Stanley A. Salzman (8th ed) (ISBN 0321357434) Mathematics for Elementary School Teachers - Phares O'Daffer (4th ed) (ISBN 0321448049) Mathematics for Physicists - Susan Lea (1st ed) (ISBN 0534379974) Mathematics of Interest Rates and Finance - Gary Guthrie (1st ed) (ISBN 0130461822) Mechanical Behavior of Materials - Norman Dowling (3rd ed) (ISBN 0131863126) Mechanics of Materials - Russell C. Hibbeler (7th ed) (ISBN 0132209918) Medical Imaging Signals and Systems - Jerry L. Prince (1st ed) (ISBN 0130653535) Microbiology with Diseases by Body System - Robert W. Bauman (2nd ed) (ISBN 032151341X) Microbiology: An Introduction - Gerard J. Tortora (9th ed) (ISBN 0805347909) Microeconomics - Glenn Hubbard (2nd ed) (ISBN 0138132771) Microeconomics - Jeffrey Perloff (4th ed) (ISBN 0321414527) Microeconomics - Jeffrey Perloff (5th ed) (ISBN 0321531191) Microeconomics - Michael Parkin (7th ed) (ISBN 0321454944) Microeconomics - Michael Parkin (8th ed) (ISBN 0321416600) Microeconomics - Richard G. Lipsey (13th ed) (ISBN 032136922X) Microeconomics - Robert Pindyck, Daniel Rubinfeld (6th ed) (ISBN 0130084611) Microeconomics - Robert Pindyck, Daniel Rubinfeld (7th ed) (ISBN 0132080230) Microeconomics: Principles and Tools - Arthur O'Sullivan, Steven Sheffrin (4th ed) (ISBN 0131536060) Microeconomics: Principles, Applications, and Tools - Arthur O'Sullivan (5th ed) (ISBN 0131572830) Microeconomics: Theory and Applications with Calculus - Jeffrey M. Perloff (1st ed) (ISBN 0321277945) Microwave Engineering - David Pozar (3rd ed) (ISBN 0471448788) Modern Control Systems - Richard C Dorf (11th ed) (ISBN 0132270285) Modern Database Management - Jeffrey Hoffer (8th ed) (ISBN 0132212110) Modern Database Management - Jeffrey Hoffer (9th ed) (ISBN 0136003915) Modern Electronic Communication - Jeff Beasley (9th ed) (ISBN 0132251132) Modern Elementary Statistics - John E. Freund (12th ed) (ISBN 013187439X) Modern Industrial Organization - Dennis Carlton, Jeffrey Perloff (4th ed) (ISBN 0321180232) Modern Labor Economics: Theory and Public Policy - Ronald Ehrenberg (10th ed) (ISBN 0321533739) Modern Labor Economics: Theory and Public Policy - Ronald Ehrenberg (9th ed) (ISBN 0321305035) Modern Management - Samuel C. Certo (10th ed) (ISBN 0131494708) Modern Physics - Randy Harris (2nd ed) (ISBN 0805303081) Modern Physics - Raymond Serway (3rd ed) (ISBN 0534493394) Modern Wireless Communications - Simon Haykin (1st ed) (ISBN 0130224723) Money, Banking and Financial Markets - Roger LeRoy Miller (3rd ed) Money, the Financial System, and the Economy - R. Glenn Hubbard (6th ed) (ISBN 0321426703) Multinational Business Finance - David K. Eiteman (11th ed) (ISBN 0321357965) Multinational Finance - Kirt C. Butler (3rd ed) (ISBN 0324177453) Multinational Management - John B. Cullen (4th ed) (ISBN 032442177X) Nanoengineering of Structural, Functional and Smart Materials - Mark J. Schulz (1st ed) (ISBN 0849316537) New Venture Management: The Entrepreneur's Roadmap - Donald Kuratko (1st ed) (ISBN 0136130321) Numerical Analysis - Timothy Sauer (1st ed) (ISBN 0321268989) Numerical Methods for Engineers - Bilal Ayyub, Richard McCuen (1st ed) (ISBN 0133373614) Numerical Methods Using Matlab - John Mathews (4th ed) (ISBN 0130652482) Occupational Safety and Health for Technologists, Engineers, and Managers - David L. Goetsch (6th ed) (ISBN 0132397609) Office Procedures 21st Century & Student Workbook Package - Sharon Burton (7th ed) (ISBN 0132343436) Operating Systems Principles - Lubomir F. Bic (1st ed) (ISBN 0130266116) Operating Systems: Internals and Design Principles - William Stallings (5th ed) (ISBN 0131479547) Operations Management - Jay Heizer (8th ed) (ISBN 0131554441) Operations Management - Jay Heizer (9th ed) (ISBN 0138128782) Operations Management - Nigel Slack (5th ed) (ISBN 0273708473) Operations Management and Student CD and Student DVD Package - Jay Heizer (9th ed) (ISBN 0138128782) Operations Management: Process and Value Chains - Lee J. Krajewski (8th ed) (ISBN 0131697390) Operations Research: An Introduction - Hamdy A. Taha (8th ed) (ISBN 0131889230) Opportunities and Challenges of Workplace Diversity: Theory, Cases, and Exercises - Kathryn Canas (1st ed) (ISBN 0131343068) Oracle 10g Programming: A Primer - Rajshekhar Sunderraman (1st ed) (ISBN 0321463048) Organic Chemistry - Paula Bruice (Test Bank only) (5th ed) (ISBN 0131963163) Organizational Behavior - Stephen P Robbins (13th ed) (ISBN 0136007171) Organizational Behavior Today - Leigh Thompson (1st ed) (ISBN 0131858114) Organizational Behavior: An Experiential Approach - Joyce S Osland (8th ed) (ISBN 0131441515) Organizational Behavior: An Introduction to Your Life in Organizations - Rae Andre (1st ed) (ISBN 013185495X) Organizational Theory, Design and Change - Gareth R. Jones (5th ed) (ISBN 0131865420) Orthopaedic Biomechanics: Mechanics and Design in Musculoskeletal Systems - Donald L. Bartel (1st ed) (ISBN 0130089095) Parallel and Distributed Computation: Numerical Methods - Dimitri Bertsekas, John Tsitsiklis (1st ed) (ISBN 0136487009) Parallel Programming - Barry Wilkinson (2nd ed) (ISBN 0131405632) Partial Differential Equations and Boundary Value Problems - Nakhle Asmar (2nd ed) (ISBN 0131480960) Payroll Accounting 2008 - Bernard Bieg (18th ed) (ISBN 0324645546) Payroll Accounting 2009 - Bernard Bieg (19th ed) (ISBN 0324663730) Performance Management - Herman Aguinis (2nd ed) (ISBN 0136151752) Personal Finance - Jeff Madura (3rd ed) (ISBN 0321409965) Personal Financial Planning - Lawrence J. Gitman (11th ed) (ISBN 0324422865) Pharmacology for Nurses: A Pathophysiological Approach - Michael Patrick Adams (2nd ed) (ISBN 0131756656) Physical Chemistry - Thomas Engel, Philip Reid (1st ed) (ISBN 080533842X) Physical Chemistry for the Life Sciences - Thomas Engel (1st ed) (ISBN 0805382771) Physics : Principles with Applications - Douglas Giancoli (6th ed) (ISBN 0130606200) Physics for Scientists & Engineers (Chs 1-37) with MasteringPhysics» - Doug Giancoli (4th ed) (ISBN 0136139264) Physics for Scientists and Engineers with Modern Physics and MasteringPhysics» - Douglas C. Giancoli (4th ed) (ISBN 0136139221) Physics with Mastering Physics - James S. Walker (3rd ed) (ISBN 0136138969) Physics: Principles with Applications with MasteringPhysics - Douglas C. Giancoli (6th ed) (ISBN 0321569830) Portfolio Construction, Management, and Protection - Robert A. Strong (4th ed) (ISBN 0324359365) Practical Financial Management - William R. Lasher (5th ed) (ISBN 0324422636) Prealgebra - Elayn El Martin-Gay (5th ed) (ISBN 0132319519) Prealgebra - Marvin L. Bittinger (5th ed) (ISBN 0321331907) === Subject: Re: Comprehensive Solution Manual for Textbooks posting-account=rLOz6QoAAAAmvEIbrGZd27QhtZqovu5R rv:1.9.0.5) Gecko/2008120121 Firefox/3.0.5,gzip(gfe),gzip(gfe) continued...Updated list per December 30, 2008 I have the comprehensive SOLUTIONS MANUAL for ALL of the following textbooks and TEST BANKS for MOST of them in electronic format (PDF/ Word). The solutions manual are comprehensive with answers to both even & odd problems in the text. The price for the solution manual is US$35 for each. The price for the test bank is also $35. The methods of payment is through PAYPAL (It is easy, safe, and you can use debit or credit card to pay even if you don't have an account). Email me at sbooks4sale[at]hotmail[dot]com if you are interested. If you could not find the book you are looking for, please let me know, I -------------------------- Statistics - James T. McClave (11th ed) (ISBN 0132069512) Statistics for Business & Economics - James T. McClave (10th ed) (ISBN 0132409356) Statistics for Business and Economics - David R. Anderson (Test Bank only) (10th ed) (ISBN 0324360681) Statistics for Business and Economics - Paul Newbold, William L. Carlson (6th ed) (ISBN 0132203847) Statistics for Management and Economics - Gerald Keller (7th ed) (ISBN 0534491243) Statistics for Managers Using Microsoft Excel - David M. Levine (5th ed) (ISBN 0136149901) Statistics for Science and Engineering - John Kinney (1st ed) (ISBN 0201437201) Statistics for the Behavioral and Social Sciences - Arthur Aron (4th ed) (ISBN 0131562789) Statistics for the Life Sciences - Myra Samuels (3rd ed) (ISBN 013041316X) (1st ed) (ISBN 0130083690) Statistics: The Art and Science of Learning from Data - Alan Agresti (2nd ed) (ISBN 0135131995) Stats: Data and Models - Richard D. De Veaux (2nd ed) (ISBN 0321433793) Steel Design - William T. Segui (4th ed) (ISBN 0495244716) Strategic Brand Management - Kevin Keller (3rd ed) (ISBN 0131888595) Strategic Compensation - Joe Martocchio (5th ed) (ISBN 0136007449) Strategic Management and Business Policy - Tom Wheelen (10th ed) (ISBN 0131494597) Strategic Management and Business Policy - Tom Wheelen (11th ed) (ISBN 013232346X) Strategic Management and Competitive Advantage - Jay Barney (2nd ed) (ISBN 013613520X) Strategic Management and Competitive Advantage: Concepts and Cases - Jay Barney (2nd ed) (ISBN 0132338238) Strategic Management in Action - Mary Coulter (4th ed) (ISBN 0132277476) Strategic Managment: A Dynamic Perspective Integrated Stratsim Simulation Experience - Print Upgrade - Mason Carpenter (1st ed) (ISBN 0136149057) Strategic Management: Concepts and Cases - Fred David (11th ed) (ISBN 0131869493) Strategic Management: Concepts and Cases - Fred David (12th ed) (ISBN 0136015700) Strategic Marketing for Non-Profit Organizations - Alan Andreasen (7th ed) (ISBN 013175372X) Strategic Staffing - Jean M. Phillips (1st ed) (ISBN 0131586947) Structural Analysis - Russell C. Hibbeler (7th ed) (ISBN 0136020607) Structural Steel Design - Jack C. McCormac (4th ed) (ISBN 013221816X) Structural Steel Design: A Practice Oriented Approach - Abi O. Aghayere (1st ed) (ISBN 0132340186) Structure and Interpretation of Signals and Systems - Edward Lee, Pravin Varaiya (1st ed) (ISBN 0201745518) Structures - Daniel Lewis Schodek (6th ed) (ISBN 0131789392) Supply Chain Management - Sunil Chopra (3rd ed) (ISBN 0131730428) Survey of Accounting - Carl S. Warren (3rd ed) (ISBN 0324312482) Survey of Accounting - Carl S. Warren (4th ed) (ISBN 0324658265) Survey of Economics - Irvin B. Tucker (6th ed) (ISBN 0324579616) Survey of Mathematics with Applications, A - Allen R. Angel (8th ed) (ISBN 0321501071) Survey of Mathematics with Applications - Allen Angel (8th ed) (ISBN 032150108X) Surveying with Construction Applications - Barry F. Kavanagh (6th ed) (ISBN 0131709321) Surveying: Principles and Applications - Barry F. Kavanagh (8th ed) (ISBN 013236512X) System Dynamics and Response - S. Graham Kelly (1st ed) (ISBN 0534549306) System Modeling and Analysis: Foundations of System Performance Evaluation - Hisashi Kobayashi (1st ed) (ISBN 013034835X) Systems Analysis and Design - Kenneth E. Kendall (7th ed) (ISBN 0132240858) Tax Research - Barbara H Karlin (4th ed) (ISBN 013601531X) Taxation for Decision Makers 2008 - Shirley Dennis-Escoffier (2nd ed) (ISBN 0324654111) Taxes & Business Strategy - Myron S. Scholes (4th ed) (ISBN 0136033156) Technical Calculus with Analytic Geometry - Allyn J. Washington (4th ed) (ISBN 0201711125) Technology Strategy for Managers and Entrepreneurs - Scott A. Shane (1st ed) (ISBN 0131879324) The Economics of Macro Issues - Roger LeRoy Miller (3rd ed) (ISBN 0321416597) The Economics of Poverty - Bradley R Schiller (10th ed) (ISBN 0131889699) The Economics of Public Issues - Roger LeRoy Miller (15th ed) (ISBN 0321416104) The Economics of Sports - Michael A. Leeds (3rd ed) (ISBN 0321415566) The Paralegal Professional - Henry Cheeseman (2nd ed) (ISBN 0131751905) The Strategy of Managing Innovation and Technology - Murray Millson (1st ed) (ISBN 0132303833) Theory of Asset Pricing - George Pennacchi (1st ed) (ISBN 032112720X) Thermodynamics: An Engineering Approach - Yunus Cengel (5th ed) (ISBN 0073107689) Thinking Mathematically - Robert F. Blitzer (4th ed) (ISBN 0131752049) Thomas' Calculus - George B. Thomas, Jr. (11th ed) (ISBN 0321185587) Thomas' Calculus, Early Transcendentals, Media Upgrade - George B. Thomas, Jr (11th ed) (ISBN 0321495756) Thomas' Calculus, Early Transcendentals, Media Upgrade, Part One - George B. Thomas, Jr. (11th ed) (ISBN 0321498747) Thomas' Calculus, Media Upgrade - George B. Thomas, Jr. (11th ed) (ISBN 032148987X) Thomas' Calculus, Media Upgrade, Part One (Single Variable) - George B. Thomas, Jr. (11th ed) (ISBN 0321498755) Thomas' Calculus, Media Upgrade, Part Two (Multivariable, Chap 11-16) - George B. Thomas, Jr. (11th ed) (ISBN 0321501039) Training in Interpersonal Skills - Stephen P. Robbins (5th ed) (ISBN 0132354993) Trigonometry - Margaret L. Lial (9th ed) (ISBN 0321528859) Trigonometry - Mark Dugopolski (2nd ed) (ISBN 032135690X) Trigonometry: A Right Triangle Approach - Michael Sullivan (5th ed) (ISBN 0136028969) Trigonometry: A Unit Circle Approach - Michael Sullivan (8th ed) (ISBN 0132392798) UFL Collective Bargaining Agreement - Louis Marino (1st ed) (ISBN 0131587668) Understanding and Managing Diversity - Carol Harvey (4th ed) (ISBN 0132069105) Understanding and Managing Organizational Behavior - Jennifer George (5th ed) (ISBN 013239457X) Understanding Fiber Optics - Jeff Hecht (5th ed) (ISBN 0131174290) Understanding Financial Statements - Lyn M. Fraser (8th ed) (ISBN 0131878565) Understanding Modern Economics - Roger Miller (1st ed) (ISBN 0321245822) University Calculus: Alternate Edition - Joel Hass (1st ed) (ISBN 0321471962) University Calculus: Alternate Edition, Part One (Single Variable, Chap 1-9) - Joel Hass (1st ed) (ISBN 0321475194) University Calculus: Elements with Early Transcendentals - Joel Hass (1st ed) (ISBN 0321533488) University Physics with Modern Physics with MasteringPhysics» - Hugh D. Young (12th ed) (ISBN 080532187X) Using and Understanding Mathematics: A Quantitative Reasoning Approach - Jeffrey O. Bennett (4th ed) (ISBN 0321458206) Using Financial Accounting Information: The Alternative to Debits & Credits - Gary A. Porter (5th ed) (ISBN 0324645104) Using Peachtree Complete 2007 for Accounting - Glenn Owen (1st ed) (ISBN 0324377975) Using Quickbooks Pro 2007 for Accounting - Glenn Owen (7th ed) (ISBN 0324378750) Vector Calculus - Susan Colley (3rd ed) (ISBN 0131858742) VHDL: A Starter's Guide - Sudhakar Yalamanchili (2nd ed) (ISBN 0131457357) Water and Wastewater Technology - Mark J. Hammer (6th ed) (ISBN 0131745425) Water Resources Engineering - David A. Chin (2nd ed) (ISBN 0131481924) Water Supply and Pollution Control - Warren Viessman, Jr. (8th ed) (ISBN 0132337177) Web 101 - Wendy G. Lehnert (3rd ed) (ISBN 0321424670) West Federal Taxation Comprehensive 2007 - William Hoffman (Solutions Manual) (30th ed) (ISBN 0324313497) West Federal Taxation Comprehensive 2007 - William Hoffman (Test Bank) (30th ed) (ISBN 0324313497) West Federal Taxation Corporations 2007 - William Hoffman (Solutions Manual) (30th ed) (ISBN 0324313616) West Federal Taxation Corporations 2007 - William Hoffman (Test Bank) (30th ed) (ISBN 0324313616) West Federal Taxation Corporations 2008 - William Hoffman (Solutions Manual) (31st ed) (ISBN 0324380437) West Federal Taxation Corporations 2008 - William Hoffman (Test Bank) (31st ed) (ISBN 0324380437) West Federal Taxation Individual 2007 - William Hoffman (Solutions Manual) (30th ed) (ISBN 0324399618) West Federal Taxation Individual 2007 - William Hoffman (Test Bank) (30th ed) (ISBN 0324399618) West Federal Taxation Individual 2008 - William Hoffman (Solutions Manual) (31st ed) (ISBN 0324380585) West Federal Taxation Individual 2008 - William Hoffman (Test Bank) (31st ed) (ISBN 0324380585) West Federal Taxation: Taxation of Business Entities 2007 - James Smith (Solutions Manual) (10th ed) (ISBN 0324313950) West Federal Taxation: Taxation of Business Entities 2007 - James Smith (Test Bank) (10th ed) (ISBN 0324313950) West Federal Taxation: Taxation of Business Entities 2008 - James Smith (Solutions Manual) (11th ed) (ISBN 0324366655) West Federal Taxation: Taxation of Business Entities 2008 - James Smith (Test Bank) (11th ed) (ISBN 0324366655) West's Business Law - Kenneth W. Clarkson (10th ed) (ISBN 0324303904) Wireless Communications & Networks - William Stallings (2nd ed) (ISBN 0131918354) Writing and Speaking at Work: A Practical Guide for Business Communication - Edward P. Bailey (4th ed) (ISBN 0131881302) Your Attitude is Showing - Sharon Lund O'Neil (12th ed) (ISBN 0132429047) === Subject: Re: Comprehensive Solution Manual for Textbooks posting-account=rLOz6QoAAAAmvEIbrGZd27QhtZqovu5R rv:1.9.0.5) Gecko/2008120121 Firefox/3.0.5,gzip(gfe),gzip(gfe) continued...Updated list per December 30, 2008 I have the comprehensive SOLUTIONS MANUAL for ALL of the following textbooks and TEST BANKS for MOST of them in electronic format (PDF/ Word). The solutions manual are comprehensive with answers to both even & odd problems in the text. The price for the solution manual is US$35 for each. The price for the test bank is also $35. The methods of payment is through PAYPAL (It is easy, safe, and you can use debit or credit card to pay even if you don't have an account). Email me at sbooks4sale[at]hotmail[dot]com if you are interested. If you could not find the book you are looking for, please let me know, I -------------------------- Prealgebra & Introductory Algebra - Elayn El Martin-Gay (2nd ed) (ISBN 0131577050) Prealgebra and Introductory Algebra - Marvin L. Bittinger (2nd ed) (ISBN 0321331893) Prealgebra: An Integrated Approach - Margaret L. Lial (1st ed) (ISBN 032135639X) Precalculus - J. S. Ratti (1st ed) (ISBN 032129646X) Precalculus - Judith A. Beecher (3rd ed) (ISBN 0321460065) Precalculus - Margaret Lial (4th ed) (ISBN 0321528840) Precalculus - Mark Dugopolski (4th ed) (ISBN 0321357795) Precalculus - Michael Sullivan (8th ed) (ISBN 0132256886) Precalculus - Michael Sullivan (8th ed) (ISBN 0132256886) Precalculus: Enhanced with Graphing Utilities - Michael Sullivan (5th ed) (ISBN 0136015786) Precalculus: Functions and Graphs - Mark Dugopolski (3rd ed) (ISBN 032150111X) Precalculus: Graphs & Models and Graphing Calculator Manual Package - Marvin L. Bittinger (4th ed) (ISBN 0321501527) Prehospital Emergency Care - Joseph J. Mistovich (8th ed) (ISBN 0131741438) Prentice Hall's Federal Taxation 2007: Comprehensive - Thomas Pope (20th ed) (ISBN 0132389479) Prentice Hall's Federal Taxation 2007: Corporations - Thomas Pope (20th ed) (ISBN 0131751484) Prentice Hall's Federal Taxation 2007: Individuals - Thomas Pope (20th ed) (ISBN 013243220X) Prentice Hall's Federal Taxation 2008: Comprehensive - Thomas Pope (21st ed) (ISBN 0132416492) Prentice Hall's Federal Taxation 2008: Corporations - Thomas Pope (21st ed) (ISBN 0136156436) Prentice Hall's Federal Taxation 2008: Individuals - Thomas Pope (21st ed) (ISBN 0136156371) Prentice Hall's Federal Taxation 2008: Comprehensive - Thomas Pope (21st ed) (ISBN 0136067190) Prentice Hall's Federal Taxation 2009: Corporations - Thomas Pope (22nd ed) (ISBN 0136067131) Prentice Hall's Federal Taxation 2009: Individuals - Thomas Pope (22nd ed) (ISBN 0136067042) Preparing Effective Business Plans: An Entrepreneurial Approach - Bruce R. Barringer (1st ed) (ISBN 0132318326) Price Theory and Applications - Steven Landsburg (7th ed) (ISBN 0324421613) Principles of Accounting - Meg Pollard (1st ed) (ISBN 0132304791) Principles of Auditing: An Introduction to International Standards on Auditing - Rick Hayes (2nd ed) (ISBN 0273684108) Principles of CMOS VLSI Design - Neil H.E. Weste (3rd ed) (ISBN 0201533766) Principles of Cost Accounting - Edward J. Vanderbeck (13th ed) (ISBN 0324191693) Principles of Cost Accounting - Edward J. Vanderbeck (14th ed) (ISBN 0324374178) Principles of Customer Relationship Management - Roger Baran (1st ed) (ISBN 0324322380) Principles of Economics - Gregory Mankiw (4th ed) (ISBN 0324224729) Principles of Economics - Karl Case (8th ed) (ISBN 0132289148) Principles of Electric Circuits: Conventional Current Version - Thomas Floyd (8th ed) (ISBN 0131701797) Principles of Finance - Scott Besley (3rd ed) (ISBN 0324232624) Principles of Foundation Engineering - Braja M. Das (6th ed) (ISBN 0495082465) Principles of Geotechnical Engineering (6th ed) (ISBN 0534551440) Principles of Heat Transfer - Frank Kreith (6th ed) (ISBN 0534375960) Principles of Law and Economics - Daniel Cole, Peter Grossman (1st ed) (ISBN 0130932612) Principles of Macroeconomics - Gregory Mankiw (4th ed) (ISBN 0324236956) Principles of Managerial Finance - Lawrence J. Gitman (12th ed) (ISBN 0321557530) Principles of Managerial Finance Brief Edition - Lawrence Gitman (5th ed) (ISBN 0321557522) Principles of Managerial Finance plus MyfinanceLab Student Access Kit - Lawrence J. Gitman (12th ed) (ISBN 0321557530) Principles of Marketing - Philip Kotler (12th ed) (ISBN 0132390027) Principles of Microeconomics - Gregory Mankiw (4th ed) (ISBN 0324319169) Principles of Microeconomics - Karl E. Case (8th ed) (ISBN 0131994859) Principles of Money, Banking & Financial Markets - Lawrence Ritter (12th ed) (ISBN 0321375572) Principles of Money, Banking, Financial Markets - Lawrence Ritter et al (11th ed) (ISBN 0321205251) Principles Of Operations Management - Jay Heizer (6th ed) (ISBN 013155445X) Principles Of Operations Management - Jay Heizer (7th ed) (ISBN 0132449757) Principles of Risk Management and Insurance - George E. Rejda (10th ed) (ISBN 0321414934) Probabilistic Systems and Random Signals - Abraham Haddad (1st ed) (ISBN 0130094552) Probability & Statistics for Engineers & Scientists - Ronald E. Walpole (8th ed) (ISBN 0131877119) Probability and Statistical Inference - Robert Hogg, Eliot Tanis (7th ed) (ISBN 0131464132) Probability and Statistics - Morris DeGroot, Mark Schervish (3rd ed) (ISBN 0201524880) Probability and Statistics for Engineers - Richard Johnson, Irwin Miller, John Freund (7th ed) (ISBN 0131437453) Probability and Statistics for Engineers and Scientists - Anthony J. Hayter (3rd ed) (ISBN 0495107573) Probability Random Variables, and Stochastic Processes - Papoulis et al (4th ed) (ISBN 0073660116) Probability, Statistics, and Random Processes For Electrical Engineering - Alberto Leon-Garcia (3rd ed) (ISBN 0131471228) Problem Solving and Program Design in C - Jeri R. Hanly (5th ed) (ISBN 0321409914) Problem Solving with C++ - Walter Savitch (6th ed) (ISBN 0321412699) Problem Solving with C++ - Walter Savitch (7th ed) (ISBN 0321531345) Problem Solving, Abstraction & Design Using C++ - Frank L. Friedman (5th ed) (ISBN 0321450051) Process Control Instrumentation Technology - Curtis Johnson (8th ed) (ISBN 0131194577) Professional Office Procedures - Susan Cooperman (5th ed) (ISBN 0135156645) Professional Selling: A Trust-Based Approach - Thomas N. Ingram (4th ed) (ISBN 032453809X) Professionalism: Real Skills for Workplace Success - Lydia E. Anderson (1st ed) (ISBN 0131714392) Programming the World Wide Web - Robert W. Sebesta (4th ed) (ISBN 0321489691) Public Relations Practices: Managerial Case Studies and Problems - Allen H. Center (7th ed) (ISBN 0132341360) Quality Control - Dale H. Besterfield (8th ed) (ISBN 0135000955) Quality Management - Donna C.S. Summers (2nd ed) (ISBN 0135005108) Quantitative Analysis for Management - Barry Render (10th ed) (ISBN 0136036252) Quantitative Analysis for Management - Barry Render (9th ed) (ISBN 0131857029) Quantum Chemistry and Spectroscopy - Thomas Engel (1st ed) (ISBN 0805339795) QuickBooks Pro 2006 with Update 2007 and CD Package - Janet Horne (9th ed) (ISBN 013242407X) Real Estate Law - George Siedel (6th ed) (ISBN 0324204809) Real Estate Law - Marianne M. Jennings (8th ed) (ISBN 0324650205) Reinforced Concrete: Mechanics and Design - James K. Wight (5th ed) (ISBN 0132281414) Retailing - Patrick M. Dunne (6th ed) (ISBN 032436279X) Rethinking Marketing: The Entrepreneurial Imperative - Minet Schindehutte (1st ed) (ISBN 0132393891) Risk Management and Insurance - James S. Trieschmann (12th ed) (ISBN 0324183208) Risk Takers: Uses and Abuses of Financial Derivatives - John Marthinsen (2nd ed) (ISBN 0321542568) Routers and Routing Basics CCNA 2 Labs and Study Guide - Allan Johnson (1st ed) (ISBN 1587131676) Short-Term Financial Management - Terry Maness (3rd ed) (ISBN 0324202938) Short-Term Financial Management - Terry Maness (Test Bank) (3rd ed) (ISBN 0324202938) Signals, Systems, and Transforms - Charles L Phillips (4th ed) (ISBN 0131989235) Social Entrepreneurship: A Modern Approach to Social Value Creation - Arthur C. Brooks (1st ed) (ISBN 0132330768) Software Engineering - Ian Sommerville (8th ed) (ISBN 0321313798) Soils and Foundations - Cheng Liu, Jack Evett (7th ed) (ISBN 0132221381) Solid State Electronic Devices - Ben Streetman (6th ed) (ISBN 013149726X) Solid State Physics: Essential Concepts - David W. Snoke (1st ed) (ISBN 0805386645) South-Western Federal Taxation 2009: Comprehensive - William Hoffman (Solutions Manual) (32nd ed) (ISBN 0324660529) South-Western Federal Taxation 2009: Comprehensive - William Hoffman (Test Bank) (32nd ed) (ISBN 0324660529) South-Western Federal Taxation 2009: Corporations - William Hoffman (Solutions Manual) (32nd ed) (ISBN 0324660219) South-Western Federal Taxation 2009: Corporations - William Hoffman (Test Bank) (32nd ed) (ISBN 0324660219) South-Western Federal Taxation 2009: Individual Income Taxes - William Hoffman (Solutions Manual) (32nd ed) (ISBN 0324660200) South-Western Federal Taxation 2009: Individual Income Taxes - William Hoffman (Test Bank) (32nd ed) (ISBN 0324660200) South-Western Federal Taxation 2009: Taxation of Business Entities - James Smith (Solutions Manual) (12th ed) (ISBN 0324660510) South-Western Federal Taxation 2009: Taxation of Business Entities - James Smith (Test Bank) (12th ed) (ISBN 0324660510) Spectral Analysis of Signals - Peter Stoica, Randolph Moses (1st ed) (ISBN 0131139568) Starting Out with Java: Early Objects - Tony Gaddis (3rd ed) (ISBN 0321497686) Starting Out with Visual Basic 2008 - Tony Gaddis (4th ed) (ISBN 0321531353) Statics and Strengths of Materials - Harold I. Morrow (6th ed) (ISBN 0131719777) Statistical Methods for the Social Sciences - Alan Agresti (4th ed) (ISBN 0130272957) Statistical Reasoning for Everyday Life - Jeffrey O. Bennett (3rd ed) (ISBN 0321286723) === Subject: Re: Comprehensive Solution Manual for Textbooks posting-account=rLOz6QoAAAAmvEIbrGZd27QhtZqovu5R rv:1.9.0.5) Gecko/2008120121 Firefox/3.0.5,gzip(gfe),gzip(gfe) continued...Updated list per December 30, 2008 I have the comprehensive SOLUTIONS MANUAL for ALL of the following textbooks and TEST BANKS for MOST of them in electronic format (PDF/ Word). The solutions manual are comprehensive with answers to both even & odd problems in the text. The price for the solution manual is US$35 for each. The price for the test bank is also $35. The methods of payment is through PAYPAL (It is easy, safe, and you can use debit or credit card to pay even if you don't have an account). Email me at sbooks4sale[at]hotmail[dot]com if you are interested. If you could not find the book you are looking for, please let me know, I -------------------------- International Management: Managing Across Borders and Cultures - Helen Deresky (6th ed) (ISBN 0136143261) International Money and Finance - Michael Melvin (7th ed) (ISBN 0201770288) Intro Stats - Richard D. De Veaux (3rd ed) (ISBN 0321500458) Introduction to Abstract Algebra - Olympia Nicodemi (1st ed) (ISBN 0131019635) Introduction to Analysis - William R. Wade (3rd ed) (ISBN 0131453335) Introduction to Business Law - Jeffrey F. Beatty (2nd ed) (ISBN 0324311427) Introduction to Business Statistics - Ronald M. Weiers (6th ed) (ISBN 0324381433) Introduction to C++ EXCEL MATLAB & Basic Engineering Numerical Methods - Harvey G. Stenger (1st ed) (ISBN 0136142931) Introduction to Chemical Principles - Stephen Stoker (9th ed) (ISBN 0132379945) Introduction to Computing Systems - Sanjay J. Patel, Yale Patt (2nd ed) (ISBN 0072467509) Introduction to Corporate Finance - William L. Megginson (1st ed) (ISBN 0324379862) Introduction to Corporate Finance - William L. Megginson (2nd ed) (ISBN 0324657935) Introduction to Cryptography with Coding Theory - Wade Trappe (2nd ed) (ISBN 0131862391) Introduction to Derivatives and Risk Management - Don M. Chance (7th ed) (ISBN 0324321392) Introduction to Econometrics - James H. Stock (2nd ed) (ISBN 0321278879) Introduction to Econometrics Brief Edition - James H. Stock (1st ed) (ISBN 0321432517) Introduction to Economic Reasoning - William D. Rohlf (7th ed) (ISBN 0321416112) Introduction to Environmental Engineering and Science - Gilbert M. Masters (3rd ed) (ISBN 0131481932) Introduction to Financial Accounting - Charles Horngren (9th ed) (ISBN 0131479725) Introduction to Fourier Optics - Joseph Goodman (3rd ed) (ISBN 0974707724) Introduction to Government and Non-for-Profit Accounting - Martin Ives (6th ed) (ISBN 0132366355) Introduction to Graph Theory - Douglas West (2nd ed) (ISBN 0130144002) Introduction to Law - Joanne Hames (3rd ed) (ISBN 0131183818) Introduction to Linear Algebra - Lee Johnson, Dean Riess, Jimmy Arnold (5th ed) (ISBN 0201658593) Introduction to Linear Programming - Leonid Vaserstein (1st ed) (ISBN 0130359173) Introduction to Management Accounting - Charles T. Horngren (14th ed) (ISBN 0136129218) Introduction to Management Accounting, Chap. 1-17: International Edition - Charles Horngren (13th ed) (ISBN 0131273078) Introduction to Management Science and Student - Bernard Taylor (8th ed) (ISBN 0131050524) Introduction to Management Science and Student - Bernard Taylor (9th ed) (ISBN 0131888099) Introduction to Materials Management - Tony Arnold (6th ed) (ISBN 0132337614) Introduction to Mathematical Statistics and Its Applications - Richard J. Larsen (4th ed) (ISBN 0131867938) Introduction to Operations and Supply Chain Management - Cecil Bozarth (2nd ed) (ISBN 0131791036) Introduction to Optics - Frank Pedrotti et al. (3rd ed) (ISBN 0131499335) Introduction to Quantum Mechanics - David Griffiths (2nd ed) (ISBN 0131118927) Introduction to Risk Management and Insurance - Mark Dorfman (8th ed) (ISBN 0131449583) Introduction to Risk Management and Insurance - Mark S. Dorfman (9th ed) (ISBN 0132242273) Introduction to Technical Mathematics - Allyn J. Washington, Mario Triola (5th ed) (ISBN 0321374177) Introduction to Telecommunications - Martha Rosengrant (2nd ed) (ISBN 0131126156) Introduction to the Design & Analysis of Experiments - George C Canavos (1st ed) (ISBN 0136158633) Introduction to the Design and Analysis of Algorithms - Anany Levitin (1st ed) (ISBN 0201743957) Introduction to the Design and Analysis of Algorithms - Anany Levitin (2nd ed) (ISBN 0321358287) Introduction to Transportation Engineering - Lester A. Hoel (1st ed) (ISBN 0534952895) Introduction to Vacuum Technology - David M. Hata (1st ed) (ISBN 0130450189) Introductory & Intermediate Algebra for College Students - Robert F. Blitzer (3rd ed) (ISBN 0136028950) Introductory Algebra - Marvin L. Bittinger (10th ed) (ISBN 0321269470) Introductory Algebra for College Students - Robert F. Blitzer (5th ed) (ISBN 0132356791) Introductory Algebra through Applications - Geoffrey Akst (2nd ed) (ISBN 0321518020) Introductory and Intermediate Algebra - Robert F Blitzer (2nd ed) (ISBN 0131492594) Introductory Chemistry - Nivaldo J. Tro (3rd ed) (ISBN 0136003826) Introductory Chemistry - Steve Russo, Michael Silver, Mike Silver (2nd ed) (ISBN 032104634X) Introductory Circuit Analysis - Robert Boylestad (11th ed) (ISBN 0131730444) Introductory Econometrics: A Modern Approach - Jeffrey Wooldridge (3rd ed) (ISBN 0324289782) Introductory Econometrics: A Modern Approach - Jeffrey Wooldridge (4th ed) (ISBN 0324581629) Introductory Linear Algebra: An Applied First Course - Bernard Kolman (8th ed) (ISBN 0131437402) Introductory Mathematical Analysis - Ernest F Haeussler (12th ed) (ISBN 0132404222) Introductory Statistics - Neil A. Weiss (8th ed) (ISBN 0321393619) Inventing Entrepreneurs: Technology Innovators and their Entrepreneurial Journey - Gerry George (1st ed) (ISBN 0131574701) Investments - Frank K. Reilly (7th ed) (ISBN 0324288999) Investments: An Introduction - Herbert B. Mayo (9th ed) (ISBN 0324561261) Java Software Solutions: Foundations of Program Design - John Lewis (5th ed) (ISBN 0321409493) Java: Introduction to Problem Solving and Programming - Walter Savitch (6th ed) (ISBN 0136072259) John E. Freund's Mathematical Statistics with Applications - Irwin Miller (7th ed) (ISBN 0131427067) Kleppner's Advertising Procedure - Ronald Lane (17th ed) (ISBN 0132308290) Labor Relations - Arthur A Sloane (12th ed) (ISBN 013196223X) Labor Relations and Collective Bargaining: Cases, Practice, and Law - Michael R. Carrell (8th ed) (ISBN 0131868721) Lakeside Company: Case Studies in Auditing - John M. Trussel (11th ed) (ISBN 0131588516) Law and Economics - Robert Cooter (5th ed) (ISBN 0321336348) Law for Business - John D. Ashcroft (16th ed) (ISBN 0324381573) Learning Microsoft Office Accounting 2007 and Student CD Package - Terri Brunsdon (1st ed) (ISBN 0131586602) Learning Peachtree Complete 2007 & Peachtree Complete CD Package - Terri Brunsdon (1st ed) (ISBN 0132405571) Learning Quickbooks Pro 2007 and Student CD Package - Terri Brunsdon (1st ed) (ISBN 0132419386) Legal Terminology - Gordon W. Brown (5th ed) (ISBN 0131568043) Level Three Leadership: Getting Below the Surface - James G Clawson (4th ed) (ISBN 0132423847) Linear Algebra and Its Applications - David C. Lay (3rd ed) (ISBN 0321287134) Linear Algebra for Engineers and Scientists Using Matlab - Kenneth Hardy (1st ed) (ISBN 0139067280) Linear Algebra with Applications - Otto Bretscher (3rd ed) (ISBN 0131453343) Linear Algebra with Applications - Steven Leon (7th ed) (ISBN 0131857851) Logic and Computer Design Fundamentals - M. Morris Mano (4th ed) (ISBN 013198926X) Machine Design: An Integrated Approach - Robert L. Norton (3rd ed) (ISBN 0131481908) Machines and Mechanisms: Applied Kinematic Analysis - David H. Myszka (3rd ed) (ISBN 0131837761) Macroeconomics - Andrew B. Abel (6th ed) (ISBN 0321451406) Macroeconomics - Glenn Hubbard (2nd ed) (ISBN 0132356694) Macroeconomics - Michael Parkin (7th ed) (ISBN 032124608X) Macroeconomics - Michael Parkin (8th ed) (ISBN 0321416570) Macroeconomics - Richard Froyen (8th ed) (ISBN 0131435825) Macroeconomics - Richard G. Lipsey (13th ed) (ISBN 0321369238) Macroeconomics - Richard T Froyen (9th ed) (ISBN 0132438356) Macroeconomics - Robert Gordon (10th ed) (ISBN 0321278801) Macroeconomics - Robert Gordon (11th ed) (ISBN 0321485513) Macroeconomics - Stephen D. Williamson (3rd ed) (ISBN 0321416589) Macroeconomics: A Modern Approach - Robert J. Barro (1st ed) (ISBN 0324178107) Macroeconomics: Principles and Policy - William J. Baumol (10th ed) (ISBN 0324537034) Macroeconomics: Principles and Tools - Arthur O'Sullivan, Steven Sheffrin (4th ed) (ISBN 0131536184) Macroeconomics: Principles, Applications, and Tools - Arthur O'Sullivan (5th ed) (ISBN 013232928X) Making Career Decisions that Count: A Practical Guide - Darrell A. Luzzo (3rd ed) (ISBN 0131712772) Making the Team - Leigh Thompson (3rd ed) (ISBN 0131861352) Management - Michael Hitt (2nd ed) (ISBN 0132354373) Management - Stephen P Robbins (9th ed) (ISBN 0132257734) Management of Organizational Behavior - Paul H Hersey (9th ed) (ISBN 0131441396) Manager's Bookshelf - Jon L. Pierce (8th ed) (ISBN 0132301652) Managerial Accounting - Carl Warren (9th ed) (ISBN 0324381913) Managerial Accounting - Linda S. Bamber (1st ed) (ISBN 0138129711) Managerial Accounting (Class Test Edition) - Linda S. Bamber (1st ed) (ISBN 0132284634) Managerial Accounting: A Focus on Ethical Decision Making - Steve Jackson, Roby Sawyers (4th ed) (ISBN 0324650647) Managerial Accounting: An Introduction to Concepts, Methods and Uses - Michael W. Maher (10th ed) (ISBN 0324639767) === Subject: Re: Comprehensive Solution Manual for Textbooks posting-account=rLOz6QoAAAAmvEIbrGZd27QhtZqovu5R rv:1.9.0.5) Gecko/2008120121 Firefox/3.0.5,gzip(gfe),gzip(gfe) continued...Updated list per December 30, 2008 I have the comprehensive SOLUTIONS MANUAL for ALL of the following textbooks and TEST BANKS for MOST of them in electronic format (PDF/ Word). The solutions manual are comprehensive with answers to both even & odd problems in the text. The price for the solution manual is US$35 for each. The price for the test bank is also $35. The methods of payment is through PAYPAL (It is easy, safe, and you can use debit or credit card to pay even if you don't have an account). Email me at sbooks4sale[at]hotmail[dot]com if you are interested. If you could not find the book you are looking for, please let me know, I -------------------------- Economic Development - Michael P. Todaro (10th ed) (ISBN 0321485734) Economic Development - Michael Todaro, Stephen Smith (9th ed) (ISBN 0321278887) Economic Growth - David N. Weil (2nd ed) (ISBN 0321416627) Economic Growth - David Weil (1st ed) (ISBN 0201680262) Economics - Michael Parkin (8th ed) (ISBN 0321423003) Economics - Richard Lipsey (13th ed) (ISBN 0321369211) Economics for Managers - Paul G Farnham (1st ed) (ISBN 0130924253) Economics of Money, Banking, and Financial Markets - Frederic Mishkin (Test Bank) (8th ed) (ISBN 0321415051) Economics of Money, Banking, and Financial Markets, Update - Frederic Mishkin (7th ed) (ISBN 0321331850) Economics Today - Roger LeRoy Miller (14th ed) (ISBN 0321422341) Economics Today: The Macro View - Roger Miller (13th ed) (ISBN 0321278992) Economics Today: The Macro View - Roger Miller (14th ed) (ISBN 0321421442) Economics Today: The Micro View - Roger Miller (13th ed) (ISBN 0321278984) Economics Today: The Micro View - Roger Miller (14th ed) (ISBN 0321425065) Economics: A Contemporary Introduction - William A. McEachern (8th ed) (ISBN 0324579217) Economics: A Tool for Critically Understanding Society - Tom Riddell (8th ed) (ISBN 0321423585) Economics: Principles and Policy - William J. Baumol (10th ed) (ISBN 0324537026) Economics: Principles and Policy - William J. Baumol (11th ed) (ISBN 0324586205) Economics: Private and Public Choice - James D. Gwartney (12th ed) (ISBN 0324580185) Effective Small Business Management - Norman M. Scarborough (9th ed) (ISBN 0136152708) Effective Writing - Claire B. May (8th ed) (ISBN 0136029086) Electric Circuits - James Nilsson (8th ed) (ISBN 0131989251) Electrical Engineering: Principles and Applications - Allan R. Hambley (4th ed) (ISBN 0131989227) Electrical Machines, Drives and Power Systems - Theodore Wildi (6th ed) (ISBN 0131776916) Electronic Communications for Technicians - Tom Wheeler (2nd ed) (ISBN 0131130498) Electronics and Computer Math - Bill R. Deem (8th ed) (ISBN 0131711377) Electronics Fundamentals: Circuits, Devices and Applications - Thomas Floyd (7th ed) (ISBN 013219709X) Elementary Algebra - George Woodbury (1st ed) (ISBN 0321166426) Elementary Algebra Early Graphing for College Students - Allen R. Angel (3rd ed) (ISBN 0136134165) Elementary Algebra: Graphs and Authentic Applications - Jay Lehmann (1st ed) (ISBN 013220164X) Elementary and Intermediate Algebra - George Woodbury (2nd ed) (ISBN 0321500067) Elementary and Intermediate Algebra: Graphs & Models - Marvin L. Bittinger (3rd ed) (ISBN 0321422406) Elementary Differential Equations - Henry Edwards (6th ed) (ISBN 0132397307) Elementary Differential Equations - Werner E. Kohler, Lee W.Johnson (1st ed) (ISBN 0201709260) Elementary Differential Equations with Boundary Value Problems - Henry Edwards (6th ed) (ISBN 0136006132) Elementary Differential Equations With Boundary Value Problems - Lee Johnson et al (1st ed) (ISBN 0321121643) Elementary Differential Equations With Boundary Value Problems - Lee Johnson et al (2nd ed) (ISBN 0321398505) Elementary Linear Algebra with Applications - Bernard Kolman (9th ed) (ISBN 0132296543) Elementary Number Theory - Kenneth H. Rosen (5th ed) (ISBN 0321237072) Elementary Statistics - Mario F. Triola (10th ed) (ISBN 0321331834) Elementary Statistics - Mario F. Triola (9th ed) (ISBN 0201775700) Elementary Statistics - Neil A. Weiss (7th ed) (ISBN 0321422090) Elementary Statistics - Ron Larson (4th ed) (ISBN 0132424339) Elementary Statistics Using Excel - Mario Triola (3rd ed) (ISBN 0321365135) Elementary Statistics Using the TI-83/84 Plus Calculator - Mario F. Triola (2nd ed) (ISBN 0321462572) Elementary Statistics With Multimedia Study Guide - Mario F. Triola (10th ed) (ISBN 0321460928) Elements of Forecasting - Francis X. Diebold (4th ed) (ISBN 032432359X) Employment Law - John J. Moran (4th ed) (ISBN 0136009964) Engineering Economy - William G Sullivan (13th ed) (ISBN 0131486497) Engineering Economy - William G. Sullivan (14th ed) (ISBN 0136142974) Engineering Economy and the Decision-Making Process - Joseph C. Hartman (1st ed) (ISBN 0131424017) Engineering Fundamentals: An Introduction to Engineering - Saeed Moaveni (3rd ed) (ISBN 0495082538) Engineering Materials: Properties and Selection - Ken Budinski (8th ed) (ISBN 0131837796) Engineering Mechanics Dynamics - Anthony M Bedford (5th ed) (ISBN 0136129161) Engineering Mechanics: Statics - Anthony M Bedford (5th ed) (ISBN 0136129153) Engineering Mechanics: Statics - Russell C. Hibbeler (11th ed) (ISBN 0132215004) Engineering Mechanics: Statics Computational Edition - Robert W. Soutas-Little (1st ed) (ISBN 0534549217) Engineering Vibration - Daniel Inman (3rd ed) (ISBN 0132281732) Enterprise Systems for Management - Luvai Motiwalla (1st ed) (ISBN 013233531X) Entrepreneurial Finance - Philip J. Adelman (4th ed) (ISBN 0132434792) Entrepreneurship: Successfully Launching New Ventures - Bruce Barringer (2nd ed) (ISBN 0132240572) Environmental and Natural Resource Economics - Tom Tietenberg (7th ed) (ISBN 0321305043) Environmental Issues: An Introduction to Sustainability - Robert L. McConnell (3rd ed) (ISBN 0131566504) Environmental Law - Nancy K. Kubasek (6th ed) (ISBN 0136142168) Environmental Science: Toward A Sustainable Future - Richard T. Wright (10th ed) (ISBN 0132302659) Error Control Coding - Daniel J. Costello Jr., Shu Lin (2nd ed) (ISBN 0130426725) Essential Foundations of Economics - Robin Bade (4th ed) (ISBN 0321522354) Essentials of Business Law - Jeffrey F. Beatty (3rd ed) (ISBN 0324537123) Essentials of College Algebra with Modeling and Visualization - Gary K. Rockswold (3rd ed) (ISBN 0321448898) Essentials of College Algebra, Alternate Edition - Margaret L. Lial (1st ed) (ISBN 0321491858) Essentials of Economics - Gregory Mankiw (4th ed) (ISBN 0324236964) Essentials of Entrepreneurship and Small Business Management - Thomas W Zimmerer (5th ed) (ISBN 0132294389) Essentials of Logic - Irving Copi (2nd ed) (ISBN 013238034X) Essentials of Management Information Systems - Jane Laudon (8th ed) (ISBN 013602579X) Essentials of Managerial Finance - Scott Besley (13th ed) (ISBN 0324258755) Essentials of Marketing - Charles W. Lamb (6th ed) (ISBN 0324656203) Essentials of Organizational Behavior - Stephen P Robbins (9th ed) (ISBN 0132431521) Essentials of Statistics - Mario F. Triola (3rd ed) (ISBN 0321434250) Essentials of the Legal Environment - Roger LeRoy Miller (2nd ed) (ISBN 0324400403) Ethics for the Information Age - Mike Quinn (3rd ed) (ISBN 0321536851) Excellence in Business Communication - John V. Thill (8th ed) (ISBN 0136157505) Exploring Business - Karen Collins (1st ed) (ISBN 0131403656) Exploring Macroeconomics - Robert L. Sexton (4th ed) (ISBN 0324395558) Federal Tax Research - William A. Raabe (8th ed) (ISBN 0324659652) Feedback Control of Dynamic Systems - Gene Franklin (5th ed) (ISBN 0131499300) Financial & Managerial Accounting - Carl S. Warren (9th ed) (ISBN 0324401884) Financial Accounting - Carl S. Warren, James M. Reeve (10th ed) (ISBN 0324380674) Financial Accounting - Carl S. Warren, James M. Reeve (11th ed) (ISBN 0324663781) Financial Accounting - Jane Reimers (1st ed) (ISBN 0131492012) Financial Accounting - Walter Harrison, Charles Horngren (6th ed) (ISBN 0131499459) Financial Accounting - Walter Harrison, Charles Horngren (7th ed) (ISBN 0138128200) Financial Accounting and Financial Tips - Walter T. Harrison (7th ed) (ISBN 0135012848) Financial Accounting, Reporting & Analysis: International Edition - Barry Elliott (2nd ed) (ISBN 027370253X) Financial Accounting: A Bridge to Decision Making - Robert Ingram (6th ed) (ISBN 0324313357) Financial Accounting: A Business Process Approach - Jane L. Reimers (2nd ed) (ISBN 0131473867) Financial Accounting: An Integrated Statements Approach - Jonathan Duchac (2nd ed) (ISBN 0324312113) Financial Accounting: An Introduction to Concepts, Methods and Uses - Clyde P. Stickney (12th ed) (ISBN 0324381980) Financial Accounting: The Impact on Decision Makers - Gary Porter (6th ed) (ISBN 0324655231) Financial and Managerial Accounting - Meg Pollard (1st ed) (ISBN 0136008984) Financial And Managerial Accounting (Ch 1-13) - Charles Horngren (1st ed) (ISBN 0135009855) Financial Economics - Zvi Bodie (2nd ed) (ISBN 0131856154) Financial Management For Public, Health, and Not-for-Profit Organizations - Steven Finkler (2nd ed) (ISBN 0131471988) Financial Management: Theory & Practice - Eugene Brigham (12th ed) (ISBN 0324422695) === Subject: Re: Comprehensive Solution Manual for Textbooks posting-account=rLOz6QoAAAAmvEIbrGZd27QhtZqovu5R rv:1.9.0.5) Gecko/2008120121 Firefox/3.0.5,gzip(gfe),gzip(gfe) Updated list per December 30, 2008 I have the comprehensive SOLUTIONS MANUAL for ALL of the following textbooks and TEST BANKS for MOST of them in electronic format (PDF/ Word). The solutions manual are comprehensive with answers to both even & odd problems in the text. The price for the solution manual is US$35 for each. The price for the test bank is also $35. The methods of payment is through PAYPAL (It is easy, safe, and you can use debit or credit card to pay even if you don't have an account). Email me at sbooks4sale[at]hotmail[dot]com if you are interested. If you could not find the book you are looking for, please let me know, I -------------------------- A Gift of Fire: Social, Legal, and Ethical Issues for Computing and the Internet - Sara Baase (3rd ed) (ISBN 0136008488) Absolute C++ - Walter Savitch (3rd ed) (ISBN 0321468937) Absolute Java - Walter Savitch (3rd ed) (ISBN 0321487923) Access 2007 Guidebook - Maggie Trigg (6th ed) (ISBN 0321517016) Accounting - Carl Warren (22nd ed) (ISBN 0324401841) Accounting - Carl Warren (23rd ed) (ISBN 0324662963) Accounting Chapters 1-13 - Charles T. Horngren et al (7th ed) (ISBN 0132249952) Accounting Chapters 1-25 - Charles T. Horngren et al (7th ed) (ISBN 0132439603) Accounting Chapters 1-26 - Charles T. Horngren et al (6th ed) (ISBN 0131088513) Accounting Chapters 12-25 - Charles T. Horngren et al (7th ed) (ISBN 0132249960) Accounting Concepts and Applications - Steve Albrecht (10th ed) (ISBN 0324376154) Accounting Concepts and Applications - Steve Albrecht (9th ed) (ISBN 0324187564) Accounting Information Systems - James Hall (5th ed) (ISBN 0324312954) Accounting Information Systems - James Hall (6th ed) (ISBN 0324560893) Accounting Information Systems - Marshall Romney, Paul Steinbart (10th ed) (ISBN 0131475916) Accounting Information Systems - Marshall Romney, Paul Steinbart (11th ed) (ISBN 0136015182) Accounting Information Systems - Ulric J. Gelinas (7th ed) (ISBN 0324378823) Additional Calculus Topics - Raymond Barnett (11th ed) (ISBN 0132318229) Administrative Law: Bureaucracy in a Democracy - Daniel E. Hall (4th ed) (ISBN 0135005183) Advanced Accounting - Floyd Beams (9th ed) (ISBN 0131851225) Advanced Accounting - Floyd Beams (10th ed) (ISBN 0136033970) Advanced Accounting - Paul Fischer (10th ed) (ISBN 0324379056) Advanced Accounting - Paul Fischer (Test Bank only) (9th ed) (ISBN 0324304013) Advanced Calculus - G. B. Folland (1st ed) (ISBN 0130652652) Advanced Engineering Mathematics - Michael Greenberg (2nd ed) (ISBN 0133214311) Advanced Engineering Mathematics - Peter V. O'Neil (6th ed) (ISBN 0534552080) Advertising - Sandra Moriarty (8th ed) (ISBN 0132224151) Algebra and Trigonometry - Judith A. Beecher (3rd ed) (ISBN 0321466209) Algebra and Trigonometry - Michael Sullivan (8th ed) (ISBN 0132329034) Algebra and Trigonometry Enhanced with Graphing Utilities - Michael Sullivan (4th ed) (ISBN 0131527398) Algebra and Trigonometry Enhanced with Graphing Utilities - Michael Sullivan (5th ed) (ISBN 013600492X) Algebra and Trigonometry: Graphs & Models and Graphing Calculator Manual Package - Marvin L. Bittinger (4th ed) (ISBN 0321501519) Algebra for College Students - Allen R. Angel (3rd ed) (ISBN 0136129080) Algebra for College Students - Margaret L. Lial (6th ed) (ISBN 0321442547) Algebra For College Students - Robert F Blitzer (6th ed) (ISBN 0136019749) An Introduction to Signals and Systems - John Alan Stuller (1st ed) (ISBN 0495073016) Dunlap (1st ed) (ISBN 0534392946) Analytical Mechanics - Grant Fowles, George Cassiday (7th ed) (ISBN 0534494927) Anatomy & Physiology - Elaine N. Marieb (3rd ed) (ISBN 0805347739) Anatomy & Physiology for Emergency Care - Bryan E. Bledsoe (2nd ed) (ISBN 0132342987) Applied Algebra - Darel Hardy (1st ed) (ISBN 0130674648) Applied Linear Algebra - Chehrzad Shakiban, Peter J. Olver (1st ed) (ISBN 0131473824) Applied Multivariate Statistical Analysis - Richard A. Johnson (6th ed) (ISBN 0131877151) Applied Partial Differential Equations - Richard Haberman (4th ed) (ISBN 0130652431) Applied Physics - Dale Ewen (9th ed) (ISBN 0135157331) Art and Science of Leadership - Afsaneh Nahavandi (5th ed) (ISBN 0136044085) Auditing and Assurance Services - Alvin A. Arens et al (11th ed) (ISBN 0131867121) Auditing and Assurance Services - Alvin A. Arens et al (12th ed) (ISBN 0135132126) Auditing Assurance and Risk - W. Robert Knechel, Steve Salterio, Brian Ballou (3rd ed) (ISBN 0324313187) Auditing Cases - Mark Beasley (3rd ed) (ISBN 0131494910) Auditing Cases - Mark S Beasley (4th ed) (ISBN 0132423502) Auditing: A Business Risk Approach - Larry E. Rittenberg (6th ed) (ISBN 0324375581) Automation, Production Systems, and Computer-Integrated Manufacturing - Mikell P. Groover (2nd ed) (ISBN 0130889784) Automation, Production Systems, and Computer-Integrated Manufacturing - Mikell P. Groover (3rd ed) (ISBN 0132393212) Basic Business Statistics - Mark L Berenson (10th ed) (ISBN 0131678310) Basic Chemistry - Karen C. Timberlake (2nd ed) (ISBN 0805344691) Basic Environmental Technology: Water Supply, Waste Management & Pollution Control - Jerry A. Nathanson (5th ed) (ISBN 0131190822) Basic Marketing Research Using Microsoft Excel Data Analysis - Alvin C Burns (2nd ed) (ISBN 0132059584) Basic Mathematics through Applications - Geoffrey Akst (4th ed) (ISBN 0321500113) Beginning & Intermediate Algebra - Elayn El Martin-Gay (5th ed) (ISBN 0136007317) Beginning Algebra - Elayn El Martin-Gay (5th ed) (ISBN 0136007023) Beginning Algebra - Margaret L. Lial (10th ed) (ISBN 0321437268) Beginning Algebra with Applications & Visualization - Gary K. Rockswold (2nd ed) (ISBN 0321500040) Beginning and Intermediate Algebra - Margaret L. Lial (4th ed) (ISBN 0321442334) Beginning and Intermediate Algebra with Applications & Visualization - Gary K. Rockswold (2nd ed) (ISBN 0321500059) Behavior in Organizations - Jerald Greenberg (9th ed) (ISBN 0131542842) Biochemistry - Mary Campbell (4th ed) (ISBN 0534405215) Biochemistry (with Lecture Notebook) - Mary Campbell (4th ed) (ISBN 0534391818) Biology - Neil A. Campbell (Test Bank only w/ TestGen Software) (7th ed) (ISBN 080537146X) Biomaterials: The Intersection of Biology and Materials Science - Johnna S. Temenoff (1st ed) (ISBN 0130097101) Biostatistics for the Health Sciences - R. Clifford Blair (1st ed) (ISBN 0131176609) Bond Markets, Analysis and Strategies - Frank Fabozzi (6th ed) (ISBN 0131986430) Brief Course in Mathematical Statistics - Elliot A. Tanis (1st ed) (ISBN 0131751395) Brock Biology of Microorganisms - Michael T. Madigan (12th ed) (ISBN 0132324601) Brock Biology of Microorganisms - Michael T. Madigan (Test Bank) (11th ed) (ISBN 0132192268) Building Construction: Principles, Materials, and Systems - Madan Mehta (1st ed) (ISBN 0130494216) Building Java Programs: A Back to Basics Approach - Stuart Reges (1st ed) (ISBN 0321382838) Business Analysis and Valuation: Using Financial Statements - Krishna Palepu (3rd ed) (ISBN 0132346451) Business and Society: Ethics and Stakeholder Management - Archie B. Carroll (7th ed) (ISBN 0324569394) Business Communication Essentials and Peak Performance Grammar and Mechanics 2.0 CD Package - Court Bovee (3rd ed) (ISBN 0132328992) Business Communication Today - Court Bovee (9th ed) (ISBN 0131995359) Business English: Writing in the Workplace - Blanche Ettinger (4th ed) (ISBN 0131565702) Business Forecasting - John Hanke (9th ed) (ISBN 0132301202) Business in Action with Real Time Updates - Court Bovee (4th ed) (ISBN 0136154085) Business Law and the Legal Environment - Jeffrey F. Beatty (4th ed) (ISBN 0324303971) Business Law and the Regulation of Business - Richard A. Mann (9th ed) (ISBN 0324537131) Business Law Principles for Today's Commercial Environment - David P. Twomey (2nd ed) (ISBN 0324303947) Business Law Today: The Essentials - Roger LeRoy Miller (8th ed) (ISBN 0324654545) Business Law: Text and Cases - Kenneth W. Clarkson (11th ed) (ISBN 0324655223) Business Law: Text and Exercises - Roger LeRoy Miller (5th ed) (ISBN 032464096X) Business Statistics: A Decision Making Approach - David F. Groebner (7th ed) (ISBN 0132416921) Calculus - Dale Varberg (9th ed) (ISBN 0131429248) Calculus and Its Applications - Larry Goldstein (11th ed) (ISBN 0131919636) Calculus and Its Applications - Marvin L. Bittinger (8th ed) (ISBN 0321166396) Calculus and Its Applications - Marvin L. Bittinger (9th ed) (ISBN 0321395344) Calculus Early Transcendentals - Henry Edwards (7th ed) (ISBN 0131569899) Calculus for Business, Economics, Life Sciences & Social Sciences - Raymond Barnett (11th ed) (ISBN 0132328186) Calculus for the Life Sciences - Marvin L. Bittinger (1st ed) (ISBN 0321279352) Calculus With Applications - Margaret L. Lial et al (8th ed) (ISBN 0321228146) Calculus with Applications for the Life Sciences - Raymond N. Greenwell (1st ed) (ISBN 0201745828) Calculus, Early Transcendentals - C. Henry Edwards (7th ed) (ISBN 0131569899) California Real Estate Law - Theodore Gordon (7th ed) (ISBN 0324654685) Capital Budgeting and Long-Term Financing Decisions - Neil Seitz (4th ed) (ISBN 0324258089) Cases in Management Accounting and Control Systems - Brandt Allen (4th ed) (ISBN 0135704251) === Subject: Re: JSH: Over a hundred years, wrong stuff posting-account=XH7n1goAAAC_c_M3JtSDv3QFzlbwvvMO .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) > Academics in the mathematical field are refusing to acknowledge being > informed of a massive error in their field which entered it over a > hundred years ago despite the simplicity of the proof of the error. > It has been six years since I discovered the error while trying to > prove Fermat's Last Theorem. 0) idiot > 1) Andrew Weyl. I can't tell if this is supposed to be Andrew Wiles, Andre Weil, Hermann Weyl, or exactly what it says. === Subject: Re: JSH: Over a hundred years, wrong stuff > Academics in the mathematical field are refusing to acknowledge being > informed of a massive error in their field which entered it over a > hundred years ago despite the simplicity of the proof of the error. > It has been six years since I discovered the error while trying to > prove Fermat's Last Theorem. > 0) idiot > 1) Andrew Weyl. > I can't tell if this is supposed to be Andrew Wiles, Andre Weil, > Hermann Weyl, or exactly what it says. Yeah Uncle Al is incompetent, no surprises there. He's a holdover from the old usenet when you could intimidate people > out of posting by insulting them. Now he's just one other person who can't get his details right. I pick Andre Weil for what he was trying to get out. Obviously, he was aiming at Andrew Wiles. My guess is that you are the only one who failed to see that. Jose Carlos Santos === Subject: Re: JSH: Over a hundred years, wrong stuff > > Academics in the mathematical field are refusing to acknowledge being > informed of a massive error in their field which entered it over a > hundred years ago despite the simplicity of the proof of the error. > > It has been six years since I discovered the error while trying to > prove Fermat's Last Theorem. > > 0) idiot > 1) Andrew Weyl. > 2) Saepe errans, numquam dubitans > > Ode to James Harris > -- > Uncle Alhttp://www.mazepath.com/uncleal/ > (Toxic URL! Unsafe for children and most > mammals)http://www.mazepath.com/uncleal/lajos.htm#a2 The Ode to James Harris would make for a great drinking song for > mathematicians. > My favorite part is quiddit: that was simply brilliant. To give credit where due, the original is by Edgar A Guest. See . > M -- --------------------------- | BBB b Barbara at LivingHistory stop co stop uk | B B aa rrr b | | BBB a a r bbb | Quidquid latine dictum sit, | B B a a r b b | altum viditur. | BBB aa a r bbb | ----------------------------- === Subject: Fitting Partial differential equation for a surface z =f(x,y) posting-account=LChCFQoAAACR0FoxHzVn6GGERsr9zp8c Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) For given data, we can fit a curve of the form y = f(x), but for a given polygon [simple_closed_surface] how to fit a partial differential equation of the form Z = f(x,y) Surface is a simple_closed_one, like a surface in Green's theorem [ vector_calculus ] Green's theorem :- integral PDx + QDy = integral (dq/dx - dp/dy)da assuming that the orientation is '+ve' the curve is 'C' which has continuous partial derivatives on the open region to cover 'D' === Subject: Re: Fitting Partial differential equation for a surface z =f(x,y) > For given data, we can fit a curve of the form y = f(x), but for a given polygon [simple_closed_surface] how to fit a partial differential equation of the form Z = f(x,y) Where's the differential? > Surface is a simple_closed_one, > like a surface in Green's theorem [ vector_calculus ] If it's a _closed_ surface, it wouldn't be z = f(x,y). Anyway, if you have in mind an equation of the form F_0(x,y,z) + sum_j a_j F_j(x,y,z) = 0 for parameters a_1,...,a_k and data points [x_i, y_i, z_i], i=1..N, you can try a least-squares fit on the linear system F_0(x_i,y_i,z_i) + sum_j a_j F_j(x_i,y_i,z_i) = 0 for i=1..N. -- Robert Israel israel@math.MyUniversitysInitials.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada === Subject: Re: #88 Chapter 2, FrontView and BackView of every number ; new book 2nd edition: New True Mathematics Please learn how to format text. +> snip <+ === Subject: Wagering: Percentage for Profitability Okay take a pari-mutuel payout of 2.40 and that's profit odds of .30 to 1 .So obviously to make a profit of 30% at odds of .30 requires 100% correct bets. But what is the percentage of correct bets that is required at odds of .60 to make an overall profit of 30% ? The answer is (30 + 100) / (.60 + 1) or 81.25% correct bets... Here is a link to the KBH Precentage for Profitability Algorithm: http://www.kbhscape.com/turf.htm === Subject: Re: Wagering: Percentage for Profitability Corrected: > Okay take a pari-mutuel payout of 2.60 and that's profit odds of .30 to 1 > .So obviously to make a profit of 30% at odds of .30 requires 100% correct > bets. But what is the percentage of correct bets that is required at odds of .60 > to make an overall profit of 30% ? The answer is (30 + 100) / (.60 + 1) or 81.25% correct bets... Here is a link to the KBH Precentage for Profitability Algorithm: http://www.kbhscape.com/turf.htm > === Subject: attempt at faking math talk? > It's the way things are, and always will be. No one >can change it Goober...not Rupert....not his instructors... >not the boys in the math ngs....not you, Goo. It isn't. Then you try changing it, or Rupert, or his instructors, or your nurses Goo... Let's see the corrected equation(s). Go: >It is worthless cracker bull that describes nothing. It >wasn't math, it wasn't an equation; it was just a bunch of letters that >you thought looked like math. It considers basic existence and also the value of the life experienced. Your moral values do not apply Goob, nor do any of your obsessions with pre-existence. >e + N = -V and e + P = +V It calculates the value of life Goo. In order to calibrate it or whatever it would get more complex, but what we've got is too much for some people like all you misnomer advocates just as it is. >(correct prediction: Goo can't think of it being any other way, >and is lying when he pretends that he can) === Subject: Re: Goowit Harrison's attempt at faking math talk? stupid pig-ing cracker, cockfighting specialist - woke up and said, How can I be even *more* stupid today than I was yesterday?, and so he lied: > No pointing out. Stupid, illiterate, convicted felon crackers do not point out. > It's the way things are > It isn't. It was just stupid cracker fake math talk. It doesn't describe anything. Then you try changing it Nothing to change. It's obvious that it's cracker fake math talk. > It is worthless cracker bull that describes nothing. It > wasn't math, it wasn't an equation; it was just a bunch of letters that > you thought looked like math. It considers It's fake math talk. It's nothing. > e + N = -V and e + P = +V It calculates the value of life It calculates nothing. It's fake. It's complete bull. You just strung some letters and a couple of arithmetic operators together at random. It's bull - the usual cracker spew from an uneducated, stupid, low-IQ cracker. === Subject: Re: Euclidean Proof of Fermat's Last Theorem > I read that most mathematicians believe that Fermat > made a mistake, and never found a Euclidean proof. No, it's not true. I have restored Fermat's lost proof successfully, namely If the diophantine equation x^n + y^n = z^n has a solution in nonzero integers when n is an odd number with n > 2, then 2 is a divisor of n. === Subject: Re: Euclidean Proof of Fermat's Last Theorem posting-account=jPnQ2goAAAA461y3QD0lbyw0oKeThma1 AppleWebKit/525.18 (KHTML, like Gecko) Version/3.1.2 Safari/525.20.1 FOH:R051,gzip(gfe),gzip(gfe) that is an interesting inference of yours; had not someone proven the case for n=3 (and, of course, the very special case of n=4) ?? > life, Fermat, in a letter, raised the question of proving that no fifth > power is a sum of two fifth powers. So, by this time, he didn't even thus: on Nondystributive Geometry. yeah; if you can't put into constructive geometrical terms, you can't do ****. yeah; you had the definitive 2-week course in Geometry from an Advanced/Remedial Viewpoint in some Mice.Space at Vanderbilt! http://wlym.com/~boston/cartoons/slides/Mice%20Space.htm thus: here is an example of the Skeptics (current Calif. or USA mag.) being unable to come-up with a rational explanation of: sodium-vapor streetlights going off, as you walk underneath them; they think it to be either a hoax or psycho/visual. also, cropcircles. also, http://www.svpvril.com/svpweb14.html. thus: even Ockham'd slice through that apple & orange, with one wild Yahoo! (tm); western astrology is the same as Ptolemy's epicyclic hoax, over 2000yo. > some have been even making into popular news. > that astrological signs may have some meaning thus: I yam lying what I bean!... of what possible use is the set of all sets, whether or not it can eventually include itself, at the end of the list of elements -- shades of AP-adics? so, perhaps we can blame Russell for the Bourbaki New Math, based upon set theory, but see what Whitehead had to say about him, not to say Godel. thus: shouldn't it be clear that photons are an artifact of the idea that actually were zero-dimensional points, but, since they are waves, as shown by Young, Huyghens et al, there is really no need for them, except in the Pauli matrix formalism of statistical bosons; eh? Schroedinger's cat is dead -- long-live Schoredinger's cat! --only 24 hours to impeach Trickier Dick from the N.Admin, metaphorically typing, or Cheeny & Zbiggy, fo'mo' years; Good Morning, Afghanistan! ... Good Afternoon, Sudan! http://tarpley.net/bush12.htm http://wlym.com/campaigner/8011.pdf -- Brits hate Shakes, Why? http://www.wlym.com/~seattle/dynamis/ http://www.21stcenturysciencetech.com/current.html http://www.rwgrayprojects.com/synergetics/plates/plates.html http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=3163 http://wlym.com/campaigner/8011.pdf -- English, not! === Subject: Re: Euclidean Proof of Fermat's Last Theorem | | > Does anyone know why the Clay Mathematics Institute | > offers million-dollar rewards for so many new problems, | > but no reward for one of the oldest unsolved math pro- | > blems (i.e. how Fermat proved his Last Theorem, using | > 17th-century math)? It seems counter-intuitive that no one | > offers a reward for solving the math problem that has con- | > sumed more mathematicians' time than any other. | | You are, of course, free to offer your own money for a solution. Yes, of course; but I have no need for a solution, because I already have one. However, if I had failed to discover it, I would be willing to pay at least $10 to someone else who had discovered it. So it looks like I should either (1) wait for someone to offer a sufficient re- ward, or (2) try to sell the solution on eBay (after they enhance their auctioning software to provide for selling information to multiple buy- ers). | > I read that most mathematicians believe that Fermat made | > a mistake, and never found a Euclidean proof. | | I'm not sure what you mean by Euclidean, I just meant, Not non-Euclidean. (I have not read Wiles' proof because I have never studied higher math; but, as Bill Dubuque suspected, I believed Marilyn Savant when she said that Wiles used non-Euclidean math.) | but yes, there are | good reasons to believe that Fermat could not have had a valid | proof. I believe that he saw it in his mind, then forgot it (after neglecting to write it down). | that marginal note is more a question of history than of mathematics. | It would be interesting if a valid proof using 17th century math | was possible after all, but it would not be particularly important I feel that there is still much mathematical and historical curiosity out there. I was once really curious about how they built the pyramids, and would have easily paid someone $10 to tell me about how they moved the blocks (by making them into axles). | - the important results in mathematics are the ones that lead to | new tools and new areas of research, and by limiting your methods | to 17th century ones you are pretty much ruling that out. I believe that there are still many simple techniques (using tools from 17th-century math) that no one has discovered. For example, the AKS primality test was just recently discovered. | The importance | of FLT is not the result itself, but in the developments that arose | out of efforts to prove it (e.g. Kummer's ideal numbers, which led | to the concept of ideals in ring theory). Yes, I agree. | -- | Robert Israel israel@math.MyUniversitysInitials.ca | Department of Mathematics http://www.math.ubc.ca/~israel | University of British Columbia Vancouver, BC, Canada === Subject: Re: Euclidean Proof of Fermat's Last Theorem > | > | > Does anyone know why the Clay Mathematics Institute > | > offers million-dollar rewards for so many new problems, > | > but no reward for one of the oldest unsolved math pro- > | > blems (i.e. how Fermat proved his Last Theorem, using > | > 17th-century math)? It seems counter-intuitive that no one > | > offers a reward for solving the math problem that has con- > | > sumed more mathematicians' time than any other. > | > | You are, of course, free to offer your own money for a solution. Yes, of course; but I have no need for a solution, because I already > have one. However, if I had failed to discover it, I would be willing > to pay at least $10 to someone else who had discovered it. So it > looks like I should either (1) wait for someone to offer a sufficient re- > ward, or (2) try to sell the solution on eBay (after they enhance their > auctioning software to provide for selling information to multiple buy- > ers). > | > I read that most mathematicians believe that Fermat made > | > a mistake, and never found a Euclidean proof. > | > | I'm not sure what you mean by Euclidean, I just meant, Not non-Euclidean. How does that explain anything, other than that you know how to construct double negations. > (I have not read Wiles' proof > because I have never studied higher math; but, as Bill Dubuque > suspected, I believed Marilyn Savant when she said that Wiles > used non-Euclidean math.) If non-Euclidean means invented since Euclid, much of mathematics is non-Euclidean, but still valid. === Subject: Re: JSH: What is a survey journal? > My demographics according to Quantcast show I have a growing appeal, > for some reason, with teenagers, while the bulk of my readers have > graduate degrees, but for some reason they tend to make under $30k per > year US. Is it at all plausible that Quantcast could reliably measure this? Seems unlikely to me, despite their claims, but perhaps someone has an informed opinion to share? -- Jesse F. Hughes That's what's annoying about Usenet as some loser will state a case, get their ass kicked, but STILL keep coming back as if nothing happened. -- James Harris explains his strategy. === Subject: Re: JSH: What is a survey journal? posting-account=wVv_VwoAAAAVTfUuyxLzug5SzYWCgHj1 5.1),gzip(gfe),gzip(gfe) > rejection email the editor begged me not to send any more papers and > said the journal is a survey journal. What's that? > which survey recent results in a specific area. Sometimes the author is surveying mostly his/her own results, and sometimes the work of many and specialized and in general proofs are not given in detail, but outlined. This is not a journal to which you would submit a short focussed paper. > You should have looked at the journal before submitting something to it. > Oh, I replied back that she works for the people so her request is > denied. She does NOT work for the people. She is not a federal employee. She is probably paid by the journal publisher (Amer Math Society), which derives its income from paying subscribers. Are you a paying subscriber? Journals are not out there to cater to the stupidity of people like you. They do not in fact owe you the time of day. You are taking advantage of their politeness. What journals want are solid, mathematically correct and rigorous papers that say something new and interesting. They do not want the kind of junk that you produce. You are wasting everyone's time. It is OK to waste people's time here because replying to you is voluntary. It is not OK to waste the time of editors, staff, and reviewers of good journals when you are incapable of putting together a two-line proof, you do not understand rigorous definitions or logical arguments, and you are totally ignorant of the literature. They reply because they are being nice and kind. They should not have to beg you to stop sending them your ; they would be well within their rights to just dump it in the trash. Nor should they have to take insulting comments from you about how they work for the people. They do not! The same is true of math profs - Barry Mazur, McKenzie, Ribet, etc.. They may have been polite to you because at first they did not realize that you were a total ignoramus and a vicious, mean-spirited, incompetent crank. When they realized what kind of twit they were talking to they gave you the polite brush-off, hoping you would go away and stay. Like journal editors, they do not work for the people. They work for their universities and their students. They do not owe you the time of day. > Power to the people!!! > Arrogant, ignorant, presumptuous idiot. The world, Grasshopper, does not owe you a living, nor even the time of day. You have to do the old- fashioned way - you have to EARN it. You have not. Marcus. > James Harris === Subject: Re: JSH: What is a survey journal? Nntp-Posting-Host: hera.cwi.nl ... > 1. I have a distributive argument showing a particular distribution > on the complex plane with the special construction > > 7*(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x)+ 7) > > where the a's are roots of > > a^2 - (7x-1)a + (49x^2 - 14x) = 0. You have not. In the complex plane both factors are divisible by every conceivable factor of 7. Both are divisible by 7, both are divisible by sqrt(7). Worse, both are divisible by 49 and 343. > 2. That result is contradicted by the result in the ring of algebraic > integers that NEITHER of the roots can have 7 as a factor when x is an > integer, but the roots are non-rational. There is no contradiction. In the algebraic integers not everything is divisible by everything as it is in the complex numbers. In the algebraic integers 2 is *not* divisible by 7, but it is in the complex numbers. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: JSH: What is a survey journal? Nntp-Posting-Host: hera.cwi.nl ... > > 1. I have a distributive argument showing a particular distribution > > on the complex plane with the special construction > > > > 7*(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x)+ 7) > > > > where the a's are roots of > > > > a^2 - (7x-1)a + (49x^2 - 14x) =3D 0. ... > There is no contradiction. In the algebraic integers not everything is > divisible by everything as it is in the complex numbers. In the > algebraic integers 2 is *not* divisible by 7, but it is in the complex > numbers. > > The factor argument in the ring of algebraic integers contradicts the > distributive argument in the complex plane. What distributive argument? That in the complex plane in the expression: 7*(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x) + 7) can be re-written as: 175x^2 - 15x + 2 = (5a_1(x)/p + 7/p)(5a_2(x)/q + 7/q) in infinitely many ways as long as p * q = 7? And that that is not possible in infinitely many ways in the algebraic integers, where p and q depend on x? What is the contradiction? -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: JSH: What is a survey journal? posting-account=1lE9SQkAAADFrJsDv61dh1YXcJ_ahy5I AppleWebKit/525.27.1 (KHTML, like Gecko) Version/3.2.1 Safari/525.27.1,gzip(gfe),gzip(gfe) > Complex plane trumps the ring of algebraic integers. Nope It is easy to note that the fact that 7 distributes through (5a 1(x) + 7) in the field of complex numbers does not mean that 7 distributes through (5a 1(x) + 7) in the ring of algebraic integers. The fact that a property holds in the complex plane does not mean the same property holds for the algebraic integers. - William Hughes === Subject: Re: JSH: What is a survey journal? posting-account=WlifZwoAAADn4Qc008FhhuRE4Syn8J58 3.011; SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) Consider some wacky person declares there are no odd numbers, so now > you just have evens: 2, 4, 6, 8, 10, etc. and now 6 has no factors!!! Ohmigod, 10 doesn't either!!! It's PRIME > in that wacky world. > Uh huh. It looks to me like 10 divides 60 = 2 x 30 in that wacky world. So which factor does 10 divide? 2 or 30? === Subject: Re: JSH: What is a survey journal? > ... > 1. I have a distributive argument showing a particular distribution > on the complex plane with the special construction > > 7*(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x)+ 7) > > where the a's are roots of > > a^2 - (7x-1)a + (49x^2 - 14x) = 0. > > You have not. In the complex plane both factors are divisible by every > conceivable factor of 7. Both are divisible by 7, both are divisible > by sqrt(7). Worse, both are divisible by 49 and 343. That is correct, but it's a red herring. The argument is not a factor > argument. > 2. That result is contradicted by the result in the ring of algebraic > integers that NEITHER of the roots can have 7 as a factor when x is an > integer, but the roots are non-rational. > > There is no contradiction. In the algebraic integers not everything is > divisible by everything as it is in the complex numbers. In the > algebraic integers 2 is *not* divisible by 7, but it is in the complex > numbers. The factor argument in the ring of algebraic integers contradicts the > distributive argument in the complex plane. How so, exactly? Recall that a contradiction occurs when we have a proof of both (A) and (not A) for some statement A. What exactly is the statement A in this case? Bear in mind also that arguments are not statements, and so cannot in themselves form a contradiction (as neither can peanut butter sandwiches...). You need your arguments to actually prove *statements* A and not A. Mike. === Subject: Re: JSH: What is a survey journal? Nntp-Posting-Host: hera.cwi.nl ... > clear and had cubics instead of quadratics, though of course the > journal later pulled the paper, and then, died, but at least now > readers know the paper was correctly published! You mean that paper of which you acknowledged that it contained a serious error? And that even before it was published? And that you refused to retract? -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: JSH: Mathematicians cheating is kind of weird > Some of the math profs are wondering if your statements about > logical fallacies in Galois theory or Algebraic number theory > are a result of you being confused, you being > deceptive, you being overconfident or some > combination of those factors, or something like that. I doubt if any professors are wondering about that. -- Jesse F. Hughes I am the barbarian at the gates. I am a revolutionary, a discoverer, a guy who didn't just try, but did, who didn't just wonder, but accomplished. -- James S. Harris gives Hollywood its tagline === Subject: Re: wow ? > Yes : one matrix is one thing. Dont make yourself > more stupid that you > are ... wrong , a matrix is a collection of things. dont make yourself more stupid 'than' you are. its 'than' not 'that' btw. This is cute. Not only the fact that your substantive response is just butt-wrong, but also this silly little typo flame, only seven minutes after you posted the following: ,---- | you always blaim me for not willing to learn. | | | but your replies are like ; | | you cant read | | your wrong as always | | etc | | but you dont teach or explain anything. | | even if i am willing to learn , you dont post math , you just insult me. `---- How many misspellings can we find here? And grammar errors? Bad punctuation? (I will even ignore the juvenile refusal to use capitalization.) [...] you didnt. your making that up. Oooh, look! Two more silly mistakes in the same post. -- I was driving down the interstate through Winslow, Arizona, I had Seven Vices on my mind -- Sloth and Avarice, Fornication, Television, Whiskey, Beer and Wine. -- Austin Lounge Lizards === Subject: Re: Would You Agree With This Statement? > Rather than be confused, why can't you look it up? free information on the internet is not always reliable. Right. So rather than depend on free information on the internet, you seek answers on Usenet. It's good that you no longer depend on free internet from the internet. -- Puts his arm around you, fiddles with your hair. You know, and he says, come on, you know, just because you like a bit of a kiss and a cuddle with another man doesn't make you gay. Which, you know, I've thought a lot about. But I think it does. I think it does. --- The Office (interviews) === Subject: Re: Problem sketching the graph of a certain quadratic In sci.math, Albert I'm now doing the next year's work from an older friend who used this > material, which means that it's not about missing classes; I'm on > holidays right now trying to teach myself this without a teacher! y = 8 - 2x + x^2 > y = x^2 - 2x + 8 Roots: x = 4, -2 > y-intercept: (0, 8) > Vertex: (1, 7) I haven't shown my working for the above 3 calculations b/c it really > isn't all that interesting... > How am I supposed to sketch this graph when the y-intercept is higher > than the 'minimum' vertex? Albert Try looking at it this way: y = (x^2 - 2x + 1) + 7 = (x - 1)^2 + 7 -- #191, ewill3@earthlink.net Useless C++ Programming Idea #889123: std::vector<...> v; for(int i = 0; i < v.size(); i++) v.erase(v.begin() + i); === Subject: Re: JSH: So why all the arguing? posting-account=oic_hBAAAADwHlOl7o5rnP5SdDbVmME4 The Narcissist as Know-it-all http://health.groups.yahoo.com/group/narcissisticabuse/message/4945 Grandiosity, Fantasies, and Narcissism http://health.groups.yahoo.com/group/narcissisticabuse/message/4923 === Subject: complements of normal subgroup conjugate? posting-account=-LXWxQoAAABcNxyUcQ6v3yytgGBuHiI5 Browser; .NET CLR 1.0.3705; .NET CLR 1.1.4322; Media Center PC 4.0; InfoPath.2; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) Let N be a normal subgroup of G and let H and K be subgroups of G. I found out that: 1. [[H complement of N] & [H and K conjugate]] -> K complement of N 2. H and K complements of N -> H and K isomorphic (If h belongs to H and h=nk for n in N and k in K then h->k is an isomorphism from H to K) Question: If H and K are complements of N can it be proved then that they are conjugate? If not then can you provide a counterexample? === Subject: Re: complements of normal subgroup conjugate? posting-account=suWj4AkAAADE1IvGmj55Nmq3f98qb17e 2.0.50727),gzip(gfe),gzip(gfe) > Let N be a normal subgroup of G and let H and K be subgroups of G. I > found out that: > 1. [[H complement of N] & [H and K conjugate]] -> K complement of N > 2. H and K complements of N -> H and K isomorphic > (If h belongs to H and h=nk for n in N and k in K then h->k is an > isomorphism from H to K) Question: If H and K are complements of N can it be proved then that > they are conjugate? > If not then can you provide a counterexample? *************************************************************** Let G = ~ the Klein group, and let N = , H = , K = ... Tonio === Subject: Re: complements of normal subgroup conjugate? posting-account=-LXWxQoAAABcNxyUcQ6v3yytgGBuHiI5 Gecko/2008120122 Firefox/3.0.5,gzip(gfe),gzip(gfe) > Let N be a normal subgroup of G and let H and K be subgroups of G. I > found out that: > 1. [[H complement of N] & [H and K conjugate]] -> K complement of N > 2. H and K complements of N -> H and K isomorphic > (If h belongs to H and h=nk for n in N and k in K then h->k is an > isomorphism from H to K) > Question: If H and K are complements of N can it be proved then that > they are conjugate? > If not then can you provide a counterexample? *************************************************************** Let G = ~ the Klein group, and let > N = , H = , K = ... Tonio Henk === Subject: Re: Amateurs are trying genetic engineering at home (AP) posting-account=rsfFvAoAAADqHCqmunbjtmaKjfuP-pwP .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; InfoPath.1; .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) >Amateurs are trying genetic engineering at home (AP) >http://tech.yahoo.com/news/ap/20081226/ap_on_hi_te/do_it_yourself_dna_ > 5 > The equipment part of basic molecular biology is absolutely no > problem. Almost everything can be build for next to nothing > or bought cheaply off eBay. > The real trouble is chemicals where the problem is two-fold, > buying them and disposing them off. Almost all mainstream > suppliers won't sell to individuals, limiting availability greatly. All you've got to do is give your home business a corporate sounding > name. > The disposal is a bigger trouble. To be 100% legit, any basement > operation would still be required to dispose off things properly. > Which isn't easy at all as far as state/city regulations go. Add to > it arcane biosafety disposal rules and you've got nothing but > trouble. Go away, BR. I do not mind thick people, but there is something about you that makes me sniff the air and then move away. Stoopid Fridge, etc. are just rather silly persons. You are unpleasantly ingratiating. We all pick up the tab for you: don't waste our money! Get help! If we put a gun in the study and a bottle of lemonade, you would be puzzled all to Hell. Col. Frobisher: I keep listening for a a shot: what is his problem? Adjutant: Lemonade, sir. Would you mind if we got some more in? -- foolsrushin. 'I'll never get to heaven if you break my harp..' > You are SICK! Go away; find help! > -- > foolsrushin. Occidental is a self-centered oddity; Sapient Fridge is simply thick; > you are EVIL. > -- > foolsrushin. A first cousin on my mother's side, a priest, worked in Ghana but now works in Nigeria. He has just left for Edinburgh, having spent Christmas with us. He is a qualified librarian, but also gave a few interesting talks here on earlier visits. About 1980, he attended one of my Ban-the-Bomb meetings. There was a nasty person there, hung around, trying to attract attention. Strange, like you. I wondered ... . Someone looking from inside someone. My cousin took one look at him ... . He told me that 'possession' is quite commonplace, and can normally be told from the eyes, 'which will seemingly look out of somebody elses's body, and have an unatural colour and a cunning look'. Reading Russell, Kant, Ayer, Ryle, Strawson, etc., did I take him seriously. Of course not! But now I do! > You are SICK! Go away; find help! > -- > foolsrushin. Occidental is a self-centered oddity; Sapient Fridge is simply thick; > you are EVIL. > -- > foolsrushin. A first cousin on my mother's side, a priest, worked in Ghana but now works in Nigeria. He has just left for Edinburgh, having spent Christmas with us. He is a qualified librarian, but also gave a few interesting talks here on earlier visits. About 1980, he attended one of my Ban-the-Bomb meetings. There was a nasty person there, hung around, trying to attract attention. Strange, like you. I wondered ... . Someone looking from inside someone. My cousin took one look at him ... . He told me that 'possession' is quite commonplace, and can normally be told from the eyes, 'which will seemingly look out of somebody elses's body, and have an unatural colour and a cunning look'. Reading Russell, Kant, Ayer, Ryle, Strawson, etc., did I take him seriously. Of course not! But now I do! http://uk.youtube.com/watch?v=v6k1lml4AvE You'll never get to heaven if YOU break my heart! -- foolsrushin. === Subject: Whether solution exists posting-account=JkOS_woAAABgjIl8MXvjOZJaNfHcjTD9 AppleWebKit/525.19 (KHTML, like Gecko) Chrome/1.0.154.36 Safari/525.19,gzip(gfe),gzip(gfe) hi, some code and found that it always exists for random permutations. Can you find non negative integers 0<=a1,a2,a3,a4,a5,a6 <100 such that { sum (i=0 to 6) |xi| } <> 0 and | x0 + { sum(i=1 to 6) xi*sqrt(ai) } | < 10^-4 doesn't have solution for integers |xi| < 10 . I tried writing some code but i always find a solution. Can anyone tell me why i can always find a solution in this case or do we have a integer vector ai so that the solution doesn't exist. Below is my code . It can be useful if you want to check try couple of values. http://codepad.org/NCljunTJ === Subject: Re: Whether solution exists posting-account=HR1dqAkAAAA9E7mXiqvduHAelsrIxH3e Gecko/20071127 Firefox/2.0.0.11,gzip(gfe),gzip(gfe) > hi, > some code and found that it always exists for random permutations. Can you find non negative integers 0<=a1,a2,a3,a4,a5,a6 <100 such > that { sum (i=0 to 6) |xi| } <> 0 > and > | x0 + { sum(i=1 to 6) xi*sqrt(ai) } | < 10^-4 doesn't have solution > for integers |xi| < 10 . I tried writing some code but i always find a solution. Can anyone > tell me why i can always find a solution in this case or do we have a > integer vector ai so that the solution doesn't exist. Below is my code . It can be useful if you want to check try couple of > values.http://codepad.org/NCljunTJ I doubt you will find a proof except by exhaustive testing. Clearly you can find a number to replace 10^-4 which will make it fail. It is not surprising that there is usually an answer. If you consider the fractional part of xi*sqrt(ai), they will be scattered around (0,1) reasonably uniformly. You have 18 choices for each xi, so there are 18^6 fractional parts for each set of ai's. This is about 34 million tries and 1/5000 of the tries should succeed-if I read you correctly there is no bound on x0, so if the fractional part is in (0,10-4) or in (.9999,1) you succeed. For a random set of xi's you have a .9998^(18^6) chance of failure, which is about 10^-29572. If any ai is a square or two are equal there will be a trivial solution, so you have C(90,6) sets of ai, or about 623 million. The chance of failure even with this many is vanishingly small. Use M for million below. Ignoring small factors like e, we can estimate how small we can make your 10^-4 and still be likely to always have a solution. Let b be the allowable miss distance (instead of 10^-4). Then we want (1-2b)^(18^6)*623M=.5. Taking natural logs of both sides, ignoring ln(2), and using ln(1-x)=-x for small x, we get b=ln(623M)/68M=20/68M so we would expect always to have a solution withing 10^-6 or so. === Subject: Re: Well ordering of reals > I read somewhere that reals are well ordered, without AC. Is it >true?. The statement does not make sense. It is false that the STANDARD order > of the reals is a well order, so saying the reals are well ordered, > without specifying an order, is wrong, whether or not you say with > AC or without AC. > Any references?. And also a small explanation if possible >please. I am quiet surprised that reals can be well ordered. The existence of a well ordering of the reals is not provable in ZF > without AC, as far as I know, though weaker axioms than AC, or > alternative axioms to AC, may very well imply it. Without knowing > exactly what you read, and given that you already seem to have garbled > your recollection, there is really no way to say what it is you read. > A semantic aside - or perhaps a piece of nonsense - There is a well ordering of the Reals, with or without the AxC. A well-ordering in ZFC is also a well ordering in ZF. As you correctly state, and the OP does not, its not about the existence of a well ordering but proving it exists. And even then, the proof is non-constructive ... === Subject: Re: Well ordering of reals > A semantic aside - or perhaps a piece of nonsense - There is a well ordering of the Reals, with or without the AxC. A > well-ordering in ZFC is also a well ordering in ZF. As you correctly > state, and the OP does not, its not about the existence of a well > ordering but proving it exists. And even then, the proof is > non-constructive ... What do you mean by a well-ordering in ZFC or a well-ordering in ZF? Your semantic aside is somewhat obscure. -- Aatu Koskensilta (aatu.koskensilta@uta.fi) Wovon man nicht sprechen kann, dar.9fber muss man schweigen - Ludwig Wittgenstein, Tractatus Logico-Philosophicus === Subject: This is not a joke!I am Isaac Newton!I am the Messiah!Ezra posting-account=xwEr8woAAADNTR7bLkqvcnWcyW7UbU2M Presto/2.1.1, DynaWeb http://www.dit-inc.us/disclaimer.php,gzip(gfe),gzip(gfe) Israel during the nation with the Western European nation,I am Isaac Newton! I am sorry for my safety, I do not have so much time to play in English made up of; invite you to the future You see it's Jesus! Your life and death has nothing to do with me! I am just a book describing the figures, the Jewish Messiah, the true Messiah, I just want to protect the Jews! Moderator: Hello hotline listeners, I am linked Wei I am: I am Mr. Guangzhou Moderator: Mr. Guangzhou, please I: Israel during the nation with the Western European nation This should be my last time in the voice of Radio Free Asia, the following information than the Dead Sea Scrolls, found that the more important, I have no doubt that the existence of a harbinger, allow me to get well prepared for the rapidly after the finish. My birth to death as early as 500 years ago was full of prophecy, I do not think I have the ability to say here's a lie. Prophet predicted that the major Israeli history has occurred, they have all been in me all come true, I really Really Is that all Jews have been waiting for the Messiah, Jesus the son of evil aliens to take my name came to the use of high technology to deceive all the people, so that the Jewish nation cast a unredressed injustice, which as early as before Christ Written on after the Bible Code in the. I have never been a Christian, I do not believe in Jesus has always been, I am not a Muslim, I never Jiubu Xin Mohammed. I was discriminated against Jews because they A Offended God, God abandoned the law in the near future to become the king of the Jews and I certainly will be in accordance with God's will you come back to correct. I like the psychological and moral England with a person exactly the same, but it is in the soul On the cause of this is entirely in religious beliefs other than. Jesus, Muhammad two big liar distorts the image of God and humanity and the contract, God is never to use intermediaries, God is there is no body of Since the ultra - However, with the power of a miracle. Likely in the near future I am going to be a prophet, a great scholar and the king. I really was, Old Testament and all of the century and John Apocalypse and after the Bible Code The prediction , Also a prophet to predict that the future since ancient times, no one's reputation can be compared with me. Israel's many prophets have long predicted that the metaphorical to my life, the people of Israel, and so I had more than 3000 years, from the I In the end who up to now, four in this book to be able to predict, for my safety, I can only tell you all come true in me, and I was all century, predicted that into the grave to another person , As a result of It must be said that my life is totally your year. Prophets of Israel is usually around things metaphorical familiar with the way God communicated to us in the Old Testament by the book to see what All Is metaphorical. Dead Sea Scrolls, predicted that the Messiah is a very strong power of the Messiah, the facts have proven that Jesus is only so-called alien made out of a God, is the so-called non-alien According to Jia Sisuo According to the literal interpretation created a big liar, by the so- called Virgin born and the bar is a serious departure from the hands and feet, the Dead Sea Scrolls, the so-called Christ's true, the Dead Sea Scrolls, and predicted that actually metaphor to point to me I will explain to you to listen to; in the Dead Sea Scrolls, predicted that will lead to all of the Jewish king was referring to me, Ma predicted to spend is the so-called alien masterpiece, John Revelation Recorded Author and we will never know his true identity, but he must not believe Jesus was a Jewish prophet, he is not written in Jesus before. In addition to the John Apocalypse, New is not credible It Repeat of the Dead Sea Scrolls, a lot of content, should be John Apocalypse and all of the century and Where Paul Huang predicted that the first into the Dead Sea Scrolls, will be composed of books that they can Known as the saint After. Maya from the books, I think the so-called ancient alien is subject to the punishment of God, fled to the vicinity of the Earth, large-scale can not breed, can not re-adapt to the environments of the Earth's ancient humans, they must be separated for some To be back at the time of the earth to supply requirements, the Earth is the only supplies they needed, the extinction of species on Earth, they can not survive; it is not so-called human-made is. Darwin once said , Found that as long as there is a kind of biological evolution in the body can not get the small parts, then his theory of evolution completely bankrupt, modern science has proven that the theory of evolution is wrong. Indeed, human beings by God Created by God has no physical strength and the supernatural miracle, because God promised in the universe formed a protein component, to land on Earth, to have had a wonderful variety of biological machine, and then a miracle Have had a variety of species like the DNA, culminating in a variety of species; As this is miraculous, I can assure you that life on Earth in the universe is indeed unique. Reference from the Falun Gong cult Toru save the world poem. Zhu century in a poem: After 500 years of attention to the people of the world, his presence is an honor that era, the great moment of inspiration in the emergence of the century with the people who have been great over Enough. , As in I do not know completely in any predictions that I said to you in the end who, while a few months later I found that as early as in a long time ago and I have long predicted would be his own regeneration, and my life as early as On the whole in mind I have set out in the definition of the Bible. Appearance from the point of view, I would definitely not a personal copy, I met the teachings of Judaism, I was absolutely out at the so- called alien unexpected. I advocate Fate By day, into the subject, predicted the existence of what I did not constitute any impact. I just did not say what, in a long time ago I spent more than 50 years, to break the Old Testament and all the prophets Predicted, I lost To the memory of the past, now I really do not know what I[CapitalEth]«'è[CapitalEth][Copyrigh t].b2Ì«, I finally know that I was his, which took place from me as a miracle, a miracle and this has long been hidden in the writing My Under the definition of the Bible, I will explain to you listen to, no one is better qualified than I see before me in the end[CapitalEth]«'è[CapitalEth][Copyri ght].b2Ì«, I think, in fact did not dare open a large number of these books, The Vatican Gang Holy See's religious leaders have long known but Jesus was a liar and who I am. There is no doubt that faith in God is my whole life, in accordance with the Old Testament as provided for in the book of God, the Jews must paste I legislation for the king of the Jews, I have to be in accordance with God to the people of Israel to come back to correct; I am really looking forward to is that the Jews have been the Messiah, I must abide by God's strong Israel, all Mu Gosling is not a place to stay out of Palestine, to lead you to the upcoming terrorist deal with a major disaster. Moderator: President of Guangzhou, the time has come I: Good-bye Moderator: Good-bye I: Good-bye ****************** It still does not understand the difference between fighting Israel and pouring concrete ay 50C. It is a bit worse than Arabic. In Arabic it translated wst jw AlmErkp as central air battle. Correct was the climatic enviromental battle in other words one factor being the rapid setting of concrete at 50C. In Arabic I have an independent reference in Buckwalter's dictionary (I use his transliteration system). - Ian Parker Isaac Newton 27 December 2008 Hotline listeners, presided over by linked Wei. Broadcast time: 0:00 Beijing Time every Tuesday to the point, two points to three points, 4:00 to 5:00. Every Wednesday through Saturday, 0:30 assigned 1:30, 4:00 to 5:00. Every Monday to Friday 12:00 to 13:00. Toll-free hotline 10810-888 275 7655,You can call the hotline to ask show host, he can prove that! I hasten to Logout, or else I will have life-threatening! http://www.rfa.org/mandarin/zhuanlan/tingzhongrexian 2.46 After great trouble for humanity, a greater one is prepared, The Great Mover renews the ages. Rain, blood, milk, famine, steel and plague, Is the heavens fire seen, a long spark running. 10.42 The humane realm of Angelican offspring, It will cause its realm to hold to peace and union. War half-captive in its enclosure, For long will it cause them to maintain peace. 4.56 After the victory of the raving tongue, The spirit tempered in tranquillity and repose: Throughout the conflict the bloody victor makes orations, Roasting the tongue and the flesh and the bones. Isaac Newton 30 December 2008 This is what I sent late Christmas present. Cities of Babylon refers to China! I was writing a book, it is called Mein Kampf. Isaac Newton 30 December 2008 I really Isaac Newton,I will soon be in Jerusalem! I just want to inform you of other Jews, Ezra. Isaac Newton 30 December 2008 1.16 A scythe joined with a pond in Sagittarius£Â at its highest ascendant. Plague, famine, death from military hands£Â the century approaches its renewal. 4.56 After the victory of the raving tongue, The spirit tempered in tranquillity and repose: Throughout the conflict the bloody victor makes orations, Roasting the tongue and the flesh and the bones. 10.74 The great seventh numberÁøs revolution, It will appear a time of the year for hecatomb. Not far from the great millennial age, When those can enter will leave the tomb. 2.46 After great trouble for humanity, a greater one is prepared, The Great Mover renews the ages. Rain, blood, milk, famine, steel and plague, Is the heavens fire seen, a long spark running. 5.84 He will be born of the gulf and unmeasured city, Born of obscure and dark family. He who the revered power of the great King, Will want to destroy through Rouen and Evreux. 10.72 The year 1999, seventh month, To bring back to life the great King of Angolmois, Before and after Mars to reign by good luck. 4.31 The Moon in the full of night over the high mountain, The new sage with a lone brain sees it. By his disciples invited to be immortal, Eyes to the south. Hands in bosoms, bodies in the fire. 10.70 Long awaited he will never return, In Europe, he will appear in Asia. One of the league issued from the great Hermes, And he will grow over all the Kings of the East. 3.94 For five hundred years more one will keep count of him, Who was the ornament of his time. Then suddenly great light will he give, He who for this century will take them back very satisfied. 10.42 The humane realm of Angelican offspring, It will cause its realm to hold to peace and union. War half-captive in its enclosure, For long will it cause them to maintain peace. 8.27 The auxiliary way, one arch upon the other£Â Many deserted except for the brave one and his genet. The writing of the Phoenix Emperor£Â seen by him which is (shown) to no other. 2.29 The Easterner will leave his seat£Â To pass the Apennine mountains to see Gaul. He will transpire the sky, the waters and the snow£Â And everyone will be struck with his rod. 5.79 The sacred pomp will come to lower its aisles£Â Through the coming of the great legislator. He will raise the humble, he will vex the rebels£Â There is no emulator on the earth. 7.17 The prince who has rare pity and clemency£Â After peace his great water barrels. Will come to change by great jurisdiction of dead£Â By great recreating, reign exquisitely. 2.13 The body without soul no longer to be sacrificed£Â Day of death put for birthday. The divine spirit will make the soul happy£Â Seeing the word in its eternity. 10.71 The earth and air will freeze a very great sea£Â When they will come to venerate Thursday. That which will be never stuffed and filled so much£Â 3.92 The world near the last period£Â Saturn will come back again late. Empire transferred towards the Dusky nation£Â The eye plucked out by the Goshawk at Narbonne. Isaac Newton 29 December 2008 === Subject: This is not a joke!I am Isaac Newton!I am the Messiah!Ezra posting-account=xwEr8woAAADNTR7bLkqvcnWcyW7UbU2M Presto/2.1.1, DynaWeb http://www.dit-inc.us/disclaimer.php,gzip(gfe),gzip(gfe) Israel during the nation with the Western European nation,I am Isaac Newton! I am sorry for my safety, I do not have so much time to play in English made up of; invite you to the future You see it's Jesus! Your life and death has nothing to do with me! I am just a book describing the figures, the Jewish Messiah, the true Messiah, I just want to protect the Jews! Moderator: Hello hotline listeners, I am linked Wei I am: I am Mr. Guangzhou Moderator: Mr. Guangzhou, please I: Israel during the nation with the Western European nation This should be my last time in the voice of Radio Free Asia, the following information than the Dead Sea Scrolls, found that the more important, I have no doubt that the existence of a harbinger, allow me to get well prepared for the rapidly after the finish. My birth to death as early as 500 years ago was full of prophecy, I do not think I have the ability to say here's a lie. Prophet predicted that the major Israeli history has occurred, they have all been in me all come true, I really Really Is that all Jews have been waiting for the Messiah, Jesus the son of evil aliens to take my name came to the use of high technology to deceive all the people, so that the Jewish nation cast a unredressed injustice, which as early as before Christ Written on after the Bible Code in the. I have never been a Christian, I do not believe in Jesus has always been, I am not a Muslim, I never Jiubu Xin Mohammed. I was discriminated against Jews because they A Offended God, God abandoned the law in the near future to become the king of the Jews and I certainly will be in accordance with God's will you come back to correct. I like the psychological and moral England with a person exactly the same, but it is in the soul On the cause of this is entirely in religious beliefs other than. Jesus, Muhammad two big liar distorts the image of God and humanity and the contract, God is never to use intermediaries, God is there is no body of Since the ultra - However, with the power of a miracle. Likely in the near future I am going to be a prophet, a great scholar and the king. I really was, Old Testament and all of the century and John Apocalypse and after the Bible Code The prediction , Also a prophet to predict that the future since ancient times, no one's reputation can be compared with me. Israel's many prophets have long predicted that the metaphorical to my life, the people of Israel, and so I had more than 3000 years, from the I In the end who up to now, four in this book to be able to predict, for my safety, I can only tell you all come true in me, and I was all century, predicted that into the grave to another person , As a result of It must be said that my life is totally your year. Prophets of Israel is usually around things metaphorical familiar with the way God communicated to us in the Old Testament by the book to see what All Is metaphorical. Dead Sea Scrolls, predicted that the Messiah is a very strong power of the Messiah, the facts have proven that Jesus is only so-called alien made out of a God, is the so-called non-alien According to Jia Sisuo According to the literal interpretation created a big liar, by the so- called Virgin born and the bar is a serious departure from the hands and feet, the Dead Sea Scrolls, the so-called Christ's true, the Dead Sea Scrolls, and predicted that actually metaphor to point to me I will explain to you to listen to; in the Dead Sea Scrolls, predicted that will lead to all of the Jewish king was referring to me, Ma predicted to spend is the so-called alien masterpiece, John Revelation Recorded Author and we will never know his true identity, but he must not believe Jesus was a Jewish prophet, he is not written in Jesus before. In addition to the John Apocalypse, New is not credible It Repeat of the Dead Sea Scrolls, a lot of content, should be John Apocalypse and all of the century and Where Paul Huang predicted that the first into the Dead Sea Scrolls, will be composed of books that they can Known as the saint After. Maya from the books, I think the so-called ancient alien is subject to the punishment of God, fled to the vicinity of the Earth, large-scale can not breed, can not re-adapt to the environments of the Earth's ancient humans, they must be separated for some To be back at the time of the earth to supply requirements, the Earth is the only supplies they needed, the extinction of species on Earth, they can not survive; it is not so-called human-made is. Darwin once said , Found that as long as there is a kind of biological evolution in the body can not get the small parts, then his theory of evolution completely bankrupt, modern science has proven that the theory of evolution is wrong. Indeed, human beings by God Created by God has no physical strength and the supernatural miracle, because God promised in the universe formed a protein component, to land on Earth, to have had a wonderful variety of biological machine, and then a miracle Have had a variety of species like the DNA, culminating in a variety of species; As this is miraculous, I can assure you that life on Earth in the universe is indeed unique. Reference from the Falun Gong cult Toru save the world poem. Zhu century in a poem: After 500 years of attention to the people of the world, his presence is an honor that era, the great moment of inspiration in the emergence of the century with the people who have been great over Enough. , As in I do not know completely in any predictions that I said to you in the end who, while a few months later I found that as early as in a long time ago and I have long predicted would be his own regeneration, and my life as early as On the whole in mind I have set out in the definition of the Bible. Appearance from the point of view, I would definitely not a personal copy, I met the teachings of Judaism, I was absolutely out at the so- called alien unexpected. I advocate Fate By day, into the subject, predicted the existence of what I did not constitute any impact. I just did not say what, in a long time ago I spent more than 50 years, to break the Old Testament and all the prophets Predicted, I lost To the memory of the past, now I really do not know what I[CapitalEth]«'è[CapitalEth][Copyrigh t].b2Ì«, I finally know that I was his, which took place from me as a miracle, a miracle and this has long been hidden in the writing My Under the definition of the Bible, I will explain to you listen to, no one is better qualified than I see before me in the end[CapitalEth]«'è[CapitalEth][Copyri ght].b2Ì«, I think, in fact did not dare open a large number of these books, The Vatican Gang Holy See's religious leaders have long known but Jesus was a liar and who I am. There is no doubt that faith in God is my whole life, in accordance with the Old Testament as provided for in the book of God, the Jews must paste I legislation for the king of the Jews, I have to be in accordance with God to the people of Israel to come back to correct; I am really looking forward to is that the Jews have been the Messiah, I must abide by God's strong Israel, all Mu Gosling is not a place to stay out of Palestine, to lead you to the upcoming terrorist deal with a major disaster. Moderator: President of Guangzhou, the time has come I: Good-bye Moderator: Good-bye I: Good-bye ****************** It still does not understand the difference between fighting Israel and pouring concrete ay 50C. It is a bit worse than Arabic. In Arabic it translated wst jw AlmErkp as central air battle. Correct was the climatic enviromental battle in other words one factor being the rapid setting of concrete at 50C. In Arabic I have an independent reference in Buckwalter's dictionary (I use his transliteration system). - Ian Parker Isaac Newton 27 December 2008 Hotline listeners, presided over by linked Wei. Broadcast time: 0:00 Beijing Time every Tuesday to the point, two points to three points, 4:00 to 5:00. Every Wednesday through Saturday, 0:30 assigned 1:30, 4:00 to 5:00. Every Monday to Friday 12:00 to 13:00. Toll-free hotline 10810-888 275 7655,You can call the hotline to ask show host, he can prove that! I hasten to Logout, or else I will have life-threatening! http://www.rfa.org/mandarin/zhuanlan/tingzhongrexian 2.46 After great trouble for humanity, a greater one is prepared, The Great Mover renews the ages. Rain, blood, milk, famine, steel and plague, Is the heavens fire seen, a long spark running. 10.42 The humane realm of Angelican offspring, It will cause its realm to hold to peace and union. War half-captive in its enclosure, For long will it cause them to maintain peace. 4.56 After the victory of the raving tongue, The spirit tempered in tranquillity and repose: Throughout the conflict the bloody victor makes orations, Roasting the tongue and the flesh and the bones. Isaac Newton 30 December 2008 This is what I sent late Christmas present. Cities of Babylon refers to China! I was writing a book, it is called Mein Kampf. Isaac Newton 30 December 2008 I really Isaac Newton,I will soon be in Jerusalem! I just want to inform you of other Jews, Ezra. Isaac Newton 30 December 2008 1.16 A scythe joined with a pond in Sagittarius£Â at its highest ascendant. Plague, famine, death from military hands£Â the century approaches its renewal. 4.56 After the victory of the raving tongue, The spirit tempered in tranquillity and repose: Throughout the conflict the bloody victor makes orations, Roasting the tongue and the flesh and the bones. 10.74 The great seventh numberÁøs revolution, It will appear a time of the year for hecatomb. Not far from the great millennial age, When those can enter will leave the tomb. 2.46 After great trouble for humanity, a greater one is prepared, The Great Mover renews the ages. Rain, blood, milk, famine, steel and plague, Is the heavens fire seen, a long spark running. 5.84 He will be born of the gulf and unmeasured city, Born of obscure and dark family. He who the revered power of the great King, Will want to destroy through Rouen and Evreux. 10.72 The year 1999, seventh month, To bring back to life the great King of Angolmois, Before and after Mars to reign by good luck. 4.31 The Moon in the full of night over the high mountain, The new sage with a lone brain sees it. By his disciples invited to be immortal, Eyes to the south. Hands in bosoms, bodies in the fire. 10.70 Long awaited he will never return, In Europe, he will appear in Asia. One of the league issued from the great Hermes, And he will grow over all the Kings of the East. 3.94 For five hundred years more one will keep count of him, Who was the ornament of his time. Then suddenly great light will he give, He who for this century will take them back very satisfied. 10.42 The humane realm of Angelican offspring, It will cause its realm to hold to peace and union. War half-captive in its enclosure, For long will it cause them to maintain peace. 8.27 The auxiliary way, one arch upon the other£Â Many deserted except for the brave one and his genet. The writing of the Phoenix Emperor£Â seen by him which is (shown) to no other. 2.29 The Easterner will leave his seat£Â To pass the Apennine mountains to see Gaul. He will transpire the sky, the waters and the snow£Â And everyone will be struck with his rod. 5.79 The sacred pomp will come to lower its aisles£Â Through the coming of the great legislator. He will raise the humble, he will vex the rebels£Â There is no emulator on the earth. 7.17 The prince who has rare pity and clemency£Â After peace his great water barrels. Will come to change by great jurisdiction of dead£Â By great recreating, reign exquisitely. 2.13 The body without soul no longer to be sacrificed£Â Day of death put for birthday. The divine spirit will make the soul happy£Â Seeing the word in its eternity. 10.71 The earth and air will freeze a very great sea£Â When they will come to venerate Thursday. That which will be never stuffed and filled so much£Â 3.92 The world near the last period£Â Saturn will come back again late. Empire transferred towards the Dusky nation£Â The eye plucked out by the Goshawk at Narbonne. Isaac Newton 29 December 2008 === Subject: I am Isaac Newton!You are able to understand the following evidence, you will not doubt my identity!Radio Free Asia!Ezra posting-account=xwEr8woAAADNTR7bLkqvcnWcyW7UbU2M Presto/2.1.1, DynaWeb http://www.dit-inc.us/disclaimer.php,gzip(gfe),gzip(gfe) === Subject: Re: Carbon footprint questions All experience is subjective. What we call 'facts' are subjective > experiences *we agree on*. In the case of unique experiences, we have a real problem. OOB experiences are however sufficiently common that one should possibly > give some statistical weight to their commonality, without going as far as > deciding what if anything they mean. > 'Statistical weight' by itself would be fine; alas, people want to take prevalence and join it to *interpretative significance* -- and that needs to be fought where the hidden agenda is to impose a counter-empirical world view and a wish-fulfilment metaphysics. Look, if someone has a supposedly OoBE and correctly reports a non-trivial, statistically improbable observation from a vantage point outside their body, then that's a highly significant discovery with potential importance to many scientific and social fields. But if a million people report the experience *without the observation*, then what we have is a commonly experienced hallucination, interesting in itself, but with no real significance to anyone except neurologists. Giaccomo. === Subject: Re: Carbon footprint questions > All experience is subjective. What we call 'facts' are subjective > experiences *we agree on*. > In the case of unique experiences, we have a real problem. > OOB experiences are however sufficiently common that one should possibly > give some statistical weight to their commonality, without going as far as > deciding what if anything they mean. 'Statistical weight' by itself would be fine; alas, people want to take > prevalence and join it to *interpretative significance* -- and that needs to > be fought where the hidden agenda is to impose a counter-empirical world > view and a wish-fulfilment metaphysics. Look, if someone has a supposedly OoBE and correctly reports a non-trivial, > statistically improbable observation from a vantage point outside their > body, then that's a highly significant discovery with potential importance > to many scientific and social fields. But if a million people report the > experience *without the observation*, then what we have is a commonly > experienced hallucination, interesting in itself, but with no real > significance to anyone except neurologists. > Exactly. However there have been - though I cant remember where the data is - several cases of people reporting in stuff that they shouldn't have been able to know about. It's not beyond the bounds of trickery though, so it pays not to get too excited. In my own mind the very few far more dilute experiences of oddities are enough to convince me that a rationalist materialist model is probably not the easiest way to start to look at these areas, but equally, I wouldn't expect anyone to take my word for it. Its always trouble when you start deciding if the material world is a function of perception, or vice versa ;-) > Giaccomo. === Subject: Ellipsoid radii Given is a unit sphere in R^n. I transform the points by an n x n-matrix to get an ellipsoid. Now the problem is to find the lengths (that is, directions can be ignored) of the (principal?) axes of the ellipsoid. I already know that the transformed ellipsoid is given by: x^T L^-1 L^-T x = 1 If we denote S = L^-1 L^-T, then what I am looking would be the eigenvalues of S. However, I wonder if I could somehow avoid computing the eigen-decomposition? This is for a graphics program so performance is of concern. -- http://kaba.hilvi.org === Subject: Re: Ellipsoid radii > To compute the eigenvalues without computing the eigenvectors, > use the characteristic polynomial. True. During this day I found that I need the eigenvectors after all, making my post a bit irrelevant for the problem... -- http://kaba.hilvi.org === Subject: Re: Eight inches of snow, <95dc2$49526107$49e5d6b$24786@DIALUPUSA.NET> <6bq4l45nllpit0q8j4rfu51m0j0fuej191@4ax.com> <21f1c$49590960$cdd08505$26081@DIALUPUSA.NET> posting-account=I3BSGAoAAADBa0hVQRltLB3YrdNlBH-l CLR 2.0.50727; .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) >I see the people from Mensa are included in the newsgroup header so >how it comes to be that I am now reduced to explaining how daily >rotation is related to the images of star trails and 'rotational >orientation (tilt) is remarkable in itself. >wreck.org.mensa has few of mensa caliber reading or posting. >It's not much different from the make believe scientists >posting so frequently to the sci newsgroups. Rather has >to do with eternal September, I'm afraid. >I am genuinely dismayed at the inability to interpret the images of >Uranus which allow for planetary comparisons in order to extract a >better understanding of what causes the seasons on Earth and as a >point of departure for climate studies. >Well don't be. I covered this aspect in my discussion >that included obvious to you. I am supportive of your >view, but not of the obviousness you attribute to it. >You originally stated that >little is known regarding the cause climate change >I never did quite say that. I've skirted around the edges >while attempting to impart the idea that there are so very >many factors we cannot be certain we really understand >all of the interactions. This is not a simple more heat >in brings about linear changes problem. >and whether it is >a human influenced thing or naturally occuring and I concur with the >additional information demonstrating just how little is actually known >to the point that not even the basic seasonal cycle is explained >correctly. >This and long term weather prediction combine to bring >about the origin of Chaos theory, in fact. > In this respect,the problem may not be climate change alone >but actually those investigating the matter for if you ask them what >the dynamic is for the Earth's seasons they will exclaim 'Tilt' ! (or >disguise it as 'obliquity) without the slightest regard for physical >considerations of that statement. >Many people have a favorite religion. >Ultimately it is not all about climate,global warming ect but rather >the genuine enjoyment of observations which modern imaging allows and >putting images in context - >http://astro.berkeley.edu/~imke/Infrared/UranusAo/ur time 2001 2005.jpg >Do you have any idea how long it takes to download something >like this with an exchange rate of 2.0 to 3.5 k/sec. I can't >do it. >Modern imaging offers a way out of a mess that men have created for >themselves,the insights are just as spectacular,the consequences are >just as important but it all relies on whether people can intepret the >images and put them in correct context such as using planetary >comparisons to extract a correct explanation for seasonal variations. >And still, that's *not* all there is. Please come back >to this subject once you've solved the much simpler >3 body problem. >Please feel free to start here. >http://www.nist.gov/dads/HTML/unsolvableProblem.html-Hide quoted text - >- Show quoted text - > You know,I have been working on the rotational dynamics of the > interior of the Earth,specifically differential rotation of the > viscous interior composition,as it applies to the enormous 40 KM > planetary spherical deviation while I see people casually talk of > 'tidal friction' slowing the Earth down as a means to account for the > 'leap second' adjustment.It is a question of taste and just as you not > find rotational dynamics exciting I most certainly do. I think rotational dynamics fascinating, actually. However > I disagree with any significance that could be lent to the > differential rotation theory where it comes to the earth. > You complained about not being able to discuss things with me and there is a very good reason because it means I have to descend to a level I am not entirely comfortable with.Differential rotation in stars is not a theory,an opinion or a guess but rather an observation, hence a direct correlation between maximum Equatorial speed,differential rotation and the degree of spherical deviation of a star.The enormous 40 Km spherical deviation of our planet and the details of the rotational dynamics via differential rotation as it applies to planetary shape work equally well with crustal motion and evolution but this is my private work as the motions of the Earth do not figure in the reasoning of any person I have ever met.The best 'theory' for plate motion is a stationary Earth concept - 'thermally driven convections cells',something I could not spend 5 minutes thinking about considering it creates more problems than it solves. > Lest you go off on a tirade about this subject, I'm not > going to engage you further on this topic as I am slowly > winding down these conversations and prefer not to dwell > on additional topics not already in play. > You did not even begin,there is nothing to distinguish you from any of the rest - a brief attempt to sound like an individual followed by personal judgements hardly constitutes a technical discussion I require.How that error regarding the premise and conclusion for daily rotation in 23 hours 56min snowballs into even department of celestial and terrestrial phenomena and basically poisins the ability to reason properly. > The great thing about differential rotation is that it is an observed > generalised principle for all rotating celestial bodies with a viscous > composition whereas dynamicists currently exempt the Earth from > rotational dynamical influences in organizing the Earth's interior > around thermally driven 'convection cell' which require no reference > to planetary shape or motion.The bonus is that differential rotation > replaces 'convection cells' as the dynamic for crustal motion or > evolution. Yet another model with potentially no relevance to reality? > Consider Escher's waterfall. > 3 body problem ? - sorry !,neither know about it or care about it even > if you find it exciting. No surprise there. But I'm glad to see you're finally > substituting a person's interest, a valid construct, > for your earlier misplaced negativity about people's > intelligence. Intelligence, you must agree, has nothing to do with > what a person's interests are.- Hide quoted text - - Show quoted text - === Subject: Re: Eight inches of snow, [...] > You complained about not being able to discuss things with me and No I didn't. You're making this up, you poor thing. > there is a very good reason because it means I have to descend to a > level I am not entirely comfortable with. This is doublespeak for Gee, I forgot to study for the test, can I take it some other time? [...] > You did not even begin,there is nothing to distinguish you from any of > the rest - a brief attempt to sound like an individual followed by > personal judgements hardly constitutes a technical discussion I > require. More doublespeak. You were given the opportunity to have a sentient discussion and chose this as a coverup for what has become your ineptitude. Instead of defending your position you chose petty, childish outbursts demonstrating that you are now a mere shadow of your former self, probably brains turned to mush and unworthy of being treated with respect. Go yourself. === Subject: Re: Eight inches of snow, <61f31$495a4446$cdd08535$30144@DIALUPUSA.NET> posting-account=I3BSGAoAAADBa0hVQRltLB3YrdNlBH-l AppleWebKit/525.19 (KHTML, like Gecko) Chrome/0.4.154.29 Safari/525.19,gzip(gfe),gzip(gfe) > Go yourself. That didn't take long === Subject: Re: Eight inches of snow, posting-account=gpERugkAAAB5_qKVhbO9UpGpOXFNrIYf 5.1),gzip(gfe),gzip(gfe) > ... and it's still a week until Christmas, yet blind Repugnicants deny > Climate Change. That'll be the Arctic melting. I worked in an ice cream factory many years ago as a student, > and once or twice their walk-in freezers needed maintenance or > defrosting. During those times it felt noticeably colder and > damper just outside the freezer door than when the freezer > was at its normal low temperature. The parallel should be obvious, but in case not I'll spell > it out. Counterintuitively, a melting Arctic produces colder > rainier (and, in winter, snowier) weather for a while. But it > won't last. I see. You think somebody left the door to the arctic open, Keerist! No bloody wonder this topic is bogged down in crap. Socks === Subject: Fuzzy Real Variables How does one define a fuzzy variable? Is it something like this: A fuzzy variable X has distribution given by the nondecreasing function f_X(x,t), where for any real x and t, f_X(x,t)=the degree of membership of the point x in the set (-infinity,t). Kerry Soileau === Subject: Re: Fuzzy Real Variables In my previous post, I should have been clearer and said that the function f_X(x,t) is nondecreasing in the *second* variable t. === Subject: urgent!! posting-account=wx7qGAoAAAB0QCogEj6lPbZVCFpostrd SV1),gzip(gfe),gzip(gfe) I need solution manual for Advanced Engineering Dynamics (2nd Ed., Jerry Ginsberg) === Subject: Re: JSH: No need for Galois theory Stated without proof. Prove if you can the statement that if a_1(x) is divisible > by 7 then so is d(x) and e(x), and give the ring. I know I deleted a statement where you say in any ring, > but you need to state that upfront if that is your > continued claim, as I'm clipping after anything unproven. I've seen this movie before. Isn't this the one where the hero (JSH, of course) demands to be spoon-fed every tiny, little detail; is forced (finally) to admit he was wrong; runs off and sulks for a while; then, comes back and continues to claim he was right all along (and mathematicians are evil for denying it)? No, wait... That one featured a simple (so-called) proof of Fermat's Last Theorem. Completely different movie. Carry on. Jim Burns === Subject: Re: JSH: No need for Galois theory <495A3965.7040108@osu.edu> posting-account=3WPJYgoAAAA55VjhzK9i07RN8h8u8eEs Gecko/2008092417 Firefox/3.0.3,gzip(gfe),gzip(gfe) I've seen this movie before. Isn't this the one where the hero (JSH, of course) demands > to be spoon-fed every tiny, little detail; is forced > (finally) to admit he was wrong; runs off and sulks for > a while; then, comes back and continues to claim he was > right all along (and mathematicians are evil for denying it)? No, wait... That one featured a simple (so-called) proof > of Fermat's Last Theorem. Completely different movie. Carry on. Jim Burns LOL! Yeah, well you know how most movies are these days: remakes and sequels. Most people probably enjoy them for the same reason they enjoy the JSH movie: it's easy to understand, predictable, and there's a doofus in the movie everyone can make fun of and feel superior to. M === Subject: Re: JSH: No need for Galois theory > On Dec 27, 11:23 am, William Hughes > Ok, your claim is that exactly one of a_1(x) and a_2(x) > should be divisible by 7. This claim contradicts simple algebra. > There is no need to even mention Galois theory. > - William Hughes > Then give the algebra, ok? > Consider the quadratic > a^2 - (7x-1)a + (49x^2 - 14x) = 0 > Then, if x is such that the quadratic is irreducible over > the rationals, then either both roots or neither > root is divisible by 7. > Let x be such that the quadaratic is irreducible over the rationals > and let a_1(x) and a_2(x) be the two roots. Then looking at the > quadratic formula, we see that a_1(x) = d(x) + e(x) where d(x) > is rational and e(x) is irrational or complex and that a_2(x) = > d(x) - > e(x). > If a_1(x) is divisible by 7 then so is d(x) and e(x) and therefore > a_2(x). > Stated without proof. > Prove if you can the statement that if a_1(x) is divisible by 7 then > so is d(x) and e(x), and give the ring. > Nope, I made a mistake. It's false in general. Yeah, I know. Oh, and I've already said that NEITHER of the a's can > have 7 as a factor in the ring of algebraic integers when non-rational > with rational x (note that requires integers for x to be in the ring). That's the wacky cool error! And readers keeping score should note that the poster DID eventually > run to the ring of algebraic integers. The region that provably has the error. Can't keep these little bastard in the field of complex numbers, now > can I? Guess they hate it. Why? Because in the field of complex numbers > they have no room to hold on to their delusion, that's why. Comfort. They're seeking comfort from the cold, hard mathematical > truth. So, NOT scientists, in any way shape or form. Oh yeah, a little more testy than normal as I just got an email from > the Bulletin. Not only did they reject my paper without explanation, > but the editor begged me not to send any more papers!!! I sent a nasty gram in reply. But she *deserved* it. Math people freaking go bonkers over this result. It's sad, but I > have to try to laugh so I don't cry. Next up is the Annals of Mathematics at Princeton. Then the New York > Journal of Mathematics as I begin to do the rounds, bringing in > journals so that later I can trash the entire modern academic system. Too bad Beckwith doesn't like you anymore and won't advise you on where to get crackpot papers published. (Beckwith, what a crackpot, a clampot!) I need to build up the potential energy to change it, as, um, it's > kind of big! (Oh, I forwarded her reply to Ribet and some other math dude. Thought > they needed the laugh.) Did you forward a copy to your daddy? James Harris === Subject: Re: Search for maintainer of pascal's matrix from top to bottom posting-account=n4TzyQkAAADLWxrRHqyiUZ-1SZdOB4vv AppleWebKit/525.19 (KHTML, like Gecko) Chrome/1.0.154.36 Safari/525.19,gzip(gfe),gzip(gfe) > Does someone know, whether the above site at > http://binomial.csueastbay.edu > is still maintained? The authors Matthew Hubbard and Tom Roby seem to > have no more email-adresses at csueastbay and > no new adress is provided. Could someone point me > to their mail-adress? > May be this one: http://www.math.uconn.edu/~troby/cv.pdf With friendly greetings Hero === Subject: Re: Search for maintainer of pascal's matrix from top to bottom Am 30.12.2008 16:41 schrieb Hero: > Does someone know, whether the above site at > http://binomial.csueastbay.edu > is still maintained? > The authors Matthew Hubbard and Tom Roby seem to > have no more email-adresses at csueastbay and > no new adress is provided. Could someone point me > to their mail-adress? May be this one: > http://www.math.uconn.edu/~troby/cv.pdf With friendly greetings > Hero Ahh - das sieht gut aus :-) Gottfried === Subject: Re: Search for maintainer of pascal's matrix from top to bottom Am 29.12.2008 21:52 schrieb Axel Vogt: If you get not sound answer you may try to > mail the administrative contact through Whois > see http://whois.domaintools.com/csueastbay.edu Hi Axel - in california. Neither M. Hubbard nor T. Roby seem to be affilitated with that institution presently (I didn't find them in the staff-list) but before asking the administration there I thought someone here could know a current address. So ... Gottfried === Subject: Re: Search for maintainer of pascal's matrix from top to bottom > Am 29.12.2008 21:52 schrieb Axel Vogt: > If you get not sound answer you may try to > mail the administrative contact through Whois > see http://whois.domaintools.com/csueastbay.edu > Hi Axel - in california. Neither M. Hubbard nor T. Roby seem to be > affilitated with that institution presently (I didn't find > them in the staff-list) but before asking the > administration there I thought someone here could know > a current address. So ... Gottfried Hallo Gottfried, Sure, it may be old - but admins are usually not listed and if they change, the current ones have their old predecessor on a forwarding list ... === Subject: Re: Simplest explanation, Occam's Razor unleashed > In the complex plane with 7*(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x)+ 7) where the a's are roots of a^2 - (7x-1)a + (49x^2 - 14x) = 0 you normalize: a_1(x) = b_1(x), and a_2(x) = b_2(x) - 1, as then you have 7*(175x^2 - 15x + 2) = (5b_1(x) + 7)(5b_2(x)+ 2) where b_1(0) = 0, b_2(0) = 0. With you so far... Now compare with 7*(x^2 + 3x + 2) = (7x + 7)(x + 2) and what is the primary difference? Hmmm, what is the purpose (in terms of furthering the proof you are trying to explain) in performing this comparison? I suppose it's OK to compare random expressions if we're bored or something, but there should be some conclusion at the end which helps you to continue with your proof. (I.e. with making more mathematical statements, definitions, conclusions etc.) OK, I'll carry on for now... The type of function: in one case you have non-linear functions b_1(x) > and b_2(x), and in the other you have linear functions 7x and x. Very interesting... I suggest to you that the distributive property does not care. No, it does not have feelings, true... If some yahoo told you that the 7 bounced around like a kangaroo with 7*(x^2 + 3x + 2) = (7x + 7)(x + 2) based on the value of x, you'd say they were bonkers. Sure, but only you have used this wording. Also, I don't see anything in your post above bouncing around, so I'm wondering if a chunk of your post got deleted or something? But if some Ph.D's scared of losing some math beliefs and their > precious notion that the mathematical field is immune to upheavals > bitch and moan for years against it, you believe them, and screw the > complex plane. Um, are you going to continue your proof at some point? You've asked me to compare two expressions (without telling me why), and I've done so. I've agreed that the distributive law applies to functions (and it does not have feelings), but this is all an aside - not part of a mathematical proof. I expect you'll continue your proof soon, e.g. start making more mathematical statements, or maybe conclude something from the comparison above... Simplest explanation. Oh! Is that it?! Simplest explanation of what, exactly? You have not stated or proved any conclusions!! Can you check your quoted text above to see if you've just omitted to include some lines in your post, as it doesn't make sense as it stands... Mike. === Subject: Re: Simplest explanation, Occam's Razor unleashed > But if some Ph.D's scared of losing some math beliefs and their > precious notion that the mathematical field is immune to upheavals > bitch and moan for years against it, you believe them, and screw the > complex plane. Simplest explanation. The simplest explanation is that you're wrong. After all, how many people agree with you? Maybe less than 5 and that's being generous. > None of you have the spines for the situation. You all lack the balls > to confront a massive failure by your freaking colleagues. You lack the courage to give up tilting at windmills. At the end of his life, even Don Quixote faced reality. > They failed. Get over it. For a hundred years plus a nasty little > bug lurked in modern number theory in pure mathematics and no one > knew because none of their math applied to anything in the real world. > And I figured it out and these turds proceeded to do their best to > punish me for it. Get a clue. Nobody cares about your incorrect math analysis. > Because I yanked away their baby blanket. Took away their fantasy. Destroyed their little bubble. delusions of grandeur > Do you know how much the Abel Prize is? Over a million dollars U.S. given every year to someone who probably > did not succeed at anything at all. Lying for a million bucks isn't noble, or academic survival in the > real world: it's just being a con artist. It's too bad for you that nobody pays trolls. === Subject: Solutions manual to Separation Process Principles, 2nd Ed.,by Seader, Henley posting-account=jGYvqQoAAAC8JVWtG92jlQ1UvZHQAEv9 .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) solutions manual (To search click in keyboard Ctrl+F) Solutions Manuals in Electronic (PDF)Format! Just contact with , sendsolutions (at) hotmail.com (my email address), these are parts of our solutions, if the solution you want is on the list, please email to me. NOTICE: if the solutions manual that in my list ,please note it in your email . Instructor Solutions manual to : Solutions manua to Financial Accounting 6e by horngren Harrison Solutions manual to Advanced Accounting, 9th edition by Hoyle, Schaefer, & Doupnik Solutions manual to Complex Variables with Applications (Pie) by A.David Wunsch Solutions manual to Computer Design Fundamentals4E by Mano and Kime. 4th Solutions manua to Computer Networks Systems Approach 3ed by davie peterson Solutions manual to COMPUTER ORGANIZATION AND ARCHITECTURE DESIGNING FOR PERFORMANCE 7e by Solutions manual to Cost Accounting, 13/e 13e by Horngren SM.zip Solutions manua to Data and Computer Communications, 7th Edition By Stallings Solutions manual to Differential Equations and Linear Algebra by Penney and Edwards, 2nd edition Solutions manual to Elementary Differential Equations and Boundary Value Problems, by Boyce andDiprima Solutions manual to Elements of engineering electromagnetics (6/ e) by N.N.RAO Solutions manual to Engineering electromagnetics (7/ e) by HAYT Solutions manual to Engineering Fluid Mechanics, 7th, By Clayton T. Crowe, Donald F. Elger, John A. Roberson Solutions manual to Engineering Mechanics - Dynamics (11th ) by R.C.HIBBELER Solutions manua to Engineering Mechanics - Statics (11th ) by R.C.HIBBELER Solutions manual to Engineering Mechanics, Statics 6th by J. L. Meriam, L. G. Kraige, Solutions manual to Engineering Mechanics, dynamics 6th by J. L. Meriam, L. G. Kraige, Solutions manual to Financial Accounting 6e by horngren Harrison Solutions manua to Financial management theory and practice 12e by Brigham Solutions manual to Fundamentals of Applied Electromagnetics 5th edition by Fawwaz T. Ulaby solution manual Solutions manual to Fundamentals of Fluid Mechanics, 5th By Bruce,R. Munson, Donald Solutions manua to Fundamentals of Signals and systems using web and matlab third edition Solutions manua to Corporate Finance 1e by Berk SM Solutions manual to Introduction to Environmental engineering and science 2e by Gilbert M. Masters Solutions manual to Introduction to Mathematical Statistics 6/E Robert V. Hogg Solutions manual to Introduction to Quantum Mechanics (1 & 2 Edition), By David J. Griffiths Solutions manua to Introduction Fluid Mechanics, 6Th Edition Solution by fox.rar Solutions manual to Linear Algebra with Applications 6 edition by Leon Solutions manual to Mathematical Methods for Physics and Engineering 3th By Riley M P Hobson Solutions manua to Mathematics for Economists Solution Manual - Simon and Blume (ver 2) Solutions manual to Mathematics for Economists Solution Manual (Blume, 1994) Solutions manual to Microelectronic circuits by R. 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Johnston Solutions manua to Young & Freedman,University Physics, 12th Edition Basic Technical Mathematics with Calculus SI Version 8th (INSTRUCTORÍS SOLUTIONS MANUAL) By John R. Martin(chapter 1 to chapter15) solution manual for Probability and Statistical Inference ( 7th edition by Hogg & Tanis) solution manual for Fundamentals of Communication Systems by John G. Proakis ,Masoud Salehi solution manual for Materials and Processes in Manufacturing,9thBy Degarmo Advanced Industrial Economics 2nd by Martin Fundamentals of Corporate Finance 8th by Ross Principles of Corporate Finance 8th by Brealey Myers Alen Investments Student Solutions Manual 6e by Zvi Bodie Statistical Inference 2nd by George Casella Solution Manual of Econometrics of Financial Market options futures and other derivatives 3rd Solution by hull Design Analysis in Rock Mechanics By William G. Pariseau Digital Design 4th by M. Morris Mano, Michael D. Ciletti Engineering and Chemical Thermodynamics by Milo D. Koretsky Fundamentals of Clas Sical Thermodynamics 6th edition by Van Wylen Mechanical Vibrations, 3rd Edition, by Singiresu S. Rao Modern Control Systems 11th by Richard C Dorf and Robert H. Bishop Modern Organic Synthesis: An Introduction by Michael H. Nantz, Hasan Palandoken, George S. Zweifel Power System Analysis By John J. Grainger, William D. Stevenson Jr. computer system architecture 3rd by M.Morris Mano Design Analysis in Rock Mechanics By William G. Pariseau Digital Design 4th by M. Morris Mano, Michael D. Ciletti Engineering and Chemical Thermodynamics by Milo D. Koretsky Fundamentals of Clas Sical Thermodynamics 6th edition by Van Wylen Mechanical Vibrations, 3rd Edition, by Singiresu S. Rao Modern Control Systems 11th by Richard C Dorf and Robert H. Bishop Modern Organic Synthesis: An Introduction by Michael H. Nantz, Hasan Palandoken, George S. Zweifel Power System Analysis By John J. Grainger, William D. Stevenson Jr. === Subject: Solutions manual to Engineering Mechanics, dynamics 6th by J. L. Meriam, L. G. Kraige, posting-account=jGYvqQoAAAC8JVWtG92jlQ1UvZHQAEv9 .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) solutions manual (To search click in keyboard Ctrl+F) Solutions Manuals in Electronic (PDF)Format! Just contact with , sendsolutions (at) hotmail.com (my email address), these are parts of our solutions, if the solution you want is on the list, please email to me. NOTICE: if the solutions manual that in my list ,please note it in your email . Instructor Solutions manual to : Solutions manua to Financial Accounting 6e by horngren Harrison Solutions manual to Advanced Accounting, 9th edition by Hoyle, Schaefer, & Doupnik Solutions manual to Complex Variables with Applications (Pie) by A.David Wunsch Solutions manual to Computer Design Fundamentals4E by Mano and Kime. 4th Solutions manua to Computer Networks Systems Approach 3ed by davie peterson Solutions manual to COMPUTER ORGANIZATION AND ARCHITECTURE Solutions manual to Cost Accounting, 13/e 13e by Horngren SM.zip Solutions manua to Data and Computer Communications, 7th Edition By Stallings Solutions manual to Differential Equations and Linear Algebra by Penney and Edwards, 2nd edition Solutions manual to Elementary Differential Equations and Boundary Value Problems, by Boyce andDiprima Solutions manual to Elements of engineering electromagnetics (6/ e) by N.N.RAO Solutions manual to Engineering electromagnetics (7/ e) by HAYT Solutions manual to Engineering Fluid Mechanics, 7th, By Clayton T. Crowe, Donald F. Elger, John A. Roberson Solutions manual to Engineering Mechanics - Dynamics (11th ) by R.C.HIBBELER Solutions manua to Engineering Mechanics - Statics (11th ) by R.C.HIBBELER Solutions manual to Engineering Mechanics, Statics 6th by J. L. Meriam, L. G. Kraige, Solutions manual to Engineering Mechanics, dynamics 6th by J. L. Meriam, L. G. Kraige, Solutions manual to Financial Accounting 6e by horngren Harrison Solutions manua to Financial management theory and practice 12e by Brigham Solutions manual to Fundamentals of Applied Electromagnetics 5th edition by Fawwaz T. Ulaby solution manual Solutions manual to Fundamentals of Fluid Mechanics, 5th By Bruce,R. Munson, Donald Solutions manua to Fundamentals of Signals and systems using web and matlab third edition Solutions manua to Corporate Finance 1e by Berk SM Solutions manual to Introduction to Environmental engineering and science 2e by Gilbert M. Masters Solutions manual to Introduction to Mathematical Statistics 6/E Robert V. Hogg Solutions manual to Introduction to Quantum Mechanics (1 & 2 Edition), By David J. Griffiths Solutions manua to Introduction Fluid Mechanics, 6Th Edition Solution by fox.rar Solutions manual to Linear Algebra with Applications 6 edition by Leon Solutions manual to Mathematical Methods for Physics and Engineering 3th By Riley M P Hobson Solutions manua to Mathematics for Economists Solution Manual - Simon and Blume (ver 2) Solutions manual to Mathematics for Economists Solution Manual (Blume, 1994) Solutions manual to Microelectronic circuits by R. Jaeger 3rd edition Solutions manua to Numerical methods for engineers 5th by Chapra Solutions manual to Probability & Statistics for Engineers & Scientists, 8th by Sharon Myers , Keying Ye, Walpole Solutions manual to Probability and Statistics for Engineering and the Sciences 7/e JAY L.DEVORE Solutions manual to Probability,Random Variables and Stochastic Processes,4th,by Athanasios Papoulis Solutions manua to Separation Process Principles, 2nd Ed.,by Seader, Henley Solutions manua to Statistics for Engineers and Scientists by William Navidi Solutions manual to Transport Phenomena by Bird, Stewart & Lightfoot, 2nd edition Solutions manual to Unit Operations of Chemical Engineering (7th) By Warren McCabe, Julian Smith Solutions manual to Vector Mechanics for Engineers: statics, 7th Edition (much same as 8th),By F. P. Beer, E. R. Johnston 8th Edition ,By F. P. Beer, E. R. Johnston Solutions manua to Young & Freedman,University Physics, 12th Edition Basic Technical Mathematics with Calculus SI Version 8th (INSTRUCTORÍS SOLUTIONS MANUAL) By John R. Martin(chapter 1 to chapter15) solution manual for Probability and Statistical Inference ( 7th edition by Hogg & Tanis) solution manual for Fundamentals of Communication Systems by John G. Proakis ,Masoud Salehi solution manual for Materials and Processes in Manufacturing,9thBy Degarmo Advanced Industrial Economics 2nd by Martin Fundamentals of Corporate Finance 8th by Ross Principles of Corporate Finance 8th by Brealey Myers Alen Investments Student Solutions Manual 6e by Zvi Bodie Statistical Inference 2nd by George Casella Solution Manual of Econometrics of Financial Market options futures and other derivatives 3rd Solution by hull Design Analysis in Rock Mechanics By William G. Pariseau Digital Design 4th by M. Morris Mano, Michael D. Ciletti Engineering and Chemical Thermodynamics by Milo D. Koretsky Fundamentals of Clas Sical Thermodynamics 6th edition by Van Wylen Mechanical Vibrations, 3rd Edition, by Singiresu S. Rao Modern Control Systems 11th by Richard C Dorf and Robert H. Bishop Modern Organic Synthesis: An Introduction by Michael H. Nantz, Hasan Palandoken, George S. Zweifel Power System Analysis By John J. Grainger, William D. Stevenson Jr. computer system architecture 3rd by M.Morris Mano Design Analysis in Rock Mechanics By William G. Pariseau Digital Design 4th by M. Morris Mano, Michael D. Ciletti Engineering and Chemical Thermodynamics by Milo D. Koretsky Fundamentals of Clas Sical Thermodynamics 6th edition by Van Wylen Mechanical Vibrations, 3rd Edition, by Singiresu S. Rao Modern Control Systems 11th by Richard C Dorf and Robert H. Bishop Modern Organic Synthesis: An Introduction by Michael H. Nantz, Hasan Palandoken, George S. Zweifel Power System Analysis By John J. Grainger, William D. Stevenson Jr. computer system architecture 3rd by M.Morris Mano === Subject: Goldbach conjecture - Brute Force I am resurrecting an old program of mine to brute force the Goldbach conjecture. According to my 1989 copy of Ribenboim (2nd edition) by that date even numbers had been tested up to 10^8. I presume that the figure is now a lot higher. How high is it? rossum === Subject: Re: Goldbach conjecture - Brute Force >I am resurrecting an old program of mine to brute force the Goldbach > conjecture. According to my 1989 copy of Ribenboim (2nd edition) by > that date even numbers had been tested up to 10^8. I presume that the > figure is now a lot higher. How high is it? July 14, 2008: 12*10^17 reached. === Subject: Re: Goldbach conjecture - Brute Force >I am resurrecting an old program of mine to brute force the Goldbach > conjecture. According to my 1989 copy of Ribenboim (2nd edition) by > that date even numbers had been tested up to 10^8. I presume that the > figure is now a lot higher. How high is it? July 14, 2008: 12*10^17 reached. > since they are already near the limit of Java longs rossum === Subject: I was writing a book, it is called Mein Kampf.The book describes the object of non-Jews. posting-account=1tc1_woAAAAWEQmFxvK_TIY4164_hcV5 Presto/2.1.1, DynaWeb http://www.dit-inc.us/disclaimer.php,gzip(gfe),gzip(gfe) The book describes the object of non-Jews, including Germans, black, yellow, the Basque people, Celtics ..., because I was the only recognition of Jehovah God's son, so I is an exception. Non-Jews did not believe me, in many forums only when I desperately Jewish Messiah evidence, please be posted to various Jewish Forum, the Bible and Les Centuries Astrologiques , etc. contains a wealth of information I can calculate my date of birth and death dates, and even small enough to present the characteristics of I, and now only I understand, as well as a large number of a specific date for the incident! I was able to unlock the key to all the information, when you see me, they can crack the Prophet's prophecy, I declare that: Even if the future proves that I really was the Messiah the Jews, even non-Jews regret for me, I absolutely He does not care about the fate of the future catastrophe only after the remaining Jews, even if only seven million people left on Earth, aliens also died, and only the Jews and I left, Ezra, documented in this a period of events. all non-Jews to die, you will be the fate of the future without any relationship with me. Isaac Newton 31 December 2008 === Subject: Re: I was writing a book, it is called Mein Kampf.The book describes the object of non-Jews. posting-account=cwKGMgkAAABBtSw0xrlwQZK5IUJeXZCy AppleWebKit/525.27.1 (KHTML, like Gecko) Version/3.2.1 Safari/525.27.1,gzip(gfe),gzip(gfe) Celtics? You hate (admittedly second rate) basketball players? If > you have a foreskin YOU WILL BURN IN HELL FOR ALL ETERNITY. Tear it > off right now and be penitent. BLEED for the God of Avrahom, > Yitzhawk, and Ja'akov. BLEED for the Pentatuch. BLEED for rainbows, > BLEED for blessings, BLEED for existence, BLEED for life, BLEED for > future generations. BLEED forever now or be forever bled. The Celtics second rate!!! next you'll be dissing the Pats and that I cannot overlook... === Subject: ODE method posting-account=oLBOFwoAAABWIQ0AR6tse1gtllnDjdMR Gecko/20081217 Firefox/2.0.0.20,gzip(gfe),gzip(gfe) What ODE method is used to solve the following for I: dI(s)/ds = -k(s)I(s) + q(s) The answer given (integrating from s0 to D) is: I(D) = I_0*exp( -int_s0^D (k(t) dt) ) + int_s0^D( q(s)*exp( - int_s^D ( k(t) dt ) ) ds ) But I am trying to figure out the steps to get to the answer. === Subject: Re: ODE method What ODE method is used to solve the following for I: dI(s)/ds = -k(s)I(s) + q(s) The answer given (integrating from s0 to D) is: I(D) = I_0*exp( -int_s0^D (k(t) dt) ) + int_s0^D( q(s)*exp( - >int_s^D ( k(t) dt ) ) ds ) But I am trying to figure out the steps to get to the answer. That is a linear first order differential equation, which can be solved using an integrating factor. See: http://www.math.ubc.ca/~aclay/m2652007/lecture2.pdf for an explanation and examples. --Lynn http://math.asu.edu/~kurtz === Subject: Re: Was Summers Right on girls and science? posting-account=szpaLgoAAADBdaVO-fj5XjAA_palKAqR Trident/4.0; SLCC1; .NET CLR 2.0.50727; .NET CLR 3.5.21022; .NET CLR 3.5.30729; .NET CLR 3.0.30618; MS-RTC LM 8; OfficeLiveConnector.1.3; OfficeLivePatch.1.3),gzip(gfe),gzip(gfe) >FACTS >participated in TIMSS physics. OK. >The average score for the 5,150 students in Botswana who took the test was 443, OK >seven of whom scored over 505, and none of whom scored over 549. Numbers pulled out of your strange orifice. >The average score for the 8,952 students in South Africa who took the test was 244 OK >thirteen of whom scored over 447, and none of whom scored over 514. Numbers pulled out of your strange orifice. >So also in Ghana, where the average score for their 5,100 students was 239 OK >seven of whom scored over 427, and none of whom scored over 514. Numbers pulled out of your strange orifice. >Conversely, the average score for the 6,018 students in Singapore was 579 OK >eight of whom scored lower than 462, and none of whom scored lower than 423. At best we can say that eight students in Singapore >MAY have scored lower than SEVERAL of the thirteen highest scoring >students in South Africa and SEVERAL of the seven highest scoring >students in Ghana. No student in Singapore scored 4 standard >deviations higher than their mean, or 735, much less 5 standard >deviations higher, at 774. Numbers pulled out of your strange orifice. >So needless to say, no student in Botswana, South Africa, nor Ghana >ever scored four standard deviations higher, or 549, 514, or 489, >respectively, either, much less five standard deviations higher, or >593, 581, or 551 respectively. Statistical nonsense pulled out of your strange orifice. >Such scores are in the range of the >average for Taipei and Korea, whose IQs are in the range of 105 IQ >points IQ has nothing to do with it. Whether the kids are taught physics in school has much to do with it. >It simply boggles the imagination Showing how poor your imagination is. >for us to be expected to >believe that Obama was the ONE Kenyan in the entire world who scored >not just one but TWO standard deviations higher than a place where NO >Ghanan, Botswanan, or South African has ever ventured. > 2) If he had taken a TIMSS test in the 8th grade, he would have been > part of US statistics and not Kenyan statistics. 3) Your use of standard deviations is statistical nonsense pulled out > of your strange orifice. >To claim that his IQ is 132 IQ points Who has done so? >yet another three standard deviations higher >than the impossible, is the height of absurdity. All of your posts are the height of absurdity. >The average IQ of Kenya is 71 IQ points, the same as for Ghana, and 1 >point lower than both Botswana and South Africa, at 72 IQ points. Numbers pulled out of your strange orifice. >Out of 38 million Kenyans, do you know how many score more than 5 standard >deviations higher than that? Only 11 do, at an IQ of only 96 IQ >points, four standard deviations higher than their mean, and NONE have >an IQ higher than 101 IQ points, five standard deviations higher than >the mean. Statistical nonsense pulled out of your strange orifice. >ObamaÍs not even a Kenyan. Of course not. He is a natural born American citizen. >HeÍs a mixed breed and most >mixed breeds of most species are of lower quality and intelligence Nonsense. >than the pure breeds (otherwise why donÍt mules race in horse races)? Because you are too stupid to have a jockey sit on you? >Obama is clearly left over from those days. You have no clue. >Why not simply require him to take the normal IQ test There is no normal IQ test >which any dog >catcher in the country has to take in order to qualify for his job? Provide a cite for ANY dog catcher opening that requires that an > applicant take an IQ test. >You can bet that this would settle the matter once and for all. What matter? That you are a subhuman racist nincompoop that pulls > obnoxious slime from your strange orifice is already well established. >Correction, Tues. Dec. 23, 2008: 7% of the population of Botswana are >Whites who score similar to their brethren back in England at 545, >meaning that the 93% whoÍre blacks scored 358. Please provide evidence as to the actual racial makeup and scores of > those who took the test in Botswana. Otherwise you are just pulling > silly numbers out of your strange orifice. >Only seven black students from Botswana scored over 456 and none of them scored over >514. Therefore, none of the lowest scoring eight students in >Singapore who scored lower than 462 are likely to have scored lower >than the seven top scoring black students from Botswana, meaning there >was no overlap of test scores between Singapore and Botswana. Numbers pulled out of your strange orifice. >This is the political culture that Obama comes from in Illinois . >And he's going to 'fix Washington politics for us? He'll do a lot better than YOU would. Wait and see. >Good luck and may YAHWEH help us. Yahweh may help us, but you are bound only for Satan. lojbab > Bob LeChevalier - artificial linguist; genealogist > loj...@lojban.org Lojban languagewww.lojban.org Here's finally someone who agrees with you, largebabble: cgfunmathguy I've tried to stay out of this one as DvF has done an admirable job of presenting the points I wanted to make. However, please allow me to add my two cents' worth. First, you are comparing different systems that do different things. You are comparisons are being made between countries where there are NATIONAL curricula, those where there are STATE curricula, and at least one where it is a hodgepodge of STATE and LOCAL curricula. So, we are comparing apples to oranges to pears. The entire PURPOSE of an international study IS to compare different education systems to each other, which is exactly what TIMSS does. Just like the entire PURPOSE of a national study like NAEP is to make state to state comparisons to see what works and what fails. ItÍs not BAD to make international and national comparisons, itÍs GOOD. cgfunmathguy Also, we need to address the differences in systemic student handling. In the US, we send the vast majority of our students to high school; other countries reverse this entirely. Thus, the 12th-grade cohorts aren't even comparable between countries, even though they are presented as such by the media (among many others). While the 4th- grade cohorts may be similar, there is even some question about the comparing 8th-grade cohorts by some. For the two reasons above, I don't believe TIMSS is as valid an indicator of differences between national systems as its exhorters proclaim. This is patently false. Fortunately, itÍs PROVABLY false. Our OWN data from NCES claims that 74% of American 18 year olds graduate from high school, compared to more than 90% in most industrialized nations: http://nces.ed.gov/pubs2001/2001034.pdf The reason nobody has ever posted a cite which disputes that is that there is no cite, AND TIMSS disputes it in a different direction, claiming that they found that only 63% of American students are in their ñTCIî, compared to 82% in Switzerland, 84% in Norway, 75% in Germany, 88% in Slovenia, etc. http://timss.bc.edu/timss1995i/TIMSSPDF/SRAppA.pdf They found that 1,245,594 American children of high school graduation age, 67% of that population, werenÍt even IN high school, and thus were never included in our already LOW TIMSS scores. If the worst students were the ones who werenÍt in high school, can you even IMAGINE how low our scores would have been had they been INCLUDED? If this is the reason you donÍt ñbelieve TIMSS is as valid an indicator of differences between national systems as its exhorters proclaimî, you need to use your new-found knowledge to go back and rethink your position. cgfunmathguy Finally, a word about why DvF keeps trying to get you to understand why comparing cohorts is important. Many states have been adjusting/ rewriting their regulations (Pennsylvania), their state-mandated tests (Ohio), and their state-mandated curricula (Georgia) for the past decade or more. In mathematics, the National Council of Teachers of Mathematics (NCTM) issued its first set of standards on K-12 mathematics in 1989. This was the first step in the reform process, and several states began the process of reforming state curricula in the early 1990s. Others waited longer. However, the process is not an instantaneous one. As an example, Georgia instituted the Georgia aren't fully implemented throughout the schools yet, and they won't be for two more years. So, yes, cohort matters, and we need to deal with the data that way. The only fair comparisons about gains and losses in the report's 12th-grade cohort would be to take the 2007 report's 12th- graders and compare that gap (assuming all the other confounding graders and to the gap found in 1999 report's 4th-graders. This assumes that the tests across that EIGHT-YEAR SPREAD are equivalent. None of which is relevant. The entire POINT of TIMSS is to make international comparisons, not state to state comparisons. Your idea that something in our education system was the ñfirst step in the reform processî is the same thing educators have been mimicking for years, and none of it ever worked. Furthermore, all American parents I know believe that every single one of these so-called ñreformsî only brought us back quicker to the stone age and improved nothing. TIMSS also proves how SAT scores have been politicized, feminized, manipulated, and watered down to the point theyÍre no longer credible. cgfunmathguy ñFor another view of it, let's look at your classroom. In a large lecture class, grades tend to be distributed normally. This being the case, curving (with its true meaning) would assign Cs to the 68% of the students whose scores are within 1 SD of the mean. So, let's assume that the mean on Test 1 was 75 with a standard deviation of 8. So, any student with a score between 67 and 83, inclusive, should get a C. However, Susie with her 81 and Johnny with his 69 both got Cs! Is the difference significant? We don't know until we run tests on the scores. Even though the difference is 12 points (which is 1.5 SD), it is likely that this difference is NOT statistically significant at any appreciable level. To constantly quote raw numbers with no test results is worthless and misleading. Even those with an agenda don't do this because they know they will be accused of trying to bamboozle the people reading the report.î You complain about referring to different cohorts, then launch into a comparison between a large lecture room and an international study of hundreds of thousands of students. You CANNOT compare these and make any sense out of it. You literally canÍt adjust for guesses on multiple choice questions in the ñlargeî lecture hall, but you CAN when there are hundreds of thousands of what TIMSS is? Before you invite anyone to ñtake a statistics classî again, you ought to invite yourself to examine their methodology. You are as wrong about this as you are about ñIn the US, we send the vast majority of our students to high schoolî. === Subject: Sum of product of all possible k selections from first n natural numbers posting-account=T18toAoAAABIMEO7Fe58Ju93zQyZ4fsR Gecko/20080528 Epiphany/2.22,gzip(gfe),gzip(gfe) S = {1, 2, ..., n}. Is there a formula to find the sum of product of all possible k selections from S? e.g. If we denote f_k(n) = the sum of product of all possible k selections from S, then. f_3(n) = 1*2*3 + 1*2*4 + ... + (n-2)*(n-1)*(n-4) [Contains C(n, 3) = n! / {3! (n-3)!} terms in all.] Is it possible to come up with a closed form or a better formual to calculate f_k(n) ? === Subject: Re: Sum of product of all possible k selections from first n natural numbers posting-account=9QOSvAoAAACEOWJVSDuswW7dB_0wApQO Gecko/20070530 Fedora/1.5.0.12-1.fc5 Firefox/1.5.0.12,gzip(gfe),gzip(gfe) > S = {1, 2, ..., n}. Is there a formula to find the sum of product of all possible k > selections from S? e.g. If we denote f_k(n) = the sum of product of all possible k > selections from S, then. f_3(n) = 1*2*3 + 1*2*4 + ... + (n-2)*(n-1)*(n-4) [Contains C(n, 3) = > n! / {3! (n-3)!} terms in all.] Is it possible to come up with a closed form or a better formual to > calculate f_k(n) ? The number you are trying to evaluate is sigma(1, 2, 3, ..., n) where sigma is the elementary symmetric polynomial of degree k and as such you can find them neatly organized as the coefficients of the polynomial (X + 1) (X + 2)... (X + n) They go by the name of (unsigned) Striling numbers of the first kind. There aren't any closed formulas for them, as far as I know, but for the most part you can do pretty much anything you want with them without such an explicit formula. -- m === Subject: Re: Sum of product of all possible k selections from first n natural numbers posting-account=oTDIagkAAACTxHurtPutBWvNQS8ZCNO9 Gecko/20081217 Firefox/2.0.0.20,gzip(gfe),gzip(gfe) > S = {1, 2, ..., n}. Is there a formula to find the sum of product of all possible k > selections from S? e.g. If we denote f_k(n) = the sum of product of all possible k > selections from S, then. f_3(n) = 1*2*3 + 1*2*4 + ... + (n-2)*(n-1)*(n-4) [Contains C(n, 3) = > n! / {3! (n-3)!} terms in all.] Is it possible to come up with a closed form or a better formual to > calculate f_k(n) ? Every k-selection for (n-1) is a k-selection for (n); so as a start, f_k(n) obeys the recurrence: f_0(n) = 1 f_k(n) = 0 for k > n and otherwise f_k(n) = f_k(n-1) + n*f_(k-1)(n-1) which (while not a closed form) is pretty easy to code up if you just want to calculate the values. === Subject: Re: Sum of product of all possible k selections from first n natural numbers posting-account=IBUqVwoAAADepmzxVr9iEYD5Z0A483SY rv:1.9.0.1) Gecko/2008070206 Firefox/3.0.1,gzip(gfe),gzip(gfe) > S = {1, 2, ..., n}. Is there a formula to find the sum of product of all possible k > selections from S? e.g. If we denote f k(n) = the sum of product of all possible k > selections from S, then. f 3(n) = 1*2*3 + 1*2*4 + ... + (n-2)*(n-1)*(n-4) [Contains C(n, 3) = > n! / {3! (n-3)!} terms in all.] Is it possible to come up with a closed form or a better formual to > calculate f k(n) ? These are essentially Stirling numbers of the first kind. === Subject: Re: Epistemology: debunking v. open-mindedness > Quite so. Nobody can ever prove that something does NOT exist! So > why all the debunking if the question is out of bounds? Ah, there > must be some POLITICS behind it, no? Yes one can, in at least two ways. A four-sided triangle can not exist. Proof: a triangle is *defined* to have three sides. A numerically largest prime number can not exist. Proof (after Euclid): assume that such a number exists and call it P. The number P!+1 has no integer factors less than or equal to P because it yields a remainder of 1 when divided by all integers less than or equal to P. Therefore either P!+1 is prime or it is divisible by an integer greater than P. In either case, P can not be the largest prime number and so P can not exist. Paul -- Paul Leyland | Hanging on in quiet desperation is Dept. of Genetics, Cambridge University | the English way. Downing Street, Cambridge, CB2 3EH, UK | The time is gone, the song is over. Tel: +44-1223-333963 Fax: +44-1223-333992 | Thought I'd something more to say. === Subject: Re: Epistemology: debunking v. open-mindedness posting-account=rsfFvAoAAADqHCqmunbjtmaKjfuP-pwP .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; InfoPath.1; .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) > (snip) >I have already explained, Gordie, how our neighbour, a pig-farmer did >it: he positioned the pig in a frame, then slit its belly from top to >bottom, collecting the blood in a bath situated underneath, the origin >of 'blood bath', maybe.' > Jon, I may have missed something here, but I don't see how this pig > farmer could place a live, active hog in this kind of frame. > That's how they did it, though. I was only there for a summer, my > parents had fallen out, though later got back together. > The way we and others in the community butchered hogs was to kill them with a > 22 caliber rifle then slit their throat, opening the primary artery to > the brain. The blood was usually drained into a bucket and fed to the > poultry. They liked it and it gave them needed protein. > After the hog was bead out, and no longer thrashing around we would > slip the carcass, head first, into a barrel that was half full of very > hot water. This had been prepared in an iron 55 gallon barrel, > supported on rocks with a wood fire under it. When the water was hot > we would dig a small pit beside the fire and maneuver the half barrel > of hot water into this pit and lean the barrel over at about a 45 > degree angle. > Then we would lift the carcass and slide the nose end into the hot > water and swish it around a bit, then pull it out and switch ends, > inserting the rear quarters into the hot water. > After this scalding process was complete the carcass was laid on a > flat platform and all the hair scraped off with ordinary butcher > knives. When all the hair had been scraped off we would wash the > carcass thoroughly. This left the carcass in a very clean, smooth > state. > Then, the very clean, hairless carcass was ready to open up and remove > the viscera. This, like you describe, entailed slitting the stomach > from throat to anal orifice and removing all the intestines, heart, > lungs, etc. > The carcass was then cut into separate pieces and moved into the smoke > house where it was treated with a salt mixture, then smoked until it > was fully cured. > Ummmm, just thinking of this makes me get the yummies. That home cured > ham and loin cuts just can't be beat. Gordon >He and his wife then turned the pig into marketable products. The >other pigs were upset for days. I, too, was upset! > I never saw any signs that this upset any of the other pigs. They were > just making grunting sounds and going about their business as usual. > Gordon >This thread is drifting away from the notion that NDEs and OBEs in >respect of (a) sighted persons and (b) blind persons actually *see* an >operation or an accident and can veridically recall it, so that we >might test their apparent perceptions. > The drift here was partly caused by my quest for information as to > just how a blind-from-birth person may reassign the part of their > brain that people with normal vision use to process their visual > sensations. If this brain region is re-assigned to handle some other > sensations, such as auditory, tactile and olfactory sensations, this > may explain the out of body experiences. > Gordie, nothing explains them, though they are numerous. Investigation > of such matters will of course only convince anybody if we can > establish that in the case of NDEs, technically dead (up to 23 > minutes), they had this or that experience. > That is, their tactile or other sensory organs may have been stimulated in > such a way as to give them a visual image that they couldn't explain, but > which others > helped them put into focus as an out of body experience. Gordon > Brilliant! I think that is what happens to them! >In the case of (b), there is a anecdotal evidence (the way science >always begins!), but there have been few studies, apart from one or >two I have quoted. >The consequences of the truth of (b) for 'materialism' would of course >mean that bodies were just machines, some better than others, no >different from computers or lawnmowers! > I'll post post a bit more evidence shortly: there is no proof. > -- > foolsrushin. >http://www.near-death.com/atwater/column/archives/2005/2005 02.html > 'The first account proposes that a person's NDE (or OBE) maybe > inspired by accounts of other people's NDEs that have been widely > disseminated in various forms of the media. That is, might a blind > person have heard that people see certain things in a near-death > encounter and unconsciously generated a fantasy that conformed to this > belief? The second potential sociocognitive explanation is somewhat > broader and posits that people, including the blind, learn about what > to expect in an afterlife from diverse sociocultural sources, and they > may rely extensively on these expectations in generating a near-death > fantasy. The expectation that, for example, the afterlife is set in a > pastoral realm is common in Western culture (Irwin, 1987a). More > significantly for the nature of NDEs in the blind, it is possible that > people in the general population are inclined to expect that in the > afterlife a person will not suffer physical or sensory disabilities > and will otherwise be in perfect form. Indeed, sighted NDErs often > re port other-worldly encounters with deceased relatives who had died > at an advanced age but who appeared to be at their physical peak in > the afterlife (Sabom, 1982, p. 72), and some OBErs have described the > appearance of their exteriorized self in similarly idealized terms > (Irwin, 1987b, p. 115). Thus, the blind may commonly have a belief > that they will suffer no visual affliction in an afterlife, and this > belief may influence the content of NDEs in the blind. It is not my > intention to promote these skeptical accounts of the NDE, nor to > advocate the pursuit of the empirical support that they still require, > but in the interests of balance Ring and Cooper should certainly have > given sociocognitive accounts due scrutiny. > A very short note, titled A Concluding Word, reiterates the proposal > that while blind NDErs and OBErs may depict their experiences in terms > of visual impressions, this tendency simply involves the unwitting > reformulation of an experience of mindsight in terms of constructs > that the experient herself or himself can comprehend. This concluding > chapter might better have given more emphasis to the most fundamental > implication of the project's finding of NDEs in congenitally totally > blind people, namely, that the perceptual-like impressions in NDEs and > OBEs evidently are not perceptual at all. > An appendix reports An Exceptional New Case of an NDE in the Blind > recruited by Dr. Tricia McGill. An inserted addendum warns, however, > that there now are grounds to believe this case is fraudulent. This > unfortunate situation is one that all researchers of anomalous > experiences are prone to encounter. > The quality of the book's production is excellent; I noted only one > typographical error. The book also is very reasonably priced. > In summary, it must be said that Ring and Cooper have neglected > several substantial issues, but despite its lacunae this book is a > significant contribution to NDE research in that it reports some > phenomenological data that an adequate theory of the NDE must be able > to accommodate. These data serve to reinforce the view that the > experient's impressions in an NDE are not perceptual in the usual > sense of this term, but the exact nature of the perceptual-like > impressions requires further clarification. As a novel stimulus to > such clarification this book is warmly recommended.' >http://www.near-death.com/sitemap.html > The above, Gordie, is a cautious advance in the direction of > overturning Cartesian dualism. It at least assents with civil leer! He > noticed only one typographical error! > Wot a prat!, though! Maybe he hopes to get tenure somewhere! Or fears > he might see it revoked. Bet he goes to church on Sundays, too! > Stoopid person, yet we have to get him out of the way before we can > have a serious discussion. > Listen to the delightful Stanton Friedman. > [Sheldrake on debunkers:http://subversivethinking.blogspot.com/2008/12/how-debunkers-and-p s eu... > ] > My mother was a Catholic, my father a studious Atheist, and I was > brought up by Jews for a third of my youth. > P. M. H. Atwater, L.H.D., Ph.D. (Hon.) : 'An in-depth look at the near- > death phenomenon': I am sorry to have to say it, but she seems to be a > sort of NDE industry! > IF, however, (and a first cousin, a doctor, on my mother's side claims > it's true) that doctors often sometimes experience NDE patients, blind > from birth, who yet seem to see outside their bodies at a critical > moment, the conventional theory of knowledge is overturned and > mechanism and materialism are in trouble. > Are they? I don't know! > -- > foolsrushin. I really think that we should give maximum exposure to the debunkers > of anything they want to debunk, then ... read more ............................ Occham was a nominalist, and ought, consitsently with his position, to have reduced the population of things and people to himself, and then committed suicide - after, of course, extensive publication of his works, but destroying the last name, his only remaining possession, his everything. Question: Can a solopsist commit suicide? [ He alone can do it? Ed.] -- foolsrushin. === Subject: Re: Epistemology: debunking v. open-mindedness posting-account=rsfFvAoAAADqHCqmunbjtmaKjfuP-pwP .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; InfoPath.1; .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) [Delete.] Occham was a nominalist, and ought, consitsently with his position, to have reduced the population of things and people to himself, and then committed suicide - after, of course, extensive publication of his works, but destroying the last name. Question: Can a solopsist commit suicide? [ He alone can do it? Ed.] -- foolsrushin. === Subject: Re: Epistemology: debunking v. open-mindedness > And the rest. BTW its generally spelt Occam..but Ockham is probably OK, > as that is how the place is spelled today. It's generally spelled a million different ways, with both Occam and Ockham very popular variants. -- Jesse F. Hughes Mathematicians don't fit in with a consistent view, unless you accept that to a strangely large extent they are acting under the influence of something very powerful, dark, and negative. -- James S. Harris === Subject: Re: Epistemology: debunking v. open-mindedness >[dius] >*See, obvious! >exceeded my limit of postings! After recent experiences, I wouldn't >trust them with a 20ft pole with a sanitary inspector tied to the end >- even if he was highly qualified! > Click on the link if you want a good laugh foolsrushin. The most debunked scientist has to be John Keely. http://edition.cnn.com/TECH/9712/02/sound.wave.energy/ > http://www.macrosonix.com/pdf%20files/Physics%20Today.pdf > http://www.freepatentsonline.com/5515684.html > http://adsabs.harvard.edu/abs/1996ASAJ..100.3480L > http://fusionanomaly.net/soundwaveenergy.html > http://www.rense.com/earthchanges/sound.htm In 1872, experimenting with a hydraulic engine John W. Keely > accidentally made his discovery of the tremendous and mysterious > energy which he afterwards pronounced to be the etheric force. His patent was refused. Specification describing a new and useful Hydro Vacuo Engine > http://www.svpvril.com/svpweb14.html The debunkors can talk all the crap they like really. At one time I had a job grinding plastics for recycling. The the > plastic grinding apparatus made a horrifying sound forcing people to > wear ear plugs and head phone kinda dampeners which didn't help at > all. Next to the device there was this anti-sound apparatus. This > apparatus was switched off, so I asked why. Doesn't seem unreasonable > to ask? Does it? The excuse was that it didn't work. I mentioned anti > sound works all over the globe, I've seen it work, what doesn't work > about it? Why not call some one to service the device? Get back to > work; was the excuse. So I ask a long time employee what was up with > it. He said it's not that it doesn't work, it works to well actually. > I'm like huh what? holding my hand behind my ear pretending to be > deaf. He said, they replaced the motor 3 times now, the anti sound > burns up the motor. So I'm looking at this small box with thin wires > on a circuit with lots of other devices on it, then I look at this > hunge 380 volt plastic grinder. If this was in the USA then the reason for the motor burning out is obvious. In any case, plastic grinders aren't known for longevity. That applies to both the machine, and humans operating them. > I ask him, this small box will break > that huge motor over distance? You expect me to believe that? He > laughed lifted his shoulders and said: well it's all I know. So my > chief comes back and I ask him why he cant switch on the anti sound > again. Asking about the burned up motor. I jokingly said if it can > increase the load it should also be able to decrease the load by > increasing the sound. He then fired me. LOL I didn't have any idea why > I was fired at the time. But now debunkers attack every word I write the year round I'm > beginning to get an idea. You do manage to attract attention. But of course you knew that already. === Subject: Re: Epistemology: debunking v. open-mindedness > Debunking is merely skepticism at work. Not at all. Debunking implies certainty in conviction (if not certainty in result). Skepticism implies doubt in conviction, and that is the opposite of certainty in conviction. To wit, debunking requires the defeat of skepticism and vice versa, i.e. they are mutual excluders. > Not so! That is what debunkers try to have you believe. The truth is > debunking' is political propaganda at work. > You make *seek* to redefine debunking, but that does not make you > correct. Skepticism is the the questioning of an assertion. Debunking > is the act of communicating one's questions about an assertion. Debunking is the genuine exposition of that which is false. She is pregnant or she is not, as it were. That being said, when debunkings are themselves debunked, as they often are ... well, all that means is that the original debunking was never, in fact, so, i.e. there was no pregnancy. > Generally the arguments > provided have nothing to do with facts but rather appeal to > authority [text books all say this], > ....Al Gore and the IPCC concensus... > proof by assertion [those > ideas are false!] > and ad hominem attack [you obviously are a kook and > wear a tinfoil helmet]. > ....deniers... > These and many others are all rhetorical devices used (sadly enough) > by *both* sides in an argument to carry on in the effort to persuade > (usually uncommitted) listeners when facts and logic fail. Look up > fallacies of informal logic for a good introduction to the elements > of rhetoric: > http://www.logicalfallacies.info/ > The measured factual approach of the skeptic is NOT part of the usual > debunking. > Actually, empiricism is the *ultimate* in debunking; I refer to such > as Galileo's debunking of Aristotle's theory of gravity. Empiricism is a valid tool for both purposes: debunking and skepticism. > Right now the evidence in support of ETs is about as strong as the > evidence in support of Satanic demons, and it is of a similar nature. > Unfortunately, neither hypothesis is amenable to disproof, as both are > of the nature of simple assertions of the existence of something. > Quite so. Nobody can ever prove that something does NOT exist! So > why all the debunking if the question is out of bounds? Ah, there > must be some POLITICS behind it, no? > There is ALWAYS politics behind everything. > And it is VERY interesting that BOTH the above are easily proved to be > true science with nothing more than a single example of each. One > crashed UFO is MORE than enough proof for the existence of ETs. Same > goes for one trapped demon. A single counterexample is always sufficient to provide disproof, as > Galileo demonstrated. Unfortunately there appear to be no wrecked UFOs > or trapped demons where they can be seen and validated for what they > are. Yet it is any hint of such evidence that > sends debunkers off into tinfoil hat attacks. Why? It only shows > an agenda must be involved. Maybe they need more than a hint of evidence. Your unsupported > surmise of a hidden agenda sounds like incipient paranoia to me. > Ockham's Razor rules. > > Ockhams Razor is bull! As Einstein noted, things should be as > simple as possible but not simpler! Those who invoke Ockham's Razor > invariably try to make things simpler ....true... because sound bites and bumper > stickers make good propaganda. What evidence do you have to support that inference? However, they are well below the limit > of simple as possible. And usually the debunkers know it. The principle is often expressed in Latin as the lex parsimoniae > (law of parsimony or law of succinctness): entia non sunt > multiplicanda praeter necessitatem, roughly translated as entities > must not be multiplied beyond necessity. An alternative version > Pluralitas non est ponenda sine necessitate translates plurality > should not be posited without necessity > The praeter necessitatem is equivalent to Einstein's but not > simpler. All told, Einstein gave an excellent and succinct > translation if the principle. > However, when the requisite parsimony dispenses with someone's pet > hypothesis off-handedly, especially when the hypothesis postulates > unnecessary entities, then they often object - You are going too > far! However, if the observations can be accounted for without > recourse to the postulation of novel objects or entities, that > alternative MUST be examined first. > Tom Davidson > Richmond, VA Interesting discussion. Question begs asking: were the events of 9/11/2001 a genuine attack by Saudi Arabian extremists wielding boxcutters ... or were they an inside job planned and carried out with some degree of complexity? And how does Einstein's principle of minimum complexity apply here? -zookumar- ps: www.infowars.com === Subject: Re: Epistemology: debunking v. open-mindedness <1230461888.8582.0@proxy01.news.clara.net> posting-account=rsfFvAoAAADqHCqmunbjtmaKjfuP-pwP .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; InfoPath.1; .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) > Copernicus............what about Aristarchus? Why did it take another > 1800+ years to debunk the geocentric model? Select all that apply..... > 1/ No one else cared > 2/ Religious intervention > 3/ Waiting for the invention of the telescope > 4/ Waiting for the laws of motion No, you forget the more releavnt reasons. Firstly, as the church realised, and Galileo didn't a model is only a > model. All knowledge is relative to core assumptions made a priori about > the nature of the world. The geocentric model is no better and no worse > than a heliocentric model, which is also false as it happens, by the > same tokens used to 'debunk' the geocentric ones. It merely happens that when mathematics is applied to the heliocentric > one, the mathematics becomes easier. The calculations are simpler. If Galileo had managed to restrict himself to that truth, he wouldn't > have become persecuted. Instead he claimed absolute knowledge, which was > learned paper after learned paper, the lesson still fails to be > understood: You cannot really have objective factual knowledge about > anything (Kant), and a model is not the reality, and is only as good as > its ability to predict results, and not be shown to have implications > that turn out to be false (cf Popper) and always contains an A priori > assumption that cannot be proved (Godel). However people require certainties beyond 'the only certain thing is > that there is no certain thing' and hence we have religion to assure us > that all is in fact well. And rational materialists to assure us that > the world we perceive is free of all perspective and assumption about > its nature, and is indeed exactly as we think it is. Blue pill or red pill? > Phil H. Phil, amazing stuff: what more can I say? Popper was not just a logician, though, but invesigated studiously how knowledge grew and what the obstacles were to its growth. Haldane, perhaps, got it right: 'The Universe is not only a queerer place than we imagine; it is a queerer place than we can imagine!' The Ancient Geeks were excited about what they could not do, whilist we are excited almost only about what we can do! -- Yrs, John. === Subject: Re: Epistemology: debunking v. open-mindedness posting-account=qHNgPQoAAAA40SLlrmjQxSJhnyKS76HY AppleWebKit/525.19 (KHTML, like Gecko) Chrome/1.0.154.36 Safari/525.19,gzip(gfe),gzip(gfe) Debunk (verb):http://onelook.com/?w=debunk&ls=a > 21 dictionaries - all the definitions have in common the concept that > the TOPIC being debated is displayed and attention is drawn to the > alleged weakness/errors of the concept. Sure, and when that runs out the debunker will go ad hominam on your ass. Eliminative journalism and litter postings provide further aid. > Skeptic (noun):http://onelook.com/?w=skeptic&ls=a > 27 dictionaries - all the definitions have in common the concept that > the person merely doubts the truth oor value of a certain idea. It's guess work in the negative sense. This is why they have such boring lives. After dishonestly suggesting themselves into non- investigation they can move on to the next subject they are not interested in. > A debumnker is a skeptic whose doubt has motivated him to action in > expressing his doubts. You are simply describing a character assassin, in the manner of naive > partisan politicians. Not at all, the septic is just boring himself to death, the debunker kills others by destroying the natural flow of things. > I have seen far too much of this on the US > political scene in the past 15 months or so. pump baby pump, drill baby drill? > ...partisan political character assassins. There is very little > skeptical or debunking about this. okay, I agree it was a ty example but I did provide a long list of other topics didn't I? Lets wall though the list. *Flying saucers: What do you know about it? Did you write any kosher posting about it? Did you cover the majority of data? There is an abundance of debunkers here. The news media is full of it. Every review is a half baked farce. *Remote viewing: What do you know about it? Did you write any kosher posting about it? Did you cover the majority of data? Plenty of debunking going on here. * Permanent magnet motors: What do you know about it? Did you write any kosher posting about it? Did you cover the majority of data? * Hemp: What do you know about it? Did you write any kosher posting about it? Did you cover the majority of data? Sure we could call debunking hemp Partisan hackery but what are the arguments for putting all those millions of people in prison? Is it septicism or debunking? * Royal Raymond Rife: What do you know about it? Did you write any kosher posting about it? Did you cover the majority of data? This is far-out debunking: en.wikipedia.org/wiki/Royal Rife Heaps of scientific data, but the wikipedia assassin claims even claims the microscope doesn't exist. This is what I refer to as debunking: en.wikipedia.org/wiki/Talk:Royal Rife A whole page full of debunking. no no, the microscope doesn't exist even if you add 100 ref's: en.wikipedia.org/w/index.php? title=Royal Rife&diff=next&oldid=248930654 A septic would be far to lazy to even look up the man. Don't gaze at the search results, middle click some links then bother to click deeper than the front pages. * Dowsing: What do you know about it? Did you write any kosher posting about it? Did you cover the majority of data? Lets have an example with this, I assume you know Magic Randi? I'm not defending Dowsing here, I'm showing you what professional debunking looks like. Imagine you are in a class taking a test. Would you want to know your score or would you find it acceptable to hear percentages for the whole class room? See? No test result was given to any dowser. If there was one who scored 80% we wouldn't know about it. But lets look at the numbers, the dowsers all claim to make a living dowsing water. brass: 0 correct / 26 attempts = 0% gold: 4 correct / 35 attempts = 12% water: 11 correct / 50 tries = 22% So the professional water dowsers actually score 120% higher than random. The debunkors final conclusion is that 15 out of 111 attempts equals 12% but in my book: 15 / 111 = 0.135135135 Magic Randi clearly leaves the truth up for speculation. So lets try. Putting the water dowsers under stress will also harm the results. How much is hard to tell but it is obvious it does make it harder. Try imagine how hard it is to fake this trick. He finds the tube and he finds the junction. There is not much room for doubt here. Look how the video is full of character assassination but at the end of the day they are Water dowsers and 11 correct out of 50 tries is well beyond random. something like 5000 tries to get a clear picture. 50 000 would be even better. If they still are at 120% above random with say 10 000 tests Randi should pay up. But in stead he chose to falsify the data 3 times. This is what I call debunking. I'm not interested in guessing if dowsing is real or not. This topic is about forging the facts to fit the agenda. * The quack who cured cancer: What do you know about it? Did you write any kosher posting about it? Did you cover the majority of data? * Mind control: What do you know about it? Did you write any kosher posting about it? Did you cover the majority of data? * Hypnosis: What do you know about it? Did you write any kosher posting about it? Did you cover the majority of data? * Inertial propulsion: What do you know about it? Did you write any kosher posting about it? Did you cover the majority of data? * Telekinesis: What do you know about it? Did you write any kosher posting about it? Did you cover the majority of data? * NLP: What do you know about it? Did you write any kosher posting about it? Did you cover the majority of data? * Pyrolysis: What do you know about it? Did you write any kosher posting about it? Did you cover the majority of data? * Sonofusion: What do you know about it? Did you write any kosher posting about it? Did you cover the majority of data? * Vimana's: What do you know about it? Did you write any kosher posting about it? Did you cover the majority of data? Are you a debunker Tadchem or are you a lazy septic to lazy to look at interesting things? Will you cherry pick a sentence again or can you address the whole post? I promise it are all very interesting subjects. That should be reason enough. Remember, lack of interest renders a person 100% incapable of doing even the most basic investigation. A boring life. http://blog.360.yahoo.com/factuurexpress === Subject: Re: Epistemology: debunking v. open-mindedness posting-account=jPnQ2goAAAA461y3QD0lbyw0oKeThma1 AppleWebKit/525.18 (KHTML, like Gecko) Version/3.1.2 Safari/525.20.1 FOH:R051,gzip(gfe),gzip(gfe) the Amuzing Randi is quite a hack, like his attack on Bienveniste's labwork in homeopathy -- he nearly destroyed the place (in Skeptical Inquirer, I think). anyway, the Skeptics were just another cult of Delphi, and most of those groups' names are used as put-downs (viz, Peripatetics, Stoics, Epicureans, Gnostics etc.), and Ochamites should be one of the latter-day ones (see below). most of your below debunkees really are garbage, other than Rife AFAIK (from KPFK-FM .-) however, remote-viewing is just a spin-off from MK-ultra, speaking of mind-control, which is really almost entirely in the realm of mass-media, strictly passive-aggressive, although there are certainly all sorts of patented devices that *could* possibly used in an organized fashion, along with nonlethal waepons; if you've ever listened to purveyors of RV on Art Bell, you know what I'm talkin'about, along with every-other profit & kook there is, who can put two audible words together -- reverse speech, every one? when you say inertial propulsion, it's just a gag-order; what kind of propulsion is non-inertial?... I presumed that your initial cite of Keeley was that you were a skeptic on it; clearly, the PTO left it out there, as an IQ test for other such patentors: if you can state the principle of the Keeley microsuck, you win! now, why did you not include catalyzed or cold fusion -- what is so impossible about that? > *Flying saucers: What do you know about it? Did you write any kosher > *Remote viewing: What do you know about it? Did you write any kosher > * Permanent magnet motors: What do you know about it? Did you write > * Hemp: What do you know about it? Did you write any kosher posting > * Dowsing: What do you know about it? Did you write any kosher > * Mind control: What do you know about it? Did you write any kosher > * Hypnosis: What do you know about it? Did you write any kosher > * Inertial propulsion: What do you know about it? Did you write any > * Telekinesis: What do you know about it? Did you write any kosher > * NLP: What do you know about it? Did you write any kosher posting > * Sonofusion: What do you know about it? Did you write any kosher thus quoth re Ockham: As Machiavelli's The Art of War and his commentaries on Livy, make the implications of the issues of the Sixteenth and early Seventeenth European centuries clearer, the Renaissance political and economic transformation of the character of the modern city and nation-state, had produced a combined scientific-technical, social, and political situation, which, in net effect, could not be mastered with any degree of finality by the so-called Aristotelean methods of the late Roman and Byzantine empires, and as prevalent in most of the times and places of the post-Charlemagne Middle Ages. This kind of failure of the so-called Aristotelean doctrine, had been utilized for the rise of power of a new Venetian faction, one premised on the dogma of William of Ockham, and led by Paolo Sarpi. The particular significance of the philosophical liberalism introduced under Sarpi's leadership of his Venetian faction, has been encapsulated, for our immediate consideration here, by attention to the systemic implications of the particular form of Sophistry which Sarpi and his lackey Galileo Galilei applied to the intent of outflanking the strategic quality of perceived threat to Venetian interests which the rise of modern science and technology had represented for ruining the efforts to continue the Aristotelean form of medieval feudal tradition of opposition to an actual form of physical science. This new form of what became a widespread moral corruption of science and society, was what became known as Anglo- Dutch Liberalism. Three Political Options That aspect of Machiavelli's influence, and the contrasting influence expressed by Sarpi's and Galileo's adoption of the wild-eyed irrationalism of the medieval William of Ockham (Latin: Occam), as catalyzed the division of the principal optional choices of form of modern nation-state among three principal ranges of types among modern European models of political-economy: 1.) The American System model (e.g., Alexander Hamilton's The American System of political-economy), as reflected, most notably, in the policies of practice of U.S. Presidents John Quincy Adams, Abraham Lincoln, and Franklin D. Roosevelt; 2.) The European model of a Liberal blending of financier- aristocracy, from above, and democracy, below, as this arrangement is typified by the European model of parliamentary systems; and, 3.) The dictatorial forms of Liberalism, which might be called the Hobbesian model, in such forms as fascism, adopted by the Liberal system when Liberal financier-oligarchical control over, and through the parliamentary system breaks down, or threatens to break down. === Subject: Re: Epistemology: debunking v. open-mindedness posting-account=qHNgPQoAAAA40SLlrmjQxSJhnyKS76HY AppleWebKit/525.19 (KHTML, like Gecko) Chrome/1.0.154.36 Safari/525.19,gzip(gfe),gzip(gfe) > the Amuzing Randi is quite a hack, like his attack > on Bienveniste's labwork in homeopathy -- he nearly > destroyed the place (in Skeptical Inquirer, I think). anyway, > the Skeptics were just another cult of Delphi, and > most of those groups' names are used as put-downs (viz, > Peripatetics, Stoics, Epicureans, Gnostics etc.), and > Ochamites should be one of the latter-day ones (see below). most of your below debunkees really are garbage, In what way? I claim there are partisan hacks under all of those. Things don't become credible until officially denied. lol > other than Rife AFAIK (from KPFK-FM .-) however, > remote-viewing is just a spin-off from MK-ultra, Nah, remote viewing is just a kind of dowsing. We have plenty of oracles and soothsayers though out history. Monks in Tibet have the far most advanced spies on the globe. lol The CIA remote viewing program was created after figuring out the Russians where using it. But you are not suppose to know about this so non of it is real, just remember that :P > speaking > of mind-control, which is really almost entirely in the realm > of mass-media, Just gazing at a screen already induces a dream like state. Just like RV our beloved debunkers will try bury it in doubts. > strictly passive-aggressive, although > there are certainly all sorts of patented devices > that *could* possibly used in an organized fashion, > along with nonlethal waepons; lol, nonlethal is the tax payer terminology. I'm pretty sure they are working at the zombie soldier while we type. That what is declassified now is already very scary, the militards cant declassify anything unless they have something that makes it look ancient. > if you've ever listened > to purveyors of RV on Art Bell, you know what I'm talkin'about, hahaha, a most professional debunking show. Not sure if I remembered it well but some dude wanted to explain water fueled cars and zero point energy aka how UFO's fly but his excuse was that he didn't believe in fusion powered cars until he drove one for at least 10 000 miles. Quite unreasonable from his position then again the show lives off the mystery you know. ;) > along with every-other profit & kook there is, > who can put two audible words together -- reverse speech, > every one? Funny topic, I hear lots of good examples but something prevents me from wanting to believe in it. I do know there are people who can double talk backwards on purpose. EVP is also funny. There are some pretty interesting testimonials but again I have jet to hear the first reasonable recording and just a recording doesn't make it credible. > when you say inertial propulsion, it's just a gag-order; > what kind of propulsion is non-inertial? Space propulsion without a rocket. Just a closed box generating thrust. You cant have one so they lie about it. lol >... I presumed that > your initial cite of Keeley was that you were a skeptic on it; nah, way to much debunkers without arguments to be septical about Keely. His actual work was destroyed, but today there are quite a few technologies that fit his description. To me that means the rest of his bizarre claims are worth keeping in mind. Or perhaps we should say treated sympathetically. To lower ourselves from musical annotation with all it's features and effects all the way down to hertzian waves is quite obviously a quantum leap backwards. > clearly, the PTO left it out there, as an IQ test > for other such patentors: if you can state the principle > of the Keeley microsuck, you win! You can have a Keely motor build if you have enough money. > now, why did you not include catalyzed or cold fusion -- > what is so impossible about that? I just named a few things, there are thousands of examples. Mythbusters couldn't even build an electrolysis cell. ehm? haha? This one is funny. http://www.youtube.com/watch?v=wt3smrXkVpE&feature=channel page Here, knock yourself out.... http://blog.360.yahoo.com/factuurexpress > *Flying saucers: What do you know about it? Did you write any kosher > *Remote viewing: What do you know about it? Did you write any kosher > * Permanent magnet motors: What do you know about it? Did you write > * Hemp: What do you know about it? Did you write any kosher posting > * Dowsing: What do you know about it? Did you write any kosher > * Mind control: What do you know about it? Did you write any kosher > * Hypnosis: What do you know about it? Did you write any kosher > * Inertial propulsion: What do you know about it? Did you write any > * Telekinesis: What do you know about it? Did you write any kosher > * NLP: What do you know about it? Did you write any kosher posting > * Sonofusion: What do you know about it? Did you write any kosher thus quoth re Ockham: > As Machiavelli's The Art of War and his commentaries on Livy, make the > implications of the issues of the Sixteenth and early Seventeenth > European centuries clearer, the Renaissance political and economic > transformation of the character of the modern city and nation-state, > had produced a combined scientific-technical, social, and political > situation, which, in net effect, could not be mastered with any degree > of finality by the so-called Aristotelean methods of the late Roman > and Byzantine empires, and as prevalent in most of the times and > places of the post-Charlemagne Middle Ages. This kind of failure of > the so-called Aristotelean doctrine, had been utilized for the rise of > power of a new Venetian faction, one premised on the dogma of William > of Ockham, and led by Paolo Sarpi. The particular significance of the philosophical liberalism introduced > under Sarpi's leadership of his Venetian faction, has been > encapsulated, for our immediate consideration here, by attention to > the systemic implications of the particular form of Sophistry which > Sarpi and his lackey Galileo Galilei applied to the intent of > outflanking the strategic quality of perceived threat to Venetian > interests which the rise of modern science and technology had > represented for ruining the efforts to continue the Aristotelean form > of medieval feudal tradition of opposition to an actual form of > physical science. This new form of what became a widespread moral > corruption of science and society, was what became known as Anglo- > Dutch Liberalism. Three Political Options > That aspect of Machiavelli's influence, and the contrasting influence > expressed by Sarpi's and Galileo's adoption of the wild-eyed > irrationalism of the medieval William of Ockham (Latin: Occam), as > catalyzed the division of the principal optional choices of form of > modern nation-state among three principal ranges of types among modern > European models of political-economy: 1.) The American System model > (e.g., Alexander Hamilton's The American System of political-economy), > as reflected, most notably, in the policies of practice of U.S. > Presidents John Quincy Adams, Abraham Lincoln, and Franklin D. > Roosevelt; 2.) The European model of a Liberal blending of financier- > aristocracy, from above, and democracy, below, as this arrangement is > typified by the European model of parliamentary systems; and, 3.) The > dictatorial forms of Liberalism, which might be called the Hobbesian > model, in such forms as fascism, adopted by the Liberal system when > Liberal financier-oligarchical control over, and through the > parliamentary system breaks down, or threatens to break down. And thus became footbal the meaning of life. ROFL === Subject: Re: Epistemology: debunking v. open-mindedness posting-account=jPnQ2goAAAA461y3QD0lbyw0oKeThma1 AppleWebKit/525.18 (KHTML, like Gecko) Version/3.1.2 Safari/525.20.1 FOH:R051,gzip(gfe),gzip(gfe) here is an example of the Skeptics (current Calif. or USA mag.) being unable to come-up with a rational explanation of: sodium-vapor streetlights going off, as you walk underneath them; they think it to be either a hoax or psycho/visual. also, cropcircles. also, I forgot. --only 24 hours to impeach Trickier Dick from the N.Admin, metaphorically typing, or Cheeny & Zbiggy, fo'mo' years; Good Morning, Afghanistan! ... Good Afternoon, Sudan! http://tarpley.net/bush12.htm http://wlym.com/campaigner/8011.pdf -- Brits hate Shakes, Why? http://www.wlym.com/~seattle/dynamis/ http://www.21stcenturysciencetech.com/current.html http://www.rwgrayprojects.com/synergetics/plates/plates.html http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=3163 http://wlym.com/campaigner/8011.pdf -- English, not! === Subject: Re: Epistemology: debunking v. open-mindedness posting-account=Yn5cwwoAAADntcMuRwk-EwLg-DMZ_hXN rv:1.9.0.5) Gecko/2008120121 Firefox/3.0.5,gzip(gfe),gzip(gfe) > Lets wall though the list. *Flying saucers: What do you know about it? Did you write any kosher > posting about it? Did you cover the majority of data? There is an abundance of debunkers here. The news media is full of it. > Every review is a half baked farce. *Remote viewing: What do you know about it? Did you write any kosher > posting about it? Did you cover the majority of data? Plenty of debunking going on here. * Permanent magnet motors: What do you know about it? Did you write > any kosher posting about it? Did you cover the majority of data? * Hemp: What do you know about it? Did you write any kosher posting > about it? Did you cover the majority of data? Sure we could call debunking hemp Partisan hackery but what are the > arguments for putting all those millions of people in prison? Is it > septicism or debunking? * Royal Raymond Rife: What do you know about it? Did you write any > kosher posting about it? Did you cover the majority of data? This is far-out debunking: en.wikipedia.org/wiki/Royal Rife Heaps of scientific data, but the wikipedia assassin claims even > claims the microscope doesn't exist. This is what I refer to as > debunking: en.wikipedia.org/wiki/Talk:Royal Rife A whole page full of debunking. no no, the microscope doesn't exist > even if you add 100 ref's: en.wikipedia.org/w/index.php? > title=Royal Rife&diff=next&oldid=248930654 A septic would be far to lazy to even look up the man. > Don't gaze at the search results, middle click some links then bother > to click deeper than the front pages. * Dowsing: What do you know about it? Did you write any kosher > posting > about it? Did you cover the majority of data? Lets have an example with this, I assume you know Magic Randi? I'm not > defending Dowsing here, I'm showing you what professional debunking > looks like. Imagine you are in a class taking a test. Would you want > to know your score or would you find it acceptable to hear percentages > for the whole class room? > See? No test result was given to any dowser. If there was one who > scored 80% we wouldn't know about it. But lets look at the numbers, > the dowsers all claim to make a living dowsing water. brass: 0 correct / 26 attempts = 0% > gold: 4 correct / 35 attempts = 12% water: 11 correct / 50 tries = 22% So the professional water dowsers actually score 120% higher than > random. The debunkors final conclusion is that 15 out of 111 attempts equals > 12% but in my book: 15 / 111 = 0.135135135 Magic Randi clearly leaves the truth up for speculation. So lets try. > Putting the water dowsers under stress will also harm the results. How > much is hard to tell but it is obvious it does make it harder. Try imagine how hard it is to fake this trick. He finds the tube and > he finds the junction. There is not much room for doubt here. > Look how the video is full of character assassination but at the end > of the day they are Water dowsers and 11 correct out of 50 tries is > well beyond random. something like 5000 tries to get a clear picture. 50 000 would be even > better. If they still are at 120% above random with say 10 000 tests > Randi should pay up. But in stead he chose to falsify the data 3 > times. This is what I call debunking. I'm not interested in guessing > if dowsing is real or not. This topic is about forging the facts to > fit the agenda. * The quack who cured cancer: What do you know about it? Did you > write > any kosher posting about it? Did you cover the majority of data? * Mind control: What do you know about it? Did you write any kosher > posting about it? Did you cover the majority of data? * Hypnosis: What do you know about it? Did you write any kosher > posting about it? Did you cover the majority of data? * Inertial propulsion: What do you know about it? Did you write any > kosher posting about it? Did you cover the majority of data? * Telekinesis: What do you know about it? Did you write any kosher > posting about it? Did you cover the majority of data? * NLP: What do you know about it? Did you write any kosher posting > about it? Did you cover the majority of data? * Pyrolysis: What do you know about it? Did you write any kosher > posting about it? Did you cover the majority of data? * Sonofusion: What do you know about it? Did you write any kosher > posting about it? Did you cover the majority of data? * Vimana's: What do you know about it? Did you write any kosher > posting about it? Did you cover the majority of data? Are you a debunker Tadchem or are you a lazy septic to lazy to look at > interesting things? Will you cherry pick a sentence again or can you > address the whole post? I promise it are all very interesting > subjects. That should be reason enough. Remember, lack of interest renders a person 100% incapable of doing > even the most basic investigation. A boring life. i remember the studies by csicop on the mars effect and birth date related effects on athleticism where they actually tried to hide the data that their study showed scientifically significant correlation that is what skepticism is that is what debunking is the so-tight desperate hold on a reality they don't quite understand but certainly don't want others knowing of course recent respectable research showing time-of-year correlations on the progress of various developmental mechanisms in early infant growth has been popping up more frequently lately in many quite respectable journals some have been even making into popular news that astrological signs may have some meaning due a very real and physically measurable effect of weather and temperature on infants is the type of data skeptics typically cannot handle === Subject: Re: Epistemology: debunking v. open-mindedness posting-account=qHNgPQoAAAA40SLlrmjQxSJhnyKS76HY AppleWebKit/525.19 (KHTML, like Gecko) Chrome/1.0.154.36 Safari/525.19,gzip(gfe),gzip(gfe) > Lets wall though the list. > *Flying saucers: What do you know about it? Did you write any kosher > posting about it? Did you cover the majority of data? > There is an abundance of debunkers here. The news media is full of it. > Every review is a half baked farce. > *Remote viewing: What do you know about it? Did you write any kosher > posting about it? Did you cover the majority of data? > Plenty of debunking going on here. > * Permanent magnet motors: What do you know about it? Did you write > any kosher posting about it? Did you cover the majority of data? > * Hemp: What do you know about it? Did you write any kosher posting > about it? Did you cover the majority of data? > Sure we could call debunking hemp Partisan hackery but what are the > arguments for putting all those millions of people in prison? Is it > septicism or debunking? > * Royal Raymond Rife: What do you know about it? Did you write any > kosher posting about it? Did you cover the majority of data? > This is far-out debunking: en.wikipedia.org/wiki/Royal Rife > Heaps of scientific data, but the wikipedia assassin claims even > claims the microscope doesn't exist. This is what I refer to as > debunking: > en.wikipedia.org/wiki/Talk:Royal Rife > A whole page full of debunking. no no, the microscope doesn't exist > even if you add 100 ref's: > en.wikipedia.org/w/index.php? > title=Royal Rife&diff=next&oldid=248930654 > A septic would be far to lazy to even look up the man. > Don't gaze at the search results, middle click some links then bother > to click deeper than the front pages. > * Dowsing: What do you know about it? Did you write any kosher > posting > about it? Did you cover the majority of data? > Lets have an example with this, I assume you know Magic Randi? I'm not > defending Dowsing here, I'm showing you what professional debunking > looks like. Imagine you are in a class taking a test. Would you want > to know your score or would you find it acceptable to hear percentages > for the whole class room? > See? No test result was given to any dowser. If there was one who > scored 80% we wouldn't know about it. But lets look at the numbers, > the dowsers all claim to make a living dowsing water. > brass: 0 correct / 26 attempts = 0% > gold: 4 correct / 35 attempts = 12% > water: 11 correct / 50 tries = 22% > So the professional water dowsers actually score 120% higher than > random. > The debunkors final conclusion is that 15 out of 111 attempts equals > 12% > but in my book: 15 / 111 = 0.135135135 > Magic Randi clearly leaves the truth up for speculation. So lets try. > Putting the water dowsers under stress will also harm the results. How > much is hard to tell but it is obvious it does make it harder. > Try imagine how hard it is to fake this trick. He finds the tube and > he finds the junction. There is not much room for doubt here. > Look how the video is full of character assassination but at the end > of the day they are Water dowsers and 11 correct out of 50 tries is > well beyond random. > something like 5000 tries to get a clear picture. 50 000 would be even > better. If they still are at 120% above random with say 10 000 tests > Randi should pay up. But in stead he chose to falsify the data 3 > times. This is what I call debunking. I'm not interested in guessing > if dowsing is real or not. This topic is about forging the facts to > fit the agenda. > * The quack who cured cancer: What do you know about it? Did you > write > any kosher posting about it? Did you cover the majority of data? > * Mind control: What do you know about it? Did you write any kosher > posting about it? Did you cover the majority of data? > * Hypnosis: What do you know about it? Did you write any kosher > posting about it? Did you cover the majority of data? > * Inertial propulsion: What do you know about it? Did you write any > kosher posting about it? Did you cover the majority of data? > * Telekinesis: What do you know about it? Did you write any kosher > posting about it? Did you cover the majority of data? > * NLP: What do you know about it? Did you write any kosher posting > about it? Did you cover the majority of data? > * Pyrolysis: What do you know about it? Did you write any kosher > posting about it? Did you cover the majority of data? > * Sonofusion: What do you know about it? Did you write any kosher > posting about it? Did you cover the majority of data? > * Vimana's: What do you know about it? Did you write any kosher > posting about it? Did you cover the majority of data? > Are you a debunker Tadchem or are you a lazy septic to lazy to look at > interesting things? Will you cherry pick a sentence again or can you > address the whole post? I promise it are all very interesting > subjects. That should be reason enough. > Remember, lack of interest renders a person 100% incapable of doing > even the most basic investigation. > A boring life. i remember the studies by csicop > on the mars effect > and birth date related effects on athleticism > where they actually tried to hide the data > that their study showed scientifically significant correlation that is what skepticism is that is what debunking is the so-tight desperate hold on a reality > they don't quite understand > but certainly don't want others knowing of course > recent respectable research > showing time-of-year correlations > on the progress of various developmental mechanisms > in early infant growth > has been popping up more frequently lately > in many quite respectable journals some have been even making into popular news that astrological signs may have some meaning > due a very real and physically measurable effect > of weather and temperature on infants > is the type of data skeptics typically cannot handle -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- > galathaea: prankster, fablist, magician, liar Yeah, thats a fun example. I didn't believe a word of it but people seemed to replace their saucer propulsion technology research with astrology. Struck me as more than a little bizarre. They must have at least some character data that fits the chart. Doesn't prove anything but it does make it interesting. I guess it's another case of divide and concur where they don't want us to know what star we came from. It was debunked good, I hear mainstream astrology doesn't even get the star signs right. In China people try to live up to the horoscopic expectations which seems some what upside down? That cant be how it originated? Can it? http://blog.360.yahoo.com/factuurexpress === Subject: Re: Epistemology: debunking v. open-mindedness posting-account=d-ESTAkAAAAG0l03yI1WJgsTVXx4ebeJ Gecko/20080829 Firefox/2.0.0.17,gzip(gfe),gzip(gfe) > that astrological signs may have some meaning > due a very real and physically measurable effect > of weather and temperature on infants > is the type of data skeptics typically cannot handle > -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- > galathaea: prankster, fablist, magician, liar Yeah, thats a fun example. I didn't believe a word of it but people seemed to replace their > saucer propulsion technology research with astrology. Struck me as > more than a little bizarre. They must have at least some character > data that fits the chart. Doesn't prove anything but it does make it > interesting. But of course this is ALWAYS the question people want to ask: Do you BELIEVE? That may be a valid question for religion but obviously has no place in science. In science we ask: Have you observed the facts? So we are all trained when reading a list of unapproved science topics to start to get defensive and start saying we do not believe in them. We start saying that there is nothing to them. And we also start saying that time would be better spent filling in the missing data in obscure handbook tables than investigating one of these off- limits topics. The implication is that humanity would be better served in that way. But all our history proves that view wrong. Sure, accurate handbooks of material properties are nice, but I don't think they've saved as many lives as say Pasteur's germ theory. The question therefore is NOT do you believe, but rather what do we know about this that is TRUE. And I'm not talking about guesses or a priori opinions. I mean REAL data. So people wonder about Astrology. Is it true? As far as I know nobody has really done the research yet beyond the most elementary and primitive stages. Today with modern database technology investigations of astrological effects are straight forward. Not easy but straight-forward. Just like the Dowsing example above, real experiments take LOTS of data. THOUSANDS of dowsers. Millions of astrologically suspected events. And who has done the experiment? Nobody. Because the debunkers say there is nothing there to investigate. How do they know if the experiment hasn't been done? They can't. It's obviously an agenda of some kind. This is where the difference between skeptics and debunkers comes in. The skeptic says my theory is different from his theory, but both admit the real theory hasn't been proved. The debunker says, That theory is WRONG, and anyone who even investigates it probably wears a tinfoil hat!. Is that science? Hardly. === Subject: Re: Epistemology: debunking v. open-mindedness posting-account=jPnQ2goAAAA461y3QD0lbyw0oKeThma1 AppleWebKit/525.18 (KHTML, like Gecko) Version/3.1.2 Safari/525.20.1 FOH:R051,gzip(gfe),gzip(gfe) even Ockham'd slice through that apple & orange, with one wild Yahoo! (tm); western astrology is the same as Ptolemy's epicyclic hoax, over 2000yo. > some have been even making into popular news. > that astrological signs may have some meaning thus: I yam lying what I bean!... of what possible use is the set of all sets, whether or not it can eventually include itself, at the end of the list of elements -- shades of AP-adics? so, perhaps we can blame Russell for the Bourbaki New Math, based upon set theory, but see what Whitehead had to say about him, not to say Godel. thus: shouldn't it be clear that photons are an artifact of the idea that actually were zero-dimensional points, but, since they are waves, as shown by Young, Huyghens et al, there is really no need for them, except in the Pauli matrix formalism of statistical bosons; eh? Schroedinger's cat is dead -- long-live Schoredinger's cat! --only 24 hours to impeach Trickier Dick from the N.Admin, metaphorically typing, or Cheeny & Zbiggy, fo'mo' years; Good Morning, Afghanistan! ... Good Afternoon, Sudan! http://tarpley.net/bush12.htm http://wlym.com/campaigner/8011.pdf -- Brits hate Shakes, Why? http://www.wlym.com/~seattle/dynamis/ http://www.21stcenturysciencetech.com/current.html http://www.rwgrayprojects.com/synergetics/plates/plates.html http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=3163 http://wlym.com/campaigner/8011.pdf -- English, not! === Subject: Re: Epistemology: debunking v. open-mindedness posting-account=Yn5cwwoAAADntcMuRwk-EwLg-DMZ_hXN rv:1.9.0.5) Gecko/2008120121 Firefox/3.0.5,gzip(gfe),gzip(gfe) > even Ockham'd slice through that apple & orange, > with one wild Yahoo! (tm); western astrology is the same > as Ptolemy's epicyclic hoax, over 2000yo. > some have been even making into popular news. > that astrological signs may have some meaning month of birth correlated to lifespan correlation with body size http://www3.interscience.wiley.com/journal/110482564/abstract correlation with summer seasonal allergies http://www3.interscience.wiley.com/journal/119633341/abstract?CRETRY=1&SRETR Y=0 among many others now there is no evidence for a segregation into 12 types as astrology does usually the studies are either mono- or bi-modal so typically 4 types may be sufficient which appears closely related to the seasonal types however that's not to say that some more subtle variations possibly even local variations like the interaction of bloom seasons that could delimit a 12-type classification the point is science isn't about debunking astrology as is way too commonly the case in skeptic communities it is about providing models for observations as a means for building language and providing for prediction as an input to technology the modern skeptic would be an affront to the classic school by the same name === Subject: Re: Epistemology: debunking v. open-mindedness > even Ockham'd slice through that apple & orange, > with one wild Yahoo! (tm); western astrology is the same > as Ptolemy's epicyclic hoax, over 2000yo. > some have been even making into popular news. > that astrological signs may have some meaning month of birth correlated to lifespan correlation with body size > http://www3.interscience.wiley.com/journal/110482564/abstract correlation with summer seasonal allergies > http://www3.interscience.wiley.com/journal/119633341/abstract?CRETRY=1&SRETR Y =0 among many others now > there is no evidence for a segregation into 12 types > as astrology does usually the studies are either mono- or bi-modal > so typically 4 types may be sufficient > which appears closely related to the seasonal types however > that's not to say that some more subtle variations > possibly even local variations > like the interaction of bloom seasons > that could delimit a 12-type classification the point is > science isn't about debunking astrology > as is way too commonly the case > in skeptic communities it is about providing models for observations > as a means for building language > and providing for prediction > as an input to technology the modern skeptic would be an affront > to the classic school by the same name I think a devil's advocate system might help. This is where a skeptic is charged with reviewing the debunker's research for over-extended claims, faults, etc. The devil's advocate's conclusions should be findable from the debunker's paper. Where alleged phenomena are viewed as pseudo-science or worse, it's better if the devil's advocate's identity be kept anonymous. Say I were a devil's advocate for a heretic mathematician. A mainstream mathematician would debunk the heretic's results. As a devil's advocate, my role would be to find weaknesses in the debunker's paper. I could send my report through an anonymous re-mailer, signed with a cryptographic key, where there would be an anonymous public key repository. Then, I could be challenged with math. problems posted on a board, and if I solved one, or my devil's advocate paper provoked a response, I could send an answer signed with the same secret key; that way, I would remain anonymous but try to show a minimum standard of mathematical competence. Ideally, the inquisitor should have some assurance that I was the one who answered. For instance, the query could be enciphered with the devil's advocate's public key. But I could decipher the message and ask someone else for help. Or, one could abandon the signing with a key part, and just have one devil's advocate's report. There's still a question of who would qualify as a devil's advocate, and how to try to exclude the less competent. Finally, we might end up with a Usenet newsgroup, and readers could put unwanted posters in a kill-file. Any editor is a sort of gate-keeper. But without an editor, anybody can reply. It's complicated. David Bernier === Subject: Re: Epistemology: debunking v. open-mindedness <1230549601.24378.0@proxy02.news.clara.net> posting-account=Yn5cwwoAAADntcMuRwk-EwLg-DMZ_hXN rv:1.9.0.5) Gecko/2008120121 Firefox/3.0.5,gzip(gfe),gzip(gfe) ockham's razor is relative to a language like all complexity measures it may be possible to apply to a single person at a single time but extending beyond that is not possible without some additional negotiation === Subject: Re: Epistemology: debunking v. open-mindedness posting-account=Yn5cwwoAAADntcMuRwk-EwLg-DMZ_hXN rv:1.9.0.5) Gecko/2008120121 Firefox/3.0.5,gzip(gfe),gzip(gfe) > ockham's razor is relative to a language > like all complexity measures it may be possible to apply to a single person > at a single time > but extending beyond that is not possible > without some additional negotiation oh yeah and popper was a hack he had no understanding of the origin of linguistic reference in meaning and resorted to giving a priori status to a logic that was already known to be incorrect at least as applied to the real world what was funniest when i was receiving my degree in philosophy was during the philosophy of science class where the professor used popper's syllogisms and some reference to evolutionary observations to claim it had been disproven lamarck's claims of somatic influence on germ line this just happened through some cosmic coincidence to be the same month i had been reading lamb and jablonka's book on neolamarckianism where evidence on just such mechanisms was being found through protein arrangements on cell membranes methylation patterns reverse transcriptase of course when analysed the problem had been one of referent ambiguity as i had been arguing the entire course it turned into my senior project for the philosophy part of my dual degree... better for the soul would be lakatos === Subject: Re: Epistemology: debunking v. open-mindedness posting-account=rsfFvAoAAADqHCqmunbjtmaKjfuP-pwP .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; InfoPath.1; .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) Septics are very uninspired people. I have hundreds of interesting > things to look into. Septics do not. Septics know only how to make > things as uninteresting as they can. They have no hobbies, values or > interests. Septic for skeptic? Is this a 'Freudian slip' or a deliberate > effort to denigrate others prejudicially and pejoratively? > The personal attack is their main tool. You demonstrate great facility with this tool - far beyond my style. > aka Truth by insult. In their > lack of interest they render themselves 100% incapable of doing even > the most basic investigation. > Let me demonstrate: > Tom Davidson is a loon, he doesn't know what he is talking about, he > is dumb and he keeps making his pet assertions that have no basis in > reality. He has his head so far up his ass he things the world is made > out of poop. A real crank. Ah! The obligatory personal ad hominem appears. > Debunkers are quite different. > They get deployed specifically to get rid of knowledge. They slander > anyone who dares to bring up a subject but not because they are > ignorant farts but they act specifically to wear out the discussion. > In contrast with septics (who really are minions) the debunkers have a > large array of tricks. Debunk (verb):http://onelook.com/?w=debunk&ls=a > 21 dictionaries - all the definitions have in common the concept that > the TOPIC being debated is displayed and attention is drawn to the > alleged weakness/errors of the concept. Skeptic (noun):http://onelook.com/?w=skeptic&ls=a > 27 dictionaries - all the definitions have in common the concept that > the person merely doubts the truth oor value of a certain idea. A debumnker is a skeptic whose doubt has motivated him to action in > expressing his doubts. You are simply describing a character assassin, in the manner of naive > partisan politicians. I have seen far too much of this on the US > political scene in the past 15 months or so. > Here you can see some debunkers debunk Ron Paul. >http://www.youtube.com/watch?v=8PIEGK0IbA4 ...partisan political character assassins. There is very little > skeptical or debunking about this. Generally office-seekers of > all flavors (and their supporters) share objectives: to gain and weild > power over the masses, much as the medieval churchmen did. The only > people fit to lead are genuine Libertarians, and none of them really > want to do it. If trhey did, they would not be Libertarians. > Catch-22. You may continue to misuse the word debunk all you wish. Be > advised, however, that the semantic gap between you and the rest of > the world can only cause you frustration until you close it yourself. Tom Davidson > Richmond, VA Excellent compilation, Tom! Upshot: America can not meet its debts - in the long run. -- foolsrushin. === Subject: Simple newbie questions about almost all posting-account=upYccwoAAABw__aPpy--AjKB-bQCoebl AppleWebKit/312.8 (KHTML, like Gecko) Safari/312.5,gzip(gfe),gzip(gfe) In regard to the phrase almost all, please let me know if I have the correct idea about its proper use. 1) When comparing an infinite set to a finite set, it's correct to say that, for example, almost all positive integers are greater than five, because the positive integers are infinite and the set of positive integers less than six is finite. 2) When comparing an uncountable set to a countably infinite one, it's correct to say that, for example, almost all irrationals are transcendental, because the irrationals are uncountable, while the subset of the irrationals that are algebraic is countable. Another example would be, almost all reals are irrational. 3) When comparing an uncountable set of positive (Lebesgue) measure to an uncountable set of measure zero, it's correct to say that, for example, almost all of the reals between 0 and 1 are not members of the Cantor set, because the the interval (0,1) has measure one, while the Cantor set has measure zero. 4) Let P(N) be the number of positive integers less than N that are composite, i.e., not prime. Since the limit as N approaches infinity of P(N)/N = 1, it's correct to say, almost all positive integers are composite. Now, consider a fat Cantor set of (let's say small) positive measure. One could NOT say that almost all reals between 0 and 1 are not members of this set, because they are both uncountable sets of positive measure. Correct? Also, one could NOT say that almost all rationals are not integers. Even though there are a countable infinity of rationals between each integer, and the rationals are dense in R, while the integers are not, each is a countably infinite set of measure zero. Correct? So, is there a way, using some terminology similar to almost all, to point out the fact that there are vastly more rationals than integers? === Subject: Re: Simple newbie questions about almost all posting-account=AdyLXQoAAABgRay99CKv1O8Y_7jjivwq InfoPath.1),gzip(gfe),gzip(gfe) > Now, consider a fat Cantor set of (let's say small) positive > measure. One could NOT say that almost all reals between > 0 and 1 are not members of this set, because they are both > uncountable sets of positive measure. Correct? Also, one could NOT say that almost all rationals are not > integers. Even though there are a countable infinity of > rationals between each integer, and the rationals are dense > in R, while the integers are not, each is a countably infinite > set of measure zero. Correct? So, is there a way, using some terminology similar to > almost all, to point out the fact that there are vastly > more rationals than integers? There are three useful notions associated with each property of smallness in a fixed set/space: small -- the set satisfies the property of smallness large -- the set is not small co-small -- the complement of the set is small I'm using the word co-small to describe the sets that form almost all, in your sense, of the set/space. For this to usefully reflect what we understand by small, two properties are important. One is that any subset of a small set is a small set. The other is that the underlying set/space is not small. If we're in the real line and small means having Lebesgue measure zero, then large sets are sets with positive Lebesgue measure zero along with sets that are not measurable (both kinds of sets are captured if we just say sets with positive outer measure) and co-small sets are those which form almost all of the real line in the sense of Lebesgue measure. If we're in an infinite set and small means being finite, then large sets are the infinite sets and co-small sets are the co-finite sets. If we're in an uncountably infinite set and small means being countable, then large sets are the uncountable sets and co-small sets are the co-countable sets. If we're in the real line (more generally, in R^n; more generally still, in any complete metric space) and small means being first category (also called meager), then large sets are the second category sets and co-small sets are the residual sets (also called generic sets, or co-meager sets). Other notions of smallness are: being nowhere dense, having Hausdorff dimension less than the dimension of the underlying space, being in the plane and having linear Lebesgue measure zero relative to every line in the plane (more generally, being in the plane and having some linear smallness notion relative to every line in the plane), being simultaneously Lebesgue measure zero and first category (more generally, use the intersection of an arbitrary collection of notions of smallness), sets in the real line whose closure is countable (this is a stronger notion of smallness than countability, one that excludes the rational numbers, the endpoints of the open intervals forming the complement of the Cantor set, etc.), being in the plane and being a subset of some countable collection of lines (or a subset of some countable collection of sets each of which is geometrically congruent to the graph of a Lipschitz function (or a C^1 function, or a C^2 function, etc.)), sets in R^n whose closures are small according to some fixed specified notion of smallness, etc. For some of these notions of smallness, every finite union of small sets is small (every example I've given has this property), and sometimes it's even the case that every countable union of small sets is small (Lebesgue measure zero, countability, first category sets, the Hausdorff dimension example, etc.). The latter property is especially useful in analysis (real analysis, complex analysis, functional analysis, etc.) because it makes the notion of smallness robust with the numerous countability features of analysis: convergence of sequences (of numbers, of functions, of sets, etc.), the separability of spaces such as R^n and L^p, the countable additivity of Lebesgue measure, etc. The above notions of large and co-small are global notions. We can get stronger notions (in the real line) by requiring the set to be large, or to be co-small, relative to every open interval, properties that I'll call locally large and locally co-small. (Note that every small set is automatically locally small.) These notions can be thought of as ways to strengthen the idea of a set being dense. For example, a set is dense in the real line if and only if it is locally large relative to the finite sets (or equivalently, locally large relative to the countable sets). A set is measure dense in the real line if it is locally large relative to the Lebesgue measure zero sets (measure dense sets are often required to be measurable, I think). A set has full measure in the real line if it is locally co-small relative to the Lebesgue measure zero sets. Incidentally, having full measure is equivalent to having a measure zero complement. In general, if a smallness notion is closed under countable unions, then a set is co-small if and only if it is locally co-small (use the second countability property of the real line). Finally, in more general spaces we can localize the notions of large and co-small by requiring the property to hold relative to every nonempty open set. Dave L. Renfro === Subject: Re: Simple newbie questions about almost all posting-account=Cbgh4AoAAAAr0dt1RqLOClWCyUWii2fU Gecko/2008121621 Ubuntu/8.04 (hardy) Firefox/3.0.5,gzip(gfe),gzip(gfe) > In regard to the phrase almost all, please let me know if I have the > correct idea about its proper use. 1) When comparing an infinite set to a finite set, it's correct to say > that, for example, almost all positive integers are greater than > five, because the positive integers are infinite and the set of > positive integers less than six is finite. 2) When comparing an uncountable set to a countably infinite one, it's > correct to say that, for example, almost all irrationals are > transcendental, because the irrationals are uncountable, while the > subset of the irrationals that are algebraic is countable. Another > example would be, almost all reals are irrational. 3) When comparing an uncountable set of positive (Lebesgue) measure to > an uncountable set of measure zero, it's correct to say that, for > example, almost all of the reals between 0 and 1 are not members of > the Cantor set, because the the interval (0,1) has measure one, while > the Cantor set has measure zero. 4) Let P(N) be the number of positive integers less than N that are > composite, i.e., not prime. Since the limit as N approaches infinity > of P(N)/N = 1, it's correct to say, almost all positive integers are > composite. Now, consider a fat Cantor set of (let's say small) positive > measure. One could NOT say that almost all reals between 0 and 1 are > not members of this set, because they are both uncountable sets of > positive measure. Correct? Also, one could NOT say that almost all rationals are not integers. > Even though there are a countable infinity of rationals between each > integer, and the rationals are dense in R, while the integers are not, > each is a countably infinite set of measure zero. Correct? So, is there a way, using some terminology similar to almost all, to > point out the fact that there are vastly more rationals than integers? Almost is often used to mean all but finitely many. In that sense Almost all reals are transcendental becomes false, however. Sometimes it is an abbreviation all up to a set of measure 0. The nice thing is that Almost all x are P(x) and Almost all x are Q (x) implies Almost all x are both P(x) and Q(x). This holds with both meanings above, but also when we just say that the exception set be of smaller cardinality (provided the total is infinite). Without specification, I hink only the all but finitely many interpretation can be considered as default interpretation. === Subject: Re: Simple newbie questions about almost all > So, is there a way, using some terminology similar to almost all, to > point out the fact that there are vastly more rationals than integers? almost all in a linear algebra sense refers to the exceptional set, >if not finite, being confined to a subspace of lower dimension. Maybe one could reasonaly use almost all in that sense for integers >in rationals in the context of p-adic fields. But then again, maybe I'm talking hogwash. In the same spirit as above, how about this ... Regarding Q as an additive abelian group, with Z as a subgroup, consider the index of Z in Q. Since the index is infinite, in that sense, almost all elements of Q are not in Z. quasi === Subject: Re: Simple newbie questions about almost all > So, is there a way, using some terminology similar to almost all, to > point out the fact that there are vastly more rationals than integers? >almost all in a linear algebra sense refers to the exceptional set, >if not finite, being confined to a subspace of lower dimension. >Maybe one could reasonaly use almost all in that sense for integers >in rationals in the context of p-adic fields. >But then again, maybe I'm talking hogwash. In the same spirit as above, how about this ... Regarding Q as an additive abelian group, with Z as a subgroup, >consider the index of Z in Q. Since the index is infinite, in that >sense, almost all elements of Q are not in Z. I should be a little more careful here. Although it's true that the quotient group Q/Z is infinite, the more relevant fact is that, for any given n in N, all but finitely many elements of Q/Z have order greater than n. quasi === Subject: Re: Simple newbie questions about almost all > So, is there a way, using some terminology similar to almost all, to > point out the fact that there are vastly more rationals than integers? >almost all in a linear algebra sense refers to the exceptional set, >if not finite, being confined to a subspace of lower dimension. >Maybe one could reasonaly use almost all in that sense for integers >in rationals in the context of p-adic fields. >But then again, maybe I'm talking hogwash. >In the same spirit as above, how about this ... >Regarding Q as an additive abelian group, with Z as a subgroup, >consider the index of Z in Q. Since the index is infinite, in that >sense, almost all elements of Q are not in Z. I should be a little more careful here. Although it's true that the quotient group Q/Z is infinite, the more >relevant fact is that, for any given n in N, all but finitely many >elements of Q/Z have order greater than n. Hmmm ... Forget the above revision -- I think my original reply is OK. As I suggested at first, the very fact that the quotient group Q/Z is infinite suffices to give a simple, informal justification of the statement almost all elements of Q are not in Z. quasi === Subject: Re: Simple newbie questions about almost all <9frkl45a9d7321gjd1m84l61bbk8h03m93@4ax.com> posting-account=9QOSvAoAAACEOWJVSDuswW7dB_0wApQO Gecko/20070530 Fedora/1.5.0.12-1.fc5 Firefox/1.5.0.12,gzip(gfe),gzip(gfe) > So, is there a way, using some terminology similar to almost all, to > point out the fact that there are vastly more rationals than integers? >almost all in a linear algebra sense refers to the exceptional set, >if not finite, being confined to a subspace of lower dimension. >Maybe one could reasonaly use almost all in that sense for integers >in rationals in the context of p-adic fields. >But then again, maybe I'm talking hogwash. In the same spirit as above, how about this ... Regarding Q as an additive abelian group, with Z as a subgroup, > consider the index of Z in Q. Since the index is infinite, in that > sense, almost all elements of Q are not in Z. There is well-established jargon for up-to-finite-index notions: virtually. For example, a group is virtually without torsion if it has a finite-index subgroup which has no torsion, etc. -- m === Subject: Re: Palindromic Card Game > This is a card game for 2 players. (Although this game doesn't > technically require cards, using them makes the game easier to play.) Start with 2n cards, n red and n black cards. (You can play with a > standard deck {no jokers}, letting n be 26, and all spades and clubs > are black, all hearts and diamonds are red. All that matters in this > game is the colors of the cards' suits.) Deal n cards to each of the players. Players arrange their n cards in any order in a row, face up. > (One row of cards per player.) After the cards are arranged, each player then tries to find as many > distinct palindromes (symmetric patterns of of redness and blackness) > within their opponent's row of cards, where each palindrome starts and > ends with a red card. By DISTINCT palindrome I mean that each > particular arrangement of reds and blacks counts only once. > For example, if we have an n of 12 and we have the following row: R B B R R B B B R B B R Then the palindrome (R B B R) would be counted once, even though it > occurs twice in the row. > (The palindrome (BBRBB) would not count at all because it starts and > ends with black cards.) A player gets this many points: (number of red cards in the player's row) - (number of DISTINCT > palindromes found by the player's opponent in the player's row). (This score will always be 0 or higher.) Highest score wins. > Leroy Quet > # Yes, the Bean Counters (Mathematicians) can reduce any complex matter to a simple case of numerics. Instead, how about a pack of cards, all alphabetics, with letter frequency as in a Scrabble game? The pack may not be essential but would facilitate sorting up letters into words, enabling the traditional palindrome to be discovered or invented. Palindromes don't need to comprise only words which read same forwards as backwards, but whole sentences. One of the best (longest) I've come across (courtesy of American Cryptogram Assn) is - Was it a car or a cat I saw? (19 letters) === Subject: Re: JSH: Simplest explanation, Occam's Razor unleashed > In the complex plane with 7*(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x)+ 7) where the a's are roots of a^2 - (7x-1)a + (49x^2 - 14x) = 0 you normalize: a_1(x) = b_1(x), and a_2(x) = b_2(x) - 1, as then you have 7*(175x^2 - 15x + 2) = (5b_1(x) + 7)(5b_2(x)+ 2) where b_1(0) = 0, b_2(0) = 0. Now compare with 7*(x^2 + 3x + 2) = (7x + 7)(x + 2) and what is the primary difference? The type of function: in one case you have non-linear functions b_1(x) > and b_2(x), and in the other you have linear functions 7x and x. I suggest to you that the distributive property does not care. If some yahoo told you that the 7 bounced around like a kangaroo with 7*(x^2 + 3x + 2) = (7x + 7)(x + 2) based on the value of x, you'd say they were bonkers. But if some Ph.D's scared of losing some math beliefs and their > precious notion that the mathematical field is immune to upheavals > bitch and moan for years against it, you believe them, and screw the > complex plane. Simplest explanation. None of you have the spines for the situation. You all lack the balls > to confront a massive failure by your freaking colleagues. > Let's talk a little about 7 bounc[ing] around like a kangaroo. I'll look at your case. Here you have a polynomial in two indeterminates: y^2 - (7x-1)y + (49x^2 - 14x) whose roots [in y] are used to factor 7 P(x) = (5^2 7^2) x^2 - 3*5*7 x + 2*7 as 7 P(x) = (5 a_1 + 7)(5 a_2 + 7). You note, correctly, that when x = 0, we have the simpler form: y^2 + y with roots 0, -1, and conclude that if you normalize the functions in your factorization, you get 7 P(x) = (5 b_1 + 7)(5 b_2 + 2) where b_1 = a_1, b_2 = a_2 + 1. The further step is to choose which of the a's gets to be a_1, and which is a_2. You're no dummy, and so you chose a_1 to be the one that is 0 when x = 0 [so the corresponding factor in the b factorization gets to be 7], and the other the one that is -1 when x = 0 [leading to the complementary factor of 2]. You conclude that this distribution holds for all x. I'll simplify the above 2-variable polynomial using w = 7x - 1, to get this: Q(w,y) = y^2 - wy + (w^2 - 1) and I'll consider the Riemann surface S: S = {(w,y) in C^2 | Q(w,y) = 0} If I consider the gradient of Q: grad Q = (2y - w)D_y + (2w - y)D_w the fact that grad Q = 0 *only* for w = y = 0, and that point is not contained in S, implies that S is a smooth (i.e., infinitely differentiable) surface of 2 real dimensions (or one complex dimension, in which case it's analytic). There is a canonical projection to the first coordinate Pr: S -----> C (w,y) |--> w This map is smooth [actually, analytic, if you're keeping track of the complex structure], and one might well ask why it's at all relevant to the discussion. Note that for w fixed, the set of elements of S that map to w under this projection consists of the roots [in y] of the polynomial Q. In other words, the fibres of Pr are the functions a_1, a_2. Next, I'll show that JSH has been tricked by a little two-card monte that this Riemann surface plays on unsuspecting tourists in the big city. Keep your eyes on the red lady, gents, just pick where that red lady ends up, and you're in the money. Ready? Here we go... There are two special points (in w) where the projection Pr is a wee bit flaky. Since (for w fixed) Q(w,y) is a quadratic in y, it might be possible for Q to have only a single solution (in y, for w fixed). Let's check it out: Q(w,y) = y^2 - w y + (w^2 - 1) The discriminant is Discr = w^2 - 4(w^2 - 1) = 4 - 3 w^2 So, when Discr = 0, we get a single solution in y, rather than two. This happens when w^2 = 4/3, or w = +/- 2/sqrt(3). Recall, we have a smooth surface S, mapping to the complex plane C Pr: S ------> C (w,y) |--> w and now we find that when w = +/- 2/sqrt(3), there is only one point of S that maps to w. Otherwise, there are two. So what? Actually, something strange and wonderful. Near these two points in S (the pre-images of w = +/- 2/sqrt(3) ), the mapping is essentially z |--> z^2, in a way I'll make precise. Let s* denote one of these two points in S, with w* = Pr(s*). Then: There is a disc neighborhood U* of s* in S, and a disc neighborhood V* of w* in C, and smooth [or analytic ...] homeomorphisms p, q from U*, V* to the unit disc D of the complex plane C, for which the diagram Pr U* --------------> V* | | | | p | | q | | v v D --------------> D z^2 is commutative; this means (p(u))^2 = q(Pr(u)) Now, what does all this mean? Notice that on the boundary circle of D, the squaring operation wraps the circle twice around its image. Looking at the inverse operation, as I follow a point once around the circle on the right side, the two points on the left do the two-card monte: They SWAP POSITIONS! What that means is, if you've chosen one y value for your a_1(x), and the other y value for your a_2(x), and then care to move x around this little circle, what you wanted to be a_1(x) will cease to be 0 at x = 0, and what you wanted to be a_2(x) will cease to be -1 at x = 0. Here's the punch line: THERE IS NO CONTINUOUS CHOICE OF a_1, a_2 OVER ALL OF C Or the equally amusing: The kangaroo is still there. You don't have to believe me. I did a numerical integration that demonstrates this happening; you can do it too. Take the equation Q(w,y) = y^2 - w y + (w^2 - 1) = 0 and form its total differential (it's the gradient with differentials dw, dy replacing the vectors D_w, D_y): dQ = (2y - w) dy + (2w - y) dw Since Q is identically 0 on the surface S, dQ = 0, and we can use this differential to relate increments of w to increments of y. We march w from -1, around the point -2/sqrt(3), back to itself: w(t_k) = -2/sqrt(3) + r exp(it_k) for t_k running from 0 to 2 pi in tiny steps (I chose constant steps of size 0.01 degree, converted to radians). We have a formula for w(k), we can replace dw by the increment (w(k+1) - w(k)), and we solve for dy(k). Finally, take y(0) = 0 (our initial value), and accumulate y values by adding the increment dy(k): y(k+1) = y(k) + dy(k). I've computed this, and here are the start and finish for a_1: Theta Re(w(k)) Im(w(k)) Re(a_1(k)) Im(a_1(k)) (deg) 0 -1.00000 +0.00000i 0.00000 +0.00000i 360 -1.00000 -0.00000i -1.00000 +0.00000i The start and finish for a_2: Theta Re(w(k)) Im(w(k)) Re(a_2(k)) Im(a_2(k)) (deg) 0 -1.00000 +0.00000i -1.00000 +0.00000i 360 -1.00000 -0.00000i 0.00000 -0.00000i Note that w runs around the circle, and a_1 swaps places from 0 to -1 with its partner a_2. What I'll list below is the record at 1-degree increments. There are 360 of these, so be patient: 0 -1.00000 +0.00000i 0.00000 +0.00000i 1 -1.00002 +0.00270i -0.00003 +0.00540i 2 -1.00009 +0.00540i -0.00010 +0.01080i 3 -1.00021 +0.00810i -0.00023 +0.01620i 4 -1.00038 +0.01079i -0.00040 +0.02160i 5 -1.00059 +0.01348i -0.00063 +0.02699i 6 -1.00085 +0.01617i -0.00091 +0.03239i 7 -1.00115 +0.01885i -0.00124 +0.03778i 8 -1.00151 +0.02153i -0.00162 +0.04316i 9 -1.00190 +0.02420i -0.00205 +0.04855i 10 -1.00235 +0.02686i -0.00253 +0.05393i 11 -1.00284 +0.02952i -0.00306 +0.05931i 12 -1.00338 +0.03216i -0.00364 +0.06468i 13 -1.00396 +0.03480i -0.00427 +0.07005i 14 -1.00460 +0.03743i -0.00495 +0.07541i 15 -1.00527 +0.04004i -0.00568 +0.08077i 16 -1.00599 +0.04264i -0.00647 +0.08611i 17 -1.00676 +0.04523i -0.00730 +0.09146i 18 -1.00757 +0.04781i -0.00818 +0.09679i 19 -1.00843 +0.05037i -0.00912 +0.10212i 20 -1.00933 +0.05291i -0.01010 +0.10744i 21 -1.01028 +0.05544i -0.01113 +0.11275i 22 -1.01126 +0.05795i -0.01222 +0.11806i 23 -1.01230 +0.06045i -0.01335 +0.12335i 24 -1.01337 +0.06292i -0.01454 +0.12863i 25 -1.01449 +0.06538i -0.01577 +0.13390i 26 -1.01566 +0.06782i -0.01706 +0.13917i 27 -1.01686 +0.07023i -0.01839 +0.14442i 28 -1.01811 +0.07263i -0.01978 +0.14966i 29 -1.01940 +0.07500i -0.02122 +0.15489i 30 -1.02073 +0.07735i -0.02270 +0.16010i 31 -1.02210 +0.07968i -0.02424 +0.16530i 32 -1.02351 +0.08198i -0.02582 +0.17049i 33 -1.02496 +0.08426i -0.02746 +0.17566i 34 -1.02645 +0.08651i -0.02914 +0.18082i 35 -1.02798 +0.08873i -0.03088 +0.18597i 36 -1.02955 +0.09093i -0.03266 +0.19110i 37 -1.03115 +0.09310i -0.03450 +0.19621i 38 -1.03279 +0.09524i -0.03638 +0.20131i 39 -1.03448 +0.09736i -0.03831 +0.20639i 40 -1.03619 +0.09944i -0.04029 +0.21146i 41 -1.03795 +0.10149i -0.04233 +0.21650i 42 -1.03974 +0.10351i -0.04441 +0.22153i 43 -1.04156 +0.10551i -0.04654 +0.22654i 44 -1.04342 +0.10746i -0.04872 +0.23153i 45 -1.04531 +0.10939i -0.05094 +0.23650i 46 -1.04724 +0.11128i -0.05322 +0.24145i 47 -1.04920 +0.11314i -0.05555 +0.24637i 48 -1.05119 +0.11496i -0.05792 +0.25128i 49 -1.05321 +0.11675i -0.06034 +0.25617i 50 -1.05526 +0.11851i -0.06281 +0.26103i 51 -1.05734 +0.12022i -0.06533 +0.26587i 52 -1.05946 +0.12191i -0.06790 +0.27069i 53 -1.06160 +0.12355i -0.07051 +0.27548i 54 -1.06377 +0.12516i -0.07317 +0.28025i 55 -1.06597 +0.12672i -0.07588 +0.28500i 56 -1.06819 +0.12825i -0.07864 +0.28972i 57 -1.07044 +0.12974i -0.08145 +0.29441i 58 -1.07272 +0.13119i -0.08430 +0.29908i 59 -1.07502 +0.13260i -0.08719 +0.30372i 60 -1.07735 +0.13397i -0.09014 +0.30833i 61 -1.07970 +0.13530i -0.09313 +0.31291i 62 -1.08207 +0.13659i -0.09617 +0.31747i 63 -1.08447 +0.13784i -0.09925 +0.32200i 64 -1.08688 +0.13904i -0.10238 +0.32649i 65 -1.08932 +0.14021i -0.10556 +0.33096i 66 -1.09178 +0.14133i -0.10878 +0.33540i 67 -1.09425 +0.14240i -0.11204 +0.33980i 68 -1.09675 +0.14344i -0.11535 +0.34418i 69 -1.09926 +0.14443i -0.11871 +0.34852i 70 -1.10179 +0.14537i -0.12210 +0.35283i 71 -1.10433 +0.14627i -0.12555 +0.35710i 72 -1.10690 +0.14713i -0.12903 +0.36134i 73 -1.10947 +0.14794i -0.13256 +0.36555i 74 -1.11206 +0.14871i -0.13614 +0.36972i 75 -1.11466 +0.14943i -0.13975 +0.37386i 76 -1.11728 +0.15011i -0.14341 +0.37796i 77 -1.11990 +0.15074i -0.14711 +0.38203i 78 -1.12254 +0.15132i -0.15085 +0.38606i 79 -1.12518 +0.15186i -0.15464 +0.39005i 80 -1.12784 +0.15235i -0.15846 +0.39400i 81 -1.13050 +0.15280i -0.16233 +0.39791i 82 -1.13317 +0.15320i -0.16623 +0.40179i 83 -1.13585 +0.15355i -0.17018 +0.40562i 84 -1.13853 +0.15385i -0.17416 +0.40942i 85 -1.14122 +0.15411i -0.17819 +0.41318i 86 -1.14391 +0.15432i -0.18225 +0.41689i 87 -1.14660 +0.15449i -0.18635 +0.42056i 88 -1.14930 +0.15461i -0.19049 +0.42419i 89 -1.15200 +0.15468i -0.19467 +0.42778i 90 -1.15470 +0.15470i -0.19888 +0.43133i 91 -1.15740 +0.15468i -0.20313 +0.43483i 92 -1.16010 +0.15461i -0.20742 +0.43829i 93 -1.16280 +0.15449i -0.21174 +0.44170i 94 -1.16549 +0.15432i -0.21610 +0.44507i 95 -1.16818 +0.15411i -0.22050 +0.44839i 96 -1.17087 +0.15385i -0.22492 +0.45167i 97 -1.17355 +0.15355i -0.22938 +0.45490i 98 -1.17623 +0.15320i -0.23388 +0.45809i 99 -1.17890 +0.15280i -0.23840 +0.46122i 100 -1.18156 +0.15235i -0.24296 +0.46431i 101 -1.18422 +0.15186i -0.24755 +0.46736i 102 -1.18686 +0.15132i -0.25218 +0.47035i 103 -1.18950 +0.15074i -0.25683 +0.47329i 104 -1.19213 +0.15011i -0.26151 +0.47619i 105 -1.19474 +0.14943i -0.26622 +0.47903i 106 -1.19734 +0.14871i -0.27096 +0.48183i 107 -1.19993 +0.14794i -0.27573 +0.48458i 108 -1.20251 +0.14713i -0.28053 +0.48727i 109 -1.20507 +0.14627i -0.28536 +0.48991i 110 -1.20761 +0.14537i -0.29021 +0.49251i 111 -1.21014 +0.14443i -0.29508 +0.49505i 112 -1.21265 +0.14344i -0.29999 +0.49753i 113 -1.21515 +0.14240i -0.30491 +0.49997i 114 -1.21762 +0.14133i -0.30986 +0.50235i 115 -1.22008 +0.14021i -0.31484 +0.50468i 116 -1.22252 +0.13904i -0.31983 +0.50696i 117 -1.22493 +0.13784i -0.32485 +0.50918i 118 -1.22733 +0.13659i -0.32989 +0.51135i 119 -1.22970 +0.13530i -0.33496 +0.51346i 120 -1.23205 +0.13397i -0.34004 +0.51552i 121 -1.23438 +0.13260i -0.34514 +0.51752i 122 -1.23668 +0.13119i -0.35026 +0.51947i 123 -1.23896 +0.12974i -0.35540 +0.52136i 124 -1.24121 +0.12825i -0.36055 +0.52320i 125 -1.24343 +0.12672i -0.36573 +0.52498i 126 -1.24563 +0.12516i -0.37092 +0.52670i 127 -1.24780 +0.12355i -0.37612 +0.52837i 128 -1.24994 +0.12191i -0.38134 +0.52998i 129 -1.25206 +0.12022i -0.38657 +0.53154i 130 -1.25414 +0.11851i -0.39182 +0.53304i 131 -1.25619 +0.11675i -0.39708 +0.53448i 132 -1.25822 +0.11496i -0.40235 +0.53586i 133 -1.26021 +0.11314i -0.40763 +0.53719i 134 -1.26216 +0.11128i -0.41292 +0.53846i 135 -1.26409 +0.10939i -0.41822 +0.53967i 136 -1.26598 +0.10746i -0.42353 +0.54082i 137 -1.26784 +0.10551i -0.42885 +0.54191i 138 -1.26967 +0.10351i -0.43418 +0.54295i 139 -1.27145 +0.10149i -0.43951 +0.54393i 140 -1.27321 +0.09944i -0.44485 +0.54485i 141 -1.27493 +0.09736i -0.45019 +0.54571i 142 -1.27661 +0.09524i -0.45554 +0.54652i 143 -1.27825 +0.09310i -0.46089 +0.54727i 144 -1.27986 +0.09093i -0.46625 +0.54795i 145 -1.28142 +0.08873i -0.47160 +0.54858i 146 -1.28295 +0.08651i -0.47696 +0.54915i 147 -1.28444 +0.08426i -0.48232 +0.54967i 148 -1.28589 +0.08198i -0.48768 +0.55012i 149 -1.28730 +0.07968i -0.49304 +0.55052i 150 -1.28868 +0.07735i -0.49840 +0.55086i 151 -1.29000 +0.07500i -0.50375 +0.55114i 152 -1.29129 +0.07263i -0.50910 +0.55136i 153 -1.29254 +0.07023i -0.51445 +0.55152i 154 -1.29374 +0.06782i -0.51979 +0.55163i 155 -1.29491 +0.06538i -0.52513 +0.55168i 156 -1.29603 +0.06292i -0.53046 +0.55167i 157 -1.29710 +0.06045i -0.53579 +0.55160i 158 -1.29814 +0.05795i -0.54111 +0.55148i 159 -1.29913 +0.05544i -0.54642 +0.55130i 160 -1.30007 +0.05291i -0.55172 +0.55106i 161 -1.30097 +0.05037i -0.55701 +0.55077i 162 -1.30183 +0.04781i -0.56229 +0.55041i 163 -1.30264 +0.04523i -0.56755 +0.55001i 164 -1.30341 +0.04264i -0.57281 +0.54954i 165 -1.30413 +0.04004i -0.57806 +0.54902i 166 -1.30481 +0.03743i -0.58329 +0.54845i 167 -1.30544 +0.03480i -0.58850 +0.54782i 168 -1.30602 +0.03216i -0.59371 +0.54713i 169 -1.30656 +0.02952i -0.59889 +0.54639i 170 -1.30705 +0.02686i -0.60406 +0.54559i 171 -1.30750 +0.02420i -0.60922 +0.54474i 172 -1.30790 +0.02153i -0.61435 +0.54384i 173 -1.30825 +0.01885i -0.61947 +0.54288i 174 -1.30855 +0.01617i -0.62457 +0.54187i 175 -1.30881 +0.01348i -0.62965 +0.54080i 176 -1.30902 +0.01079i -0.63470 +0.53968i 177 -1.30919 +0.00810i -0.63974 +0.53851i 178 -1.30931 +0.00540i -0.64476 +0.53729i 179 -1.30938 +0.00270i -0.64975 +0.53602i 180 -1.30940 +0.00000i -0.65472 +0.53469i 181 -1.30938 -0.00270i -0.65967 +0.53332i 182 -1.30931 -0.00540i -0.66459 +0.53189i 183 -1.30919 -0.00810i -0.66949 +0.53042i 184 -1.30902 -0.01079i -0.67436 +0.52889i 185 -1.30881 -0.01348i -0.67921 +0.52732i 186 -1.30855 -0.01617i -0.68403 +0.52570i 187 -1.30825 -0.01885i -0.68882 +0.52403i 188 -1.30790 -0.02153i -0.69359 +0.52231i 189 -1.30750 -0.02420i -0.69832 +0.52054i 190 -1.30705 -0.02686i -0.70303 +0.51873i 191 -1.30656 -0.02952i -0.70771 +0.51687i 192 -1.30602 -0.03216i -0.71236 +0.51497i 193 -1.30544 -0.03480i -0.71698 +0.51302i 194 -1.30481 -0.03743i -0.72156 +0.51102i 195 -1.30413 -0.04004i -0.72612 +0.50898i 196 -1.30341 -0.04264i -0.73064 +0.50690i 197 -1.30264 -0.04523i -0.73513 +0.50478i 198 -1.30183 -0.04781i -0.73959 +0.50261i 199 -1.30097 -0.05037i -0.74401 +0.50040i 200 -1.30007 -0.05291i -0.74840 +0.49815i 201 -1.29913 -0.05544i -0.75275 +0.49586i 202 -1.29814 -0.05795i -0.75707 +0.49353i 203 -1.29710 -0.06045i -0.76136 +0.49116i 204 -1.29603 -0.06292i -0.76561 +0.48875i 205 -1.29491 -0.06538i -0.76982 +0.48630i 206 -1.29374 -0.06782i -0.77399 +0.48381i 207 -1.29254 -0.07023i -0.77813 +0.48129i 208 -1.29129 -0.07263i -0.78223 +0.47873i 209 -1.29000 -0.07500i -0.78630 +0.47614i 210 -1.28868 -0.07735i -0.79032 +0.47351i 211 -1.28730 -0.07968i -0.79431 +0.47084i 212 -1.28589 -0.08198i -0.79826 +0.46814i 213 -1.28444 -0.08426i -0.80216 +0.46541i 214 -1.28295 -0.08651i -0.80603 +0.46265i 215 -1.28142 -0.08873i -0.80986 +0.45985i 216 -1.27986 -0.09093i -0.81365 +0.45702i 217 -1.27825 -0.09310i -0.81740 +0.45417i 218 -1.27661 -0.09524i -0.82111 +0.45128i 219 -1.27493 -0.09736i -0.82478 +0.44836i 220 -1.27321 -0.09944i -0.82840 +0.44541i 221 -1.27145 -0.10149i -0.83199 +0.44244i 222 -1.26967 -0.10351i -0.83553 +0.43944i 223 -1.26784 -0.10551i -0.83903 +0.43641i 224 -1.26598 -0.10746i -0.84249 +0.43336i 225 -1.26409 -0.10939i -0.84591 +0.43028i 226 -1.26216 -0.11128i -0.84929 +0.42718i 227 -1.26021 -0.11314i -0.85262 +0.42405i 228 -1.25822 -0.11496i -0.85591 +0.42090i 229 -1.25619 -0.11675i -0.85916 +0.41773i 230 -1.25414 -0.11851i -0.86236 +0.41453i 231 -1.25206 -0.12022i -0.86553 +0.41132i 232 -1.24994 -0.12191i -0.86865 +0.40808i 233 -1.24780 -0.12355i -0.87172 +0.40482i 234 -1.24563 -0.12516i -0.87476 +0.40155i 235 -1.24343 -0.12672i -0.87775 +0.39826i 236 -1.24121 -0.12825i -0.88069 +0.39495i 237 -1.23896 -0.12974i -0.88360 +0.39162i 238 -1.23668 -0.13119i -0.88646 +0.38828i 239 -1.23438 -0.13260i -0.88928 +0.38492i 240 -1.23205 -0.13397i -0.89205 +0.38154i 241 -1.22970 -0.13530i -0.89478 +0.37816i 242 -1.22733 -0.13659i -0.89747 +0.37476i 243 -1.22493 -0.13784i -0.90012 +0.37134i 244 -1.22252 -0.13904i -0.90272 +0.36791i 245 -1.22008 -0.14021i -0.90528 +0.36448i 246 -1.21762 -0.14133i -0.90780 +0.36103i 247 -1.21515 -0.14240i -0.91027 +0.35757i 248 -1.21265 -0.14344i -0.91270 +0.35410i 249 -1.21014 -0.14443i -0.91509 +0.35062i 250 -1.20761 -0.14537i -0.91744 +0.34714i 251 -1.20507 -0.14627i -0.91975 +0.34364i 252 -1.20251 -0.14713i -0.92201 +0.34014i 253 -1.19993 -0.14794i -0.92423 +0.33664i 254 -1.19734 -0.14871i -0.92641 +0.33313i 255 -1.19474 -0.14943i -0.92855 +0.32961i 256 -1.19213 -0.15011i -0.93065 +0.32609i 257 -1.18950 -0.15074i -0.93271 +0.32256i 258 -1.18686 -0.15132i -0.93472 +0.31903i 259 -1.18422 -0.15186i -0.93670 +0.31550i 260 -1.18156 -0.15235i -0.93864 +0.31197i 261 -1.17890 -0.15280i -0.94053 +0.30843i 262 -1.17623 -0.15320i -0.94239 +0.30489i 263 -1.17355 -0.15355i -0.94420 +0.30136i 264 -1.17087 -0.15385i -0.94598 +0.29782i 265 -1.16818 -0.15411i -0.94772 +0.29428i 266 -1.16549 -0.15432i -0.94942 +0.29075i 267 -1.16280 -0.15449i -0.95109 +0.28721i 268 -1.16010 -0.15461i -0.95271 +0.28368i 269 -1.15740 -0.15468i -0.95430 +0.28015i 270 -1.15470 -0.15470i -0.95585 +0.27663i 271 -1.15200 -0.15468i -0.95736 +0.27311i 272 -1.14930 -0.15461i -0.95884 +0.26959i 273 -1.14660 -0.15449i -0.96028 +0.26608i 274 -1.14391 -0.15432i -0.96169 +0.26257i 275 -1.14122 -0.15411i -0.96306 +0.25907i 276 -1.13853 -0.15385i -0.96440 +0.25557i 277 -1.13585 -0.15355i -0.96570 +0.25208i 278 -1.13317 -0.15320i -0.96697 +0.24860i 279 -1.13050 -0.15280i -0.96820 +0.24512i 280 -1.12784 -0.15235i -0.96941 +0.24165i 281 -1.12518 -0.15186i -0.97058 +0.23819i 282 -1.12254 -0.15132i -0.97171 +0.23474i 283 -1.11990 -0.15074i -0.97282 +0.23129i 284 -1.11728 -0.15011i -0.97389 +0.22786i 285 -1.11466 -0.14943i -0.97494 +0.22443i 286 -1.11206 -0.14871i -0.97595 +0.22102i 287 -1.10947 -0.14794i -0.97694 +0.21761i 288 -1.10690 -0.14713i -0.97789 +0.21422i 289 -1.10433 -0.14627i -0.97882 +0.21083i 290 -1.10179 -0.14537i -0.97971 +0.20746i 291 -1.09926 -0.14443i -0.98058 +0.20409i 292 -1.09675 -0.14344i -0.98142 +0.20074i 293 -1.09425 -0.14240i -0.98224 +0.19740i 294 -1.09178 -0.14133i -0.98303 +0.19407i 295 -1.08932 -0.14021i -0.98379 +0.19076i 296 -1.08688 -0.13904i -0.98453 +0.18745i 297 -1.08447 -0.13784i -0.98524 +0.18416i 298 -1.08207 -0.13659i -0.98593 +0.18088i 299 -1.07970 -0.13530i -0.98659 +0.17761i 300 -1.07735 -0.13397i -0.98723 +0.17435i 301 -1.07502 -0.13260i -0.98785 +0.17111i 302 -1.07272 -0.13119i -0.98845 +0.16788i 303 -1.07044 -0.12974i -0.98902 +0.16467i 304 -1.06819 -0.12825i -0.98957 +0.16146i 305 -1.06597 -0.12672i -0.99011 +0.15827i 306 -1.06377 -0.12516i -0.99062 +0.15510i 307 -1.06160 -0.12355i -0.99111 +0.15193i 308 -1.05946 -0.12191i -0.99158 +0.14878i 309 -1.05734 -0.12022i -0.99203 +0.14565i 310 -1.05526 -0.11851i -0.99247 +0.14252i 311 -1.05321 -0.11675i -0.99289 +0.13941i 312 -1.05119 -0.11496i -0.99329 +0.13632i 313 -1.04920 -0.11314i -0.99367 +0.13323i 314 -1.04724 -0.11128i -0.99404 +0.13016i 315 -1.04531 -0.10939i -0.99439 +0.12711i 316 -1.04342 -0.10746i -0.99472 +0.12406i 317 -1.04156 -0.10551i -0.99504 +0.12103i 318 -1.03974 -0.10351i -0.99535 +0.11801i 319 -1.03795 -0.10149i -0.99564 +0.11501i 320 -1.03619 -0.09944i -0.99592 +0.11202i 321 -1.03448 -0.09736i -0.99618 +0.10904i 322 -1.03279 -0.09524i -0.99643 +0.10607i 323 -1.03115 -0.09310i -0.99667 +0.10311i 324 -1.02955 -0.09093i -0.99690 +0.10017i 325 -1.02798 -0.08873i -0.99711 +0.09724i 326 -1.02645 -0.08651i -0.99732 +0.09432i 327 -1.02496 -0.08426i -0.99751 +0.09141i 328 -1.02351 -0.08198i -0.99770 +0.08851i 329 -1.02210 -0.07968i -0.99787 +0.08563i 330 -1.02073 -0.07735i -0.99804 +0.08275i 331 -1.01940 -0.07500i -0.99819 +0.07989i 332 -1.01811 -0.07263i -0.99834 +0.07703i 333 -1.01686 -0.07023i -0.99848 +0.07419i 334 -1.01566 -0.06782i -0.99861 +0.07135i 335 -1.01449 -0.06538i -0.99873 +0.06853i 336 -1.01337 -0.06292i -0.99885 +0.06571i 337 -1.01230 -0.06045i -0.99895 +0.06290i 338 -1.01126 -0.05795i -0.99906 +0.06010i 339 -1.01028 -0.05544i -0.99915 +0.05731i 340 -1.00933 -0.05291i -0.99924 +0.05453i 341 -1.00843 -0.05037i -0.99932 +0.05176i 342 -1.00757 -0.04781i -0.99940 +0.04899i 343 -1.00676 -0.04523i -0.99947 +0.04623i 344 -1.00599 -0.04264i -0.99953 +0.04347i 345 -1.00527 -0.04004i -0.99959 +0.04073i 346 -1.00460 -0.03743i -0.99965 +0.03798i 347 -1.00396 -0.03480i -0.99970 +0.03525i 348 -1.00338 -0.03216i -0.99975 +0.03252i 349 -1.00284 -0.02952i -0.99979 +0.02979i 350 -1.00235 -0.02686i -0.99983 +0.02707i 351 -1.00190 -0.02420i -0.99986 +0.02435i 352 -1.00151 -0.02153i -0.99989 +0.02163i 353 -1.00115 -0.01885i -0.99992 +0.01892i 354 -1.00085 -0.01617i -0.99994 +0.01621i 355 -1.00059 -0.01348i -0.99996 +0.01351i 356 -1.00038 -0.01079i -0.99997 +0.01080i 357 -1.00021 -0.00810i -0.99999 +0.00810i 358 -1.00009 -0.00540i -0.99999 +0.00540i 359 -1.00002 -0.00270i -1.00000 +0.00270i 360 -1.00000 -0.00000i -1.00000 +0.00000i > They failed. Get over it. For a hundred years plus a nasty little > bug lurked in modern number theory in pure mathematics and no one > knew because none of their math applied to anything in the real world. > Never thought of actually seeing whether a_1 and a_2 could be defined in the way you wanted over the whole complex plane, now, did you? > And I figured it out and these turds proceeded to do their best to > punish me for it. Because I yanked away their baby blanket. Took away their fantasy. Destroyed their little bubble. So they're bitching, whining and running away from the damn problem > versus getting to the truth, confronting their loss, and moving > forward with real research versus the crap they are still doing and > teaching now. The only extra is you are part of the duplicity now, if you do > nothing. Doing nothing is letting them get funding, get prizes for failure, and > teach students junk. Do you know how much the Abel Prize is? Over a million dollars U.S. given every year to someone who probably > did not succeed at anything at all. Lying for a million bucks isn't noble, or academic survival in the > real world: it's just being a con artist. > James Harris I just had to leave the tirade. It's too precious. Dale === Subject: Re: JSH: Simplest explanation, Occam's Razor unleashed posting-account=wVv_VwoAAAAVTfUuyxLzug5SzYWCgHj1 Gecko/20081203 Firefox/2.0.0.19,gzip(gfe),gzip(gfe) On Dec 30, 1:47 pm, W. Dale Hall > In the complex plane with > 7*(175x^2 - 15x + 2) = (5a 1(x) + 7)(5a 2(x)+ 7) > where the a's are roots of > a^2 - (7x-1)a + (49x^2 - 14x) = 0 > you normalize: > a 1(x) = b 1(x), and a 2(x) = b 2(x) - 1, as then you have > 7*(175x^2 - 15x + 2) = (5b 1(x) + 7)(5b 2(x)+ 2) > where b 1(0) = 0, b 2(0) = 0. > Now compare with > 7*(x^2 + 3x + 2) = (7x + 7)(x + 2) > and what is the primary difference? > The type of function: in one case you have non-linear functions b 1(x) > and b 2(x), and in the other you have linear functions 7x and x. > I suggest to you that the distributive property does not care. > If some yahoo told you that the 7 bounced around like a kangaroo with > 7*(x^2 + 3x + 2) = (7x + 7)(x + 2) > based on the value of x, you'd say they were bonkers. > But if some Ph.D's scared of losing some math beliefs and their > precious notion that the mathematical field is immune to upheavals > bitch and moan for years against it, you believe them, and screw the > complex plane. > Simplest explanation. > None of you have the spines for the situation. You all lack the balls > to confront a massive failure by your freaking colleagues. Let's talk a little about 7 bounc[ing] around like a kangaroo. I'll look at your case. Here you have a polynomial in two > indeterminates: y^2 - (7x-1)y + (49x^2 - 14x) whose roots [in y] are used to factor 7 P(x) = (5^2 7^2) x^2 - 3*5*7 x + 2*7 as 7 P(x) = (5 a 1 + 7)(5 a 2 + 7). You note, correctly, that when x = 0, we have > the simpler form: y^2 + y with roots 0, -1, and conclude that if you normalize > the functions in your factorization, you get 7 P(x) = (5 b 1 + 7)(5 b 2 + 2) where b 1 = a 1, b 2 = a 2 + 1. The further step is to choose which of the a's gets to be a 1, > and which is a 2. You're no dummy, and so you chose a 1 to be the > one that is 0 when x = 0 [so the corresponding factor in the b > factorization gets to be 7], and the other the one that is -1 > when x = 0 [leading to the complementary factor of 2]. You conclude that this distribution holds for all x. I'll simplify the above 2-variable polynomial using w = 7x - 1, > to get this: Q(w,y) = y^2 - wy + (w^2 - 1) and I'll consider the Riemann surface S: S = {(w,y) in C^2 | Q(w,y) = 0} If I consider the gradient of Q: grad Q = (2y - w)D y + (2w - y)D w the fact that grad Q = 0 *only* for w = y = 0, and that > point is not contained in S, implies that S is a smooth > (i.e., infinitely differentiable) surface of 2 real > dimensions (or one complex dimension, in which case it's > analytic). There is a canonical projection to the first coordinate Pr: S -----> C (w,y) |--> w This map is smooth [actually, analytic, if you're keeping > track of the complex structure], and one might well ask why > it's at all relevant to the discussion. Note that for w fixed, the set of elements of S that map to w > under this projection consists of the roots [in y] of the > polynomial Q. In other words, the fibres of Pr are the functions > a 1, a 2. Next, I'll show that JSH has been tricked by a little two-card monte > that this Riemann surface plays on unsuspecting tourists in the > big city. Keep your eyes on the red lady, gents, just pick where that > red lady ends up, and you're in the money. Ready? Here we go... There are two special points (in w) where the projection Pr is a > wee bit flaky. Since (for w fixed) Q(w,y) is a quadratic in y, it > might be possible for Q to have only a single solution (in y, for > w fixed). Let's check it out: Q(w,y) = y^2 - w y + (w^2 - 1) The discriminant is Discr = w^2 - 4(w^2 - 1) = 4 - 3 w^2 So, when Discr = 0, we get a single solution in y, rather than two. This happens when w^2 = 4/3, or w = +/- 2/sqrt(3). Recall, we have a smooth surface S, mapping to the complex plane C Pr: S ------> C > (w,y) |--> w and now we find that when w = +/- 2/sqrt(3), there is only one > point of S that maps to w. Otherwise, there are two. So what? Actually, something strange and wonderful. Near these two points > in S (the pre-images of w = +/- 2/sqrt(3) ), the mapping is essentially > z |--> z^2, in a way I'll make precise. Let s* denote one of these > two points in S, with w* = Pr(s*). Then: There is a disc neighborhood U* of s* in S, and a disc > neighborhood V* of w* in C, and smooth [or analytic ...] > homeomorphisms p, q from U*, V* to the unit disc D of > the complex plane C, for which the diagram Pr > U* --------------> V* > | | > | | > p | | q > | | > v v > D --------------> D > z^2 is commutative; this means (p(u))^2 = q(Pr(u)) Now, what does all this mean? Notice that on the boundary circle of D, > the squaring operation wraps the circle twice around its image. Looking > at the inverse operation, as I follow a point once around the circle > on the right side, the two points on the left do the two-card monte: > They SWAP POSITIONS! What that means is, if you've chosen one y value for your a 1(x), and > the other y value for your a 2(x), and then care to move x around this > little circle, what you wanted to be a 1(x) will cease to be 0 at x = 0, > and what you wanted to be a 2(x) will cease to be -1 at x = 0. Here's the punch line: THERE IS NO CONTINUOUS CHOICE OF a 1, a 2 OVER ALL OF C Or the equally amusing: The kangaroo is still there. You don't have to believe me. I did a numerical integration that > demonstrates this happening; you can do it too. Take the equation Q(w,y) = y^2 - w y + (w^2 - 1) = 0 and form its total differential (it's the gradient with differentials > dw, dy replacing the vectors D w, D y): dQ = (2y - w) dy + (2w - y) dw Since Q is identically 0 on the surface S, dQ = 0, and we can use > this differential to relate increments of w to increments of y. We march w from -1, around the point -2/sqrt(3), back to itself: w(t k) = -2/sqrt(3) + r exp(it k) for t k running from 0 to 2 pi in tiny steps (I chose constant steps > of size 0.01 degree, converted to radians). We have a formula for w(k), > we can replace dw by the increment (w(k+1) - w(k)), and we solve > for dy(k). Finally, take y(0) = 0 (our initial value), and accumulate > y values by adding the increment dy(k): y(k+1) = y(k) + dy(k). I've computed this, and here are the start and finish for a 1: Theta Re(w(k)) Im(w(k)) Re(a 1(k)) Im(a 1(k)) > (deg) > 0 -1.00000 +0.00000i 0.00000 +0.00000i > 360 -1.00000 -0.00000i -1.00000 +0.00000i The start and finish for a 2: Theta Re(w(k)) Im(w(k)) Re(a 2(k)) Im(a 2(k)) > (deg) > 0 -1.00000 +0.00000i -1.00000 +0.00000i > 360 -1.00000 -0.00000i 0.00000 -0.00000i Note that w runs around the circle, and a 1 swaps places from 0 to -1 > with its partner a 2. What I'll list below is the record at 1-degree increments. There are 360 > of these, so be patient: 0 -1.00000 +0.00000i 0.00000 +0.00000i > 1 -1.00002 +0.00270i -0.00003 +0.00540i > 2 -1.00009 +0.00540i -0.00010 +0.01080i > 3 -1.00021 +0.00810i -0.00023 +0.01620i > 4 -1.00038 +0.01079i -0.00040 +0.02160i > 5 -1.00059 +0.01348i -0.00063 +0.02699i > 6 -1.00085 +0.01617i -0.00091 +0.03239i > 7 -1.00115 +0.01885i -0.00124 +0.03778i > 8 -1.00151 +0.02153i -0.00162 +0.04316i > 9 -1.00190 +0.02420i -0.00205 +0.04855i > 10 -1.00235 +0.02686i -0.00253 +0.05393i > 11 -1.00284 +0.02952i -0.00306 +0.05931i > 12 -1.00338 +0.03216i -0.00364 +0.06468i > 13 -1.00396 +0.03480i -0.00427 +0.07005i > 14 -1.00460 +0.03743i -0.00495 +0.07541i > 15 -1.00527 +0.04004i -0.00568 +0.08077i > 16 -1.00599 +0.04264i -0.00647 +0.08611i > 17 -1.00676 +0.04523i -0.00730 +0.09146i > 18 -1.00757 +0.04781i -0.00818 +0.09679i > 19 -1.00843 +0.05037i -0.00912 +0.10212i > 20 -1.00933 +0.05291i -0.01010 +0.10744i > 21 -1.01028 +0.05544i -0.01113 +0.11275i > 22 -1.01126 +0.05795i -0.01222 +0.11806i > 23 -1.01230 +0.06045i -0.01335 +0.12335i > 24 -1.01337 +0.06292i -0.01454 +0.12863i > 25 -1.01449 +0.06538i -0.01577 +0.13390i > 26 -1.01566 +0.06782i -0.01706 +0.13917i > 27 -1.01686 +0.07023i -0.01839 +0.14442i > 28 -1.01811 +0.07263i -0.01978 +0.14966i > 29 -1.01940 +0.07500i -0.02122 +0.15489i > 30 -1.02073 +0.07735i -0.02270 +0.16010i > 31 -1.02210 +0.07968i -0.02424 +0.16530i > 32 -1.02351 +0.08198i -0.02582 +0.17049i > 33 -1.02496 +0.08426i -0.02746 +0.17566i > 34 -1.02645 +0.08651i -0.02914 +0.18082i > 35 -1.02798 +0.08873i -0.03088 +0.18597i > 36 -1.02955 +0.09093i -0.03266 +0.19110i > 37 -1.03115 +0.09310i -0.03450 +0.19621i > 38 -1.03279 +0.09524i -0.03638 +0.20131i > 39 -1.03448 +0.09736i -0.03831 +0.20639i > 40 -1.03619 +0.09944i -0.04029 +0.21146i > 41 -1.03795 +0.10149i -0.04233 +0.21650i > 42 -1.03974 +0.10351i -0.04441 +0.22153i > 43 -1.04156 +0.10551i -0.04654 +0.22654i > 44 -1.04342 +0.10746i -0.04872 +0.23153i > 45 -1.04531 +0.10939i -0.05094 +0.23650i > 46 -1.04724 +0.11128i -0.05322 +0.24145i > 47 -1.04920 +0.11314i -0.05555 +0.24637i > 48 -1.05119 +0.11496i -0.05792 +0.25128i > 49 -1.05321 +0.11675i -0.06034 +0.25617i > 50 -1.05526 +0.11851i -0.06281 +0.26103i > 51 -1.05734 +0.12022i -0.06533 +0.26587i > 52 -1.05946 +0.12191i -0.06790 +0.27069i > 53 -1.06160 +0.12355i -0.07051 +0.27548i > 54 -1.06377 +0.12516i -0.07317 +0.28025i > 55 -1.06597 +0.12672i -0.07588 +0.28500i > 56 -1.06819 +0.12825i -0.07864 +0.28972i > 57 -1.07044 +0.12974i -0.08145 +0.29441i > 58 -1.07272 +0.13119i -0.08430 +0.29908i > 59 -1.07502 +0.13260i -0.08719 +0.30372i > 60 -1.07735 +0.13397i -0.09014 +0.30833i > 61 -1.07970 +0.13530i -0.09313 +0.31291i > 62 -1.08207 +0.13659i -0.09617 +0.31747i > 63 -1.08447 +0.13784i -0.09925 +0.32200i > 64 -1.08688 +0.13904i -0.10238 +0.32649i > 65 -1.08932 +0.14021i -0.10556 +0.33096i > 66 -1.09178... read more é That massize WHOOSH you hear is the sound of this entire argument going about a mile over JSH's head, at roughly Mach 0.99. If only he were smart enough and knew enough for this to have been the explanation for his erroneous conclusion. Recall however that his mathematical competence is at about the level of Punxatawny Phil. Marcus. Marcus. === Subject: Re:JSH: Simplest explanation, Occam's Razor unleashed real world: it's just being a con artist. > James Harris JSH = con artist. === Subject: Re: JSH: Simplest explanation, Occam's Razor unleashed > Lying for a million bucks isn't noble, or academic survival in the > real world: it's just being a con artist. > James Harris JSH = con artist. He's been duped by a game of two-card monte. be the root that becomes 0 when x = 0, and a_2(x) to be the root that becomes -1 when x = 0, then there is no continuous choice for a_1, a_2 over the complex plane, due to ramification of the Riemann surface S = {(x,y) in C^2 | y^2 - (7x - 1)y + (49x^2 - 14x) = 0} over the points where the discriminant Discr = (7x - 1)^2 - 4(49x^2 - 14x) vanishes. If you drag x from 0, around either of the points x = (1 +/- 2/sqrt(3))/7 and back to 0, then the two roots swap positions, leading to a_1 & a_2 exchanging roles: a_1(0) = -1, a_2(0) = 0. Dale === Subject: Re: JSH: Simplest explanation, Occam's Razor unleashed .... One doesn't unleash a razor, one unsheathes a razor. -- But you see, I can believe a thing without understanding it. It's all a matter of training. --Lord Peter Wimsey in Dorothy L Sayers' _Have His Carcase_ === Subject: Re: JSH: Simplest explanation, Occam's Razor unleashed posting-account=Cbgh4AoAAAAr0dt1RqLOClWCyUWii2fU Gecko/2008121621 Ubuntu/8.04 (hardy) Firefox/3.0.5,gzip(gfe),gzip(gfe) > In the complex plane with Where is the complex plane C used in the following? Is x a complex number (in C)? Or do you consider the ring C[x]? Or the algebraic closure of C(x)? Or the ring of functions C->C? > 7*(175x^2 - 15x + 2) = (5a 1(x) + 7)(5a 2(x)+ 7) where the a's are roots of a^2 - (7x-1)a + (49x^2 - 14x) = 0 you normalize: a 1(x) = b 1(x), and a 2(x) = b 2(x) - 1, as then you have 7*(175x^2 - 15x + 2) = (5b 1(x) + 7)(5b 2(x)+ 2) where b 1(0) = 0, b 2(0) = 0. Now compare with 7*(x^2 + 3x + 2) = (7x + 7)(x + 2) and what is the primary difference? The type of function: in one case you have non-linear functions b 1(x) > and b 2(x), and in the other you have linear functions 7x and x. ... which simply suggests that e.g. the function x |-> b 1(x) differs from the function x |-> 7/5 x. So what? I suggest to you that the distributive property does not care. If some yahoo told you that the 7 bounced around like a kangaroo with 7*(x^2 + 3x + 2) = (7x + 7)(x + 2) based on the value of x, you'd say they were bonkers. I won't. I might ask that yahoo for an argument in support of his claim, for which a few numerical example suffice. In the same manner let me ask you for an argument in support of your claim (a mathematical argument that is not based on any kind of they-are-bonkers axiom). But if some Ph.D's scared of losing some math beliefs and their > precious notion that the mathematical field is immune to upheavals > bitch and moan for years against it, you believe them, and screw the > complex plane. Simplest explanation. None of you have the spines for the situation. You all lack the balls > to confront a massive failure by your freaking colleagues. They failed. Get over it. For a hundred years plus a nasty little > bug lurked in modern number theory in pure mathematics and no one > knew because none of their math applied to anything in the real world. A lot of pure math has applications in the real world, for example in cryptography as used for bank transfers. And I figured it out and these turds proceeded to do their best to > punish me for it. Sorry, I do not see you have figured anything out. Because I yanked away their baby blanket. Took away their fantasy. Destroyed their little bubble. So they're bitching, whining and running away from the damn problem > versus getting to the truth, confronting their loss, and moving > forward with real research versus the crap they are still doing and > teaching now. The only extra is you are part of the duplicity now, if you do > nothing. Doing nothing is letting them get funding, get prizes for failure, and > teach students junk. Do you know how much the Abel Prize is? Over a million dollars U.S. given every year to someone who probably > did not succeed at anything at all. Then you have still hope? Lying for a million bucks isn't noble, or academic survival in the > real world: it's just being a con artist. James Harris === Subject: Re: JSH: Simplest explanation, Occam's Razor unleashed posting-account=wVv_VwoAAAAVTfUuyxLzug5SzYWCgHj1 5.1),gzip(gfe),gzip(gfe) > In the complex plane with 7*(175x^2 - 15x + 2) = (5a 1(x) + 7)(5a 2(x)+ 7) where the a's are roots of a^2 - (7x-1)a + (49x^2 - 14x) = 0 you normalize: a 1(x) = b 1(x), and a 2(x) = b 2(x) - 1, as then you have 7*(175x^2 - 15x + 2) = (5b 1(x) + 7)(5b 2(x)+ 2) where b 1(0) = 0, b 2(0) = 0. Now compare with 7*(x^2 + 3x + 2) = (7x + 7)(x + 2) and what is the primary difference? > 1. Your original polynomial is factored as a polynomial in 5, not in the variable x/ 2. b 1(x) is not a polynomial variable. 3. In your second equation, 7*(x^2 + 3x + 2) = (7x + 7)(x + 2) there are in fact infinitely many ways to distribute 7 across the TWO factors (note - not just one factor, as in the distributive property), and indeed, 7 can be distributed in ways that are dependent on x. For example, 7 = s(x) * t(x), where s(x) = 7/(1 + x^2), t(x) = 1 + x^2, and 7*(x^2 + 3x + 2) = (s(x)*x + s(x)*(t(x)*x + 2t(x)), in the complex plane. Is this incorrect? Does it involve any violation of the distributive property? If so, please specify. > The type of function: in one case you have non-linear functions b 1(x) > and b 2(x), and in the other you have linear functions 7x and x. I suggest to you that the distributive property does not care. > I suggest to you that whether a property cares or not does not constitute anything resembling a rigorous mathematical argument. The burden of proof is on you. If a certain distribution is not mathematically incorrect, you need to consider the possibility that it exists. You are not free to simply discard variable distributions simply because you do not like them. You have to have a RIGOROUS, MATHEMATICAL REASON to discard them. And clearly you don't, because specfic factorizations show that variable distributions are EXACTLY WHAT MUST HAPPEN. > If some yahoo told you that the 7 bounced around like a kangaroo with 7*(x^2 + 3x + 2) = (7x + 7)(x + 2) based on the value of x, you'd say they were bonkers. > No, YOU would say that. Again, trying to ridicule variable ways of distributing values by saying they bounce around like a kangaroo is NOT MATHEMATICS. If it is POSSIBLE, you must consider it. Look at the function f(n) = n*(n + 1) in the integers. You can always factor 2 out of it. And the 2 bounces around like a kangaroo, sometimes dividing the n term and sometimes dividing the n + 1 term. Yet in spite of this bouncing around, it always factors out! Or, consider n*(n + 1)*(n + 2). This is always divisible by 6. Sometimes 6 divides n. Sometimes 2 divides n and 3 divides n + 1, Sometimes 3 divides n and 2 divides n + 2. How 6 splits up among the three factors is dependent on n. It sure does a lot of bouncing around! The factoring out of 6 cares what the value of n is. You try to make this sound silly, but it's not. It's what actually happens. > But if some Ph.D's scared of losing some math beliefs and their > precious notion that the mathematical field is immune to upheavals > bitch and moan for years against it, you believe them, and screw the > complex plane. > Back to the complex plane, eh? Is the following factorization invalid in the complex plane? 7*(x^2 + 3x + 2) = (s(x)*x + s(x))*(t(x)*x + 2t(x)), where s(x) = 7/(1 + x^2), t(x) = (1 + x^2) ? Yes or no? > Simplest explanation. > Marcus. === Subject: Re: JSH: Simplest explanation, Occam's Razor unleashed posting-account=jPnQ2goAAAA461y3QD0lbyw0oKeThma1 AppleWebKit/525.18 (KHTML, like Gecko) Version/3.1.2 Safari/525.20.1 FOH:R051,gzip(gfe),gzip(gfe) on Nondystributive Geometry. yeah; if you can't put into constructive geometrical terms, you can't do ****. yeah; you had the definitive 2-week course in Geometry from an Advanced/Remedial Viewpoint in some Mice.Space at Vanderbilt! thus: here is an example of the Skeptics (current Calif. or USA mag.) being unable to come-up with a rational explanation of: sodium-vapor streetlights going off, as you walk underneath them; they think it to be either a hoax or psycho/visual. also, cropcircles. also, http://www.svpvril.com/svpweb14.html. thus: even Ockham'd slice through that apple & orange, with one wild Yahoo! (tm); western astrology is the same as Ptolemy's epicyclic hoax, over 2000yo. > some have been even making into popular news. > that astrological signs may have some meaning thus: I yam lying what I bean!... of what possible use is the set of all sets, whether or not it can eventually include itself, at the end of the list of elements -- shades of AP-adics? so, perhaps we can blame Russell for the Bourbaki New Math, based upon set theory, but see what Whitehead had to say about him, not to say Godel. thus: shouldn't it be clear that photons are an artifact of the idea that actually were zero-dimensional points, but, since they are waves, as shown by Young, Huyghens et al, there is really no need for them, except in the Pauli matrix formalism of statistical bosons; eh? Schroedinger's cat is dead -- long-live Schoredinger's cat! --only 24 hours to impeach Trickier Dick from the N.Admin, metaphorically typing, or Cheeny & Zbiggy, fo'mo' years; Good Morning, Afghanistan! ... Good Afternoon, Sudan! http://tarpley.net/bush12.htm http://wlym.com/campaigner/8011.pdf -- Brits hate Shakes, Why? http://www.wlym.com/~seattle/dynamis/ http://www.21stcenturysciencetech.com/current.html http://www.rwgrayprojects.com/synergetics/plates/plates.html http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=3163 http://wlym.com/campaigner/8011.pdf -- English, not! === Subject: Re: JSH: Simple math but bad math habits > It was done long before you did it: > There is one big difference, though. The methods Alpern gives actually > work. Yours fail in many cases. > Go to the web page cited above, and click on methods. What binary > quadratic Diophantine equation can your methods solve that Alpern's > methods do not solve? > -- > --Tim Smith >So why doesn't he claim it's a general solution then? it solves all the cases, therefore it is a general solution. >Do you know what a general solution in mathematics is? it solves all the cases. >A remarkable bit of computer programming but not a general solution. why dont you ask him for source code? Written by Dario Alpern. I am sure he could teach you a lot, JSH. Especially programming skills, your's are plug and chug, and perhaps math, >Have you ever heard the phrase plug and chug, for instance? >James Harris === Subject: Re: JSH: Simple math but bad math habits On Dec 27, 5:19 am, Frederick Williams I defined mathematical proof. Don't believe me? Google it. Google: > define mathematical proof > > To quote from > http://mymath.blogspot.com/2005/07/definition-of-mathematical-proof.html: > > A mathematical proof is a mathematical argument that > begins with a truth and proceeds by logical steps to a > conclusion which then must be true. > > How would one prove (in this sense) that the sum of the internal angles > of a triangle is 180 degrees? (Or is more than 180 degrees, or is less > than 180 degrees, if you prefer.) What is the truth that one begins > with? And how does one know that it is a truth? Good questions. But not good enough for you to even try to answer. -- But you see, I can believe a thing without understanding it. It's all a matter of training. --Lord Peter Wimsey in Dorothy L Sayers' _Have His Carcase_ === Subject: Re: JSH: Simple math but bad math habits posting-account=wVv_VwoAAAAVTfUuyxLzug5SzYWCgHj1 5.1),gzip(gfe),gzip(gfe) > It is hard to hear that you have been taught wrong, and harder still > to confront dogma, because mathematical proof is just a phrase for > most of you as you've never been put in a situation where you really > did not wish to accept a result, so you avoid the mathematical proof > but by rationalizing continue to *believe* yourselves to be > mathematicians or real students of mathematics, when you no longer > are. I defined mathematical proof. Don't believe me? Google it. Google: > define mathematical proof I come up #2 now in most venues. Physics students *should* do better. Physicists know about resistance > to results and hard to understand results which challenge accepted > views, but the field has softened because of the dominance of > mathematical techniques, so people who are really mathematicians get > to pretend to be physicists, when they are not, and there is a worship > as well of authority, so that when the math people say *false* physics > students follow along because, what else can they do? Resist > authority? But, but, but...how can they? All of that is a preamble for one of the simplest most powerful > mathematical arguments in the history of human civilization which > mathematicians have resisted for over 6 years now despite how easy it > is to prove. It only requires you accept the distributive property and believe that > proof is, well, proof. The distributive property is: a*(b + c) = a*b + a*c > Does the distributive property say that a*(b + c)*(d + e) must equal (a*b + a*c)*(d + e)? Or does it also allow (b + c)*(a*d + a*e) ? Does that somehow violate the distributive property in the complex plane? And if a = s*t, does the following also violate the distributive property in the complex plane? s*t(b + c)*(d + e) = (s*b + s*c)*(t*d + t*e)? Is that OK with respect to the distributive property? And if all the symbols in sight are functions of x, i.e., a = a(x) = s(x)*(t(x), b = b(x), c = c(x), d = d(x), e = e(x), does the following violate the distributive property? s(x)*t(x)*(b(x) + c(x))*(d(x) + e(x)) = (s(x)*b(x) + s(x)*c(x))*(t(x)*d(x) + t(x)*e(x)) ? Is that legal, according to the distributive property? Yes or no? > In the complex plane with 7*(175x^2 - 15x + 2) = (5a 1(x) + 7)(5a 2(x)+ 7) where the a's are roots of a^2 - (7x-1)a + (49x^2 - 14x) = 0 you normalize: a 1(x) = b 1(x), and a 2(x) = b 2(x) - 1, as then you have 7*(175x^2 - 15x + 2) = (5b 1(x) + 7)(5b 2(x)+ 2) where b 1(0) = 0, b 2(0) = 0. And you have one factorization out of infinity and in THAT > factorization the 7 has distributed in one way, which is easily > verifiable at x=0, as then you it distributed through 5b 1(0) + 7, as that equals 7(0 + 1), so with the distributive property you have > a=7, b=0, c=1. > This is assuming that the factorization is constant. Why do you assume that? See my last example above. Does that example violate the distributive property in some way? Does the distributive property say that the factorization must be constant? Can you give a reference that says that? And doesn't the distributive property really only talk about multiplying something through one sum inside a parenthesis, not about two such? If you have a product of two sums inside parentheses, and a term outside, does the distributive property say there is ONLY ONE way to split up the outside term and distribute it across the terms in the parentheses? Where do you find a reference that says there is ONLY ONE way? > EASY. But remember 6 years of mathematicians arguing against this > result!!! > You are making assumptions that are not justified. You are assuming much more than what the distributive property actually says. You are discarding other perfectly valid ways to distribute 7 or whatever across products of terms in parentheses. You keep doing it withou justifying it. > Now if we consider that a*(b+c) = a*b + a*c, is true if one of the > elements is a function then I have a*(f(x) + b) = a*f(x) + a*b and the TYPE of the function does NOT MATTER; however, that challenges > current mathematical intuition, so while with something like 7(x^2 + 3x + 2) = (7x + 7)(x + 2) math people found it hard to dispute the distributive property, hide > the 7 away with: 7*(175x^2 - 15x + 2) = (5b 1(x) + 7)(5b 2(x)+ 2) and they disputed the result as they don't want to believe that with a^2 - (7x-1)a + (49x^2 - 14x) = 0 only one root should have 7 as a factor as that's what the > distribution shows. > In what ring? The complex plane? Some subring of the complex plane? What subring? Is every theorem which is true in the complex plane also hold true in every subring of the complex plane? Yes or no? Does your proof hold in the ring of algebraic integers? If not, what step in your proof is not valid if you are talking about the ring of algebraic integers? If there is no such step, then your proof must be just as valid in the ring of algebraic integers as in any other ring. You say that what you have shown contradicts Galois theory. What do you mean by that? If a 1(x) is divisible by 7 in some ring OTHER THAN the ring of algebraic integers, how do you know that Galois theory applies to that ring? Do the conclusions of Galois theory regarding divisibility apply to EVERY ring? How do you know that? > (Remember the factorization is normalized and a 1(x) = b 1(x), and a 2(x) = b 2(x) - 1.) Now in case you forgot your algebra classes, it is NOT taught in them > that only one of the roots of a^2 - (7x-1)a + (49x^2 - 14x) = 0 in general should have 7 as a factor. You can verify one case easily > enough, x=0: a^2 + a = 0 as one root is 0, and 0, of course has 7 as a factor. But use x=1, > and you get a^2 - 6a + 35 = 0 and only one of its roots actually has 7 as a factor, Stop right there. Are you, or are you not, claiming that only one of the roots of a^2 - 6a + 35 = 0 has exactly one of its roots divisible by 7? If yes, in what ring? In the ring of complex numbers? In the ring of algebraic integers? In some other ring? What ring? > but you can > prove in the ring of algebraic integers that NEITHER root has 7 as a > factor as neither root does--IN THAT RING. > So when you say one root DOES has 7 as a factor, what ring are you talking about? > The ring gives bad results. Techniques based on it give wrong > results. > You keep not quite stating what is wrong. You say that in the ring of algebraic integers, you can prove that a 1(x) does not have 7 as a factor. Then you say that is a wrong result. How can be that you can prove it and that it is a wrong result? If you can prove it, why is it wrong? Do you, or do you not, have an outright contradiction of Galois theory? Yes or no? Just give a straight answer for once. You cannot say the ring is wrong. A ring is just a ring. You might say that certain theorems about the ring are wrong. Which theorems? > So you have an advancement of human knowledge: it's now possible in > this case to determine 7 is a factor of a root without being able to > see it directly, where it's also not determined which root. > I have given explicit, arithmetic expressions which show that a 1(1) and a 2(1) both have nonunit factors of 7, and neither is divisible by 7, in the ring of algebraic integers. You are saying this is wrong. But you can check it for yourself. It's just plain arithmetic. You will have to conclude that either you are wrong, or arithmetic is wrong. If the latter, you can no longer trust that 1 + 1 = 2. Which do you think is more likely? > There is an ambiguity which cannot be removed which means the > solutions are paired or entangled in a way that cannot be beaten. You > must take them by two's. Absolutely NOT TRUE. The two roots of a^2 - 6a + 35 = 0 are 3 + sqrt(-26) and 3 - sqrt(-26). For each of those, I showed explicitly what factors they had in common with 7. The answers were in terms of roots of 6th degree polynomials. The results were completely explicit. There was no mystery and nothing was hidden. > With quarks Marcus. === Subject: Re: JSH: Simple math but bad math habits >Does the distributive property say that a*(b + c)*(d + e) must equal (a*b + a*c)*(d + e)? Or does it also allow (b + c)*(a*d + a*e) ? Does that somehow violate the distributive >property in the complex plane? Perhaps a very simple demonstration might help. Start with Marcus' expression: a * (b + c) * (d + e) Now use the fact that multiplication is associative (x*y)*z = x*(y*z) to add an extra pair of parentheses: a * ((b + c) * (d + e)) Now use the fact that multiplication is commutative to switch b+c and d+e around: a * ((d + e) * (b + c)) Now use the associative property to rearrange the parentheses: (a * (d + e)) * (b + c) Now use the distributive property to multiply the a through d+e: (a*d + a*e) * (b + c) where I have dropped the now useless extra set of parentheses. Now use the fact the multiplication is commutative to switch the order of the two parentheses: (b + c) * (a*d + a*e) QED. rossum === Subject: Re: L_3/2 <7476189.1230658490261.JavaMail.jakarta@nitrogen.mathforum.org>, > Its quite well known that fourier series converges to > their functions almost everywhere if that function is > periodic and L-2 integrable. It's well known that it's true, but it's not well known why it's true. It's a very difficult result. > but what about L-3/2 spaces ? ??? It's true for all p > 1, which has been posted a number of times. > what typical series are used for them ? > > i havent seen this subject in sci.math before , how > come ? I need to learn more about this. no book references plz. > > > > tommy1729 ( i changed L_3 towards L_3/2 because L_3 made no sense ) Why do you think L^3 makes no sense? === Subject: Re: nothing anyone would want to read (or: crank boxing (or: the death of the dance)) <13996160.1230656177045.JavaMail.jakarta@nitrogen.mathforum.org> posting-account=EL3hgwoAAABtyRFrR2z7EBO1tnJeMiO7 Gecko/2008120122 Firefox/3.0.5,gzip(gfe),gzip(gfe) > a = b,[b,a] ? accept or not. Forget about accept or not for now; please just say what the SYNTAX of that is. What are your primitives and your syntax rules? Unless you say, no one can give a meaningful opinion on such things as a = b,[b,a] MoeBlee === Subject: Re: nothing anyone would want to read (or: crank boxing (or: the death of the dance)) <27820145.1230412654769.JavaMail.jakarta@nitrogen.mathforum.org> posting-account=EL3hgwoAAABtyRFrR2z7EBO1tnJeMiO7 Gecko/2008120122 Firefox/3.0.5,gzip(gfe),gzip(gfe) > Please state EXACTLY what you think is incorrect in > Jesse's > demonstration and also with my own demonstration that > tommy1729's (or > whatever his name was then) theory at that time is > inconsistent. > point is , most already conclude inconsistant after seeing x = [x]. I don't know about most, but I do know that it doesn't include me. I [x] = is the set that contains x ( only ) however x may be a set itself. MoeBlee === Subject: Re: nothing anyone would want to read (or: crank boxing (or: the death of the dance)) posting-account=EL3hgwoAAABtyRFrR2z7EBO1tnJeMiO7 Gecko/2008120122 Firefox/3.0.5,gzip(gfe),gzip(gfe) > Yes, tommy1729 says he adopts an empty set axiom , but > as it turns out, it's not the same empty set axiom as > the one in ZFC. WHERE previous to my proof of inconsistency does this turn out in tommy1729's posts? He was asked at least a few times for any clarifications on his axioims. As to the axiom of the empty set he said: perhaps i should drop the axiom the empty set or clarify : empty set exists It is only reasonable for me to take him as meaning there is a set that has no members. He says (no matter what else he says, and despite his confusion in thinking this perhaps requires dropping the axiom of the empty set), the empty set exists. Without him stating some special variant, it is quite reasonable that one would take him to mean the ordinary empty set axiom. He stated no other empty set axiom and he did not stipulate that he doesn't mean the ordinary empty set axiom, and even his confused qualification restates that there exists an empty set, so it is only reasonable to take him to mean that there is a set that has no members. If I tell you that I adopt axiom of the empty set and/or that the empty set exists I would never fault you for taking me at face value: there is a set that has no members. You are grasping at infinitesimal straws (and losing more and more credibility) when you try to make out that it is MY fault for taking him to mean the ordinary empty set axiom when he does not specify otherwise and when indeed he even reiterates the empty set exists. Then why did you bother to leave it in and have me read it? > In an earlier thread, I was wondering how NBG could > have an Axiom of Pairing, after MoeBlee pointed out that > the Axiom of Pairing implies that every object must be a > set rather than a proper class. MoeBlee's response was > that the ZFC Pairing Axiom implies that every object > is a set, but the NBG Pairing Axiom is distinct from > the ZFC Pairing Axiom and doesn't imply that every > object is a set. > So just as ZFC and NBG have distinct Pairing Axioms, we > see that ZFC and TST have distinct Empty Set Axioms. No we don't see. Rather YOU argue spuriously. The analogy doeesn't hold. The pairing axiom is different in NBG from ZFC because there is a relativization to sets. tommy1729 mentioned no relativization, exception or variation. IF he had, then that would be a different story. But he didn't. And in the case of the pairing axiom in ZFC as opposed to NBG, you will see that ordinarily the exact distinction is part of the very formulation. In NBG, the formulation of the pairing axiom IS stated differently from than in ZFC. This contrasts with tommy1729 who, when he first posted axiom of the empty set did NOT stipulate that he means something other than the ordinary empty set axiom. If he had meant a formulation other than the ordinary exmpty set axiom, then he should have provided that formulation. Your analogy is terribly off. > And > since MoeBlee directed me to the Stanford site, I see > that the Stanford Empty Set Axiom (or Bottom) is more > appropriate for TST than ZFC's Empty Set Axiom. That is a DIFFERENT question. That one can find some other axiom that would be consistent is not at issue. tommy1729 did not state any such axiom of bottom. (By the way, though this still has no bearing on are YOU just CALLING it that? And what exactly is the axiom?) > Just as I should've known that the NBG Pairing Axiom is > more appropriate than the ZFC Pairing Axiom when there > are proper classes floating around, MoeBlee should have > known that the Stanford Empty Set Axiom is more > appropriate than the ZFC Empty Set Axiom where there is > a flattened mereology floating around. (1) I just addressed the matter of the analogy. (2) My proof of the inconsistency of tommy1729's axioms was addressed in the context in which his stated axioms were given. He did not specify that these were not the ordinary set theory axioms as he had listed them by name, and he didn't stipulate that this was a theory of a flattened mereology so that his simply named set theoretic axioms should be understood in some OTHER sense NOT even mentioned by him! You are just beyond credibility arguing that people are not reasonable to take such things as axiom of the empty set and the empty set exits in the context of a set theory to mean the ordinary empty set axiom rather than some other axiom about bottoms from some other theory that has not even been mentioned. You conflate on the one hand, your willingness to - AFTER THE FACT - RECONSTIUTE a theory with variant axioms and on the other hand, the axiomatization as it was originally given and which does NOT include such measures of reconstitution. > And just as MoeBlee criticized me for attempting to use > ZFC's Pairing Axiom to prove NBG inconsistent, I am > criticizing MoeBlee for attempting to use ZFC's Empty > Set Axiom to prove TST inconsistent. Again, a terrible comparision, for the reasons I mentioned above. > Hopefully this is a much better analogy than my first. Pathetic. MoeBlee === Subject: Re: nothing anyone would want to read (or: crank boxing (or: the death of the dance)) posting-account=Yn5cwwoAAADntcMuRwk-EwLg-DMZ_hXN rv:1.9.0.5) Gecko/2008120121 Firefox/3.0.5,gzip(gfe),gzip(gfe) i don't think anyone has said your assumption was a fault or even a poor assumption but i may have missed an exchange of course anyone having even slight familiarity with mereological containments alternative to zfc would have noticed that when tommy had _previously_ said = [] = [[]] = ... that emptiness here was not to be defined solely on membership relations but must use some atomic primitive i wouldn't blame you for making your assumption it's just a poor match to what tommy had already said maybe short-sighted is a better term for your approach here? lwalke3's analogy is completely accurate here === Subject: Re: nothing anyone would want to read (or: crank boxing (or: the death of the dance)) posting-account=EL3hgwoAAABtyRFrR2z7EBO1tnJeMiO7 Gecko/2008120122 Firefox/3.0.5,gzip(gfe),gzip(gfe) > i don't think anyone has said your assumption > was a fault > or even a poor assumption > but i may have missed an exchange It was said that I should have and that I am being criticized for. > of course > anyone having even slight familiarity > with mereological containments alternative to zfc > would have noticed that when tommy had previously said = [] = [[]] = ... that emptiness here was not to be defined > solely on membership relations > but must use some atomic primitive tommy1729 stated no such primitive nor that his axiom was to be taken in any special sense other than the empty set exists. That he splattered other notation in his posts does not vitiate that his axioms, as one is quite reasonable to take them in their ordinary way (since he did not stipulate otherwise), are inconsistent even with his own clarification: [x] = is the set that contains x ( only ) however x may be a set itself. > i wouldn't blame you for making your assumption > it's just a poor match to what tommy had already said I took his axioms as he posted them as the first post in a thread, along with whatever comments he made prior to my own posts. > maybe short-sighted is a better term > for your approach here? No. Just not as overreachingly generous as yours. I've said many times that I have no objection to finding a way to get a consistent theory by reconsituting what tommy1729 posted. But that does not entail that I was incorrect (espcially egregiously so, as you have been charging) or even the least bit unreasonable in my original posts showing the inconsistency of his axioms as he posted them. A reasonable response to the posts of Jesse, David, and me would have been something like Oh, yes, I can see how one would take those axioms as inconsistent; and I don't claim that your proof of inconsistency is incorrect. But if we revise the axioms and definitions [in such and such a way] then we don't have those inconsistencies. In that case, I'd not claim that the revision was inconsistent with itself unless it were and I could prove it. > lwalke3's analogy is completely accurate here It is pathetically off the mark, as, unlike you, I gave reasons for my assessment. MoeBlee === Subject: Re: nothing anyone would want to read (or: crank boxing (or: the death of the dance)) posting-account=Yn5cwwoAAADntcMuRwk-EwLg-DMZ_hXN rv:1.9.0.5) Gecko/2008120121 Firefox/3.0.5,gzip(gfe),gzip(gfe) > i don't think anyone has said your assumption > was a fault > or even a poor assumption > but i may have missed an exchange It was said that I should have and that I am being criticized for. well with your capitalisation tizzies where you accuse others of putting words in your mouth you (still) do so yourself quite consistently > of course > anyone having even slight familiarity > with mereological containments alternative to zfc > would have noticed that when tommy had previously said > = [] = [[]] = ... > that emptiness here was not to be defined > solely on membership relations > but must use some atomic primitive tommy1729 stated no such primitive nor that his axiom was to be taken > in any special sense other than the empty set exists. That he > splattered other notation in his posts does not vitiate that his > axioms, as one is quite reasonable to take them in their ordinary way > (since he did not stipulate otherwise), are inconsistent even with his > own clarification: [x] = is the set that contains x ( only ) > however x may be a set itself. you keep posting this even though this makes perfect sense in the explanation i gave for it (long long ago) why you think this statement of his supports your claims is your issue not mine > i wouldn't blame you for making your assumption > it's just a poor match to what tommy had already said I took his axioms as he posted them as the first post in a thread, > along with whatever comments he made prior to my own posts. > maybe short-sighted is a better term > for your approach here? No. Just not as overreachingly generous as yours. I've said many times > that I have no objection to finding a way to get a consistent theory > by reconsituting what tommy1729 posted. But that does not entail that > I was incorrect (espcially egregiously so, as you have been charging) > or even the least bit unreasonable in my original posts showing the > inconsistency of his axioms as he posted them. A reasonable response > to the posts of Jesse, David, and me would have been something like > Oh, yes, I can see how one would take those axioms as inconsistent; > and I don't claim that your proof of inconsistency is incorrect. But > if we revise the axioms and definitions [in such and such a way] then > we don't have those inconsistencies. In that case, I'd not claim that > the revision was inconsistent with itself unless it were and I could > prove it. why people still think my interpretation is overreachingly generous i do not know it was the first thing to pop into my mind after seeing his very first descriptions and it was my first response to him long before even the thread being discussed it immediately reminded me of a problem i had worked out the fact that others haven't studied the same books as me is not something i blame on others (like you do) but i do find it strange that the one who constantly screams about others reading books has been whining and pissing and moaning and CAPITALISING because he himself hadn't read a certain book that may have made the understanding as immediate for them > lwalke3's analogy is completely accurate here It is pathetically off the mark, as, unlike you, I gave reasons for my > assessment. i gave my understanding very early on i learned it from a book === Subject: Re: nothing anyone would want to read (or: crank boxing (or: the death of the dance)) posting-account=EL3hgwoAAABtyRFrR2z7EBO1tnJeMiO7 Gecko/2008120122 Firefox/3.0.5,gzip(gfe),gzip(gfe) > where you accuse others of putting words in your mouth > you (still) do so yourself quite consistently Let alone CONSISTENTLY, you've not mentioned a single specific instance (let alone a SIGNFICANT one). And the above is not such an instance. But I don't deny that I may be mistaken in paraphrasing sometimes. I try not to do it, but it may happen unwittingly. If it is brought to my attention, I hope to recognize the error and I surely do not go on and on and on for months systematically misparaphrasing a poster (indeed FABRICATING asserttions, as does lwal). > [x] = is the set that contains x ( only ) > however x may be a set itself. you keep posting this > even though this makes perfect sense > in the explanation i gave for it > (long long ago) why you think this statement of his > supports your claims > is your issue > not mine You STILL have not shown any error in the line 1-10 proof I posted. > why people still think my interpretation > is overreachingly generous > i do not know I've explained why I feel that it is. Over and over by now. > it was the first thing to pop into my mind > after seeing his very first descriptions > and it was my first response to him > long before even the thread being discussed it immediately reminded me of a problem i had worked out I do NOT say it is overgenerous to say that a presentation may be reconstituted. What is overgenerous to the poster of the messed up presentation is to claim that other people are incorrect when they post their proofs that the system, as it was presented (not necessarily as one might reconstitute it), is inconsistent. > the fact that others haven't studied the same books as me > is not something i blame on others > (like you do) I don't blame people merely for not studying the same books as me. Rather, I blame people who spout ignorantly and vastly incorrectly, on and on and on, about a subject of which they haven't even read a (though I may suggest ones I think are good). I don't even think they MUST read books at all; except that when they ignorantly and incorrectly spout on and on then I think are better to correct themselves starting by recourse to good texts. > but i do find it strange that the one > who constantly screams about others reading books > has been whining and pissing and moaning and CAPITALISING > because he himself hadn't read a certain book > that may have made the understanding as immediate for them I claimed nothing about what would or would not be my understanding of tommy1729's system if it were reconstituted. Rather, I showed that it is inconsistent as he conveyed it. > lwalke3's analogy is completely accurate here > It is pathetically off the mark, as, unlike you, I gave reasons for my > assessment. i gave my understanding very early on i learned it from a book Then you still keep private what that is that you learned in a book that makes you feel that lwal's analogy is apt in contrast with my arguments showing that it is not apt. MoeBlee === Subject: Re: nothing anyone would want to read (or: crank boxing (or: the death of the dance)) posting-account=euF15goAAACbw3KIqEWxZHCIPUc2KPmU .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) > [x] = is the set that contains x ( only ) > however x may be a set itself. > you keep posting this > even though this makes perfect sense > in the explanation i gave for it > (long long ago) And we've already pointed out, numerous times, that tommy1729's [x] corresponds to U({x}), not to {x}, in ZFC. > You STILL have not shown any error in the line 1-10 proof I posted. The error is in line 4 and any subsequent line that is based on the faulty assumption that contains acts like contains as an element in ZFC when it really acts more like contains as a subset, and treating [x] like {x} when it ought to be treated more like U({x}). === Subject: Re: nothing anyone would want to read (or: crank boxing (or: the death of the dance)) posting-account=EL3hgwoAAABtyRFrR2z7EBO1tnJeMiO7 Gecko/2008120122 Firefox/3.0.5,gzip(gfe),gzip(gfe) > [x] = is the set that contains x ( only ) > however x may be a set itself. > you keep posting this > even though this makes perfect sense > in the explanation i gave for it > (long long ago) And we've already pointed out, numerous times, that > tommy1729's [x] corresponds to U({x}), not to {x}, > in ZFC. See my remarks in previous post. > You STILL have not shown any error in the line 1-10 proof I posted. The error is in line 4 and any subsequent line that > is based on the faulty assumption that contains > acts like contains as an element in ZFC when it > really acts more like contains as a subset, and > treating [x] like {x} when it ought to be treated > more like U({x}). (1) Now you've changed your argument. First you objected to 'the axiom of the empty set' being understood as the empty set axiom. That was an embarrassingly self-defeating tack for you. Now you say it's in 'contains'. About that, see my previous post. (3) And now you say acts more like. Please don't let that be yet another wedge of ambiguity. You need to say that it IS subsethood, or, if not, then you need to say WHAT it is. And if you introduce a parthood primitive then keep in mind that you're NOT talking about what tommy1729 presentation as first discussed by Ullrich, Hughes, and me. And please say that [x] IS U{[x}, or, if not, then please say WHAT it is, and keep in mind the difference between YOUR reconstitution of what tommy1729 posted and what he posted. MoeBlee === Subject: Re: Russels Revenge <31196560.1230590812177.JavaMail.jakarta@nitrogen.mathforum.org> posting-account=EL3hgwoAAABtyRFrR2z7EBO1tnJeMiO7 Gecko/2008120122 Firefox/3.0.5,gzip(gfe),gzip(gfe) > On Dec 25, 1:41pm, amy666 the axiom of seperation only tells that the set of > all sets cannot be a set. > still sounds like a paradox hmm > It sounds like a paradox due to the informal language > used to describe > the actual formal mathematial result. If you were to > consult the > actual formal mathematics, you'd discover that there > is not an actual > contradiction you could produce. But that precision > is not something > you're interested in, is it? you either dont understand or are trying to make me look bad ... I'd like you to look good, which you can do by informing yourself of some basics of this subject. > notice i said : ' sounds ' I noticed. > as for the resolution , thats the whole issue here , and requires reading the entire OP , instead of snipping a tiny part. The rest of your analysis is no improvement and offers nothing toward a resolution other than more of your confusion. That is not the way it has to be though... > my posts are more subtle then they seem. Oh, 'subtle' is what you call it, eh? MoeBlee === Subject: Re: Russels Revenge <31196560.1230590812177.JavaMail.jakarta@nitrogen.mathforum.org> posting-account=jPnQ2goAAAA461y3QD0lbyw0oKeThma1 AppleWebKit/525.18 (KHTML, like Gecko) Version/3.1.2 Safari/525.20.1 FOH:R051,gzip(gfe),gzip(gfe) that was more-or-less what I said, two; Russel's paradoxes were simply pidgen -- I yam lying what I bean; not, I yam lying what I yam! the same applies to Korzybski (sp.?) and his E' (and probably his whole general semantics, unless the first was a purposeful joke). thus: that is an interesting inference of yours; had not someone proven the case for n=3 (and, of course, the very special case of n=4) ?? > life, Fermat, in a letter, raised the question of proving that no fifth > power is a sum of two fifth powers. So, by this time, he didn't even thus: on Nondystributive Geometry. yeah; if you can't put into constructive geometrical terms, you can't do ****. yeah; you had the definitive 2-week course in Geometry from an Advanced/Remedial Viewpoint in some Mice.Space at Vanderbilt! http://wlym.com/~boston/cartoons/slides/Mice%20Space.htm thus: here is an example of the Skeptics (current Calif. or USA mag.) being unable to come-up with a rational explanation of: sodium-vapor streetlights going off, as you walk underneath them; they think it to be either a hoax or psycho/visual. also, cropcircles. also, http://www.svpvril.com/svpweb14.html. thus: even Ockham'd slice through that apple & orange, with one wild Yahoo! (tm); western astrology is the same as Ptolemy's epicyclic hoax, over 2000yo. > some have been even making into popular news. > that astrological signs may have some meaning thus: I yam lying what I bean!... of what possible use is the set of all sets, whether or not it can eventually include itself, at the end of the list of elements -- shades of AP-adics? so, perhaps we can blame Russell for the Bourbaki New Math, based upon set theory, but see what Whitehead had to say about him, not to say Godel. thus: shouldn't it be clear that photons are an artifact of the idea that actually were zero-dimensional points, but, since they are waves, as shown by Young, Huyghens et al, there is really no need for them, except in the Pauli matrix formalism of statistical bosons; eh? Schroedinger's cat is dead -- long-live Schoredinger's cat! --only 24 hours to impeach Trickier Dick from the N.Admin, metaphorically typing, or Cheeny & Zbiggy, fo'mo' years; Good Morning, Afghanistan! ... Good Afternoon, Sudan! http://tarpley.net/bush12.htm http://wlym.com/campaigner/8011.pdf -- Brits hate Shakes, Why? http://www.wlym.com/~seattle/dynamis/ http://www.21stcenturysciencetech.com/current.html http://www.rwgrayprojects.com/synergetics/plates/plates.html http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=3163 http://wlym.com/campaigner/8011.pdf -- English, not! === Subject: Re: JSH: Questioning Galois Theory >The error is the ability to demonstrate an apparent contradiction-- >anathema to mathematics. > understanding what it is you think you have shown. In addition to the > other things I know about whatever it is, I now know that it is an > apparent contradiction. > However I STILL DO NOT KNOW WHAT THE CONTRADICTION IS! > Again my apologies for shouting, but you are not making yourself > clear. Could you please give a clear short answer along the lines of: > 1 Galois theory (or whatever) states ****************. > Ok, there was a request for an explanation which I'm giving, but you > want the advanced stuff, which you haven't understood up until now, > but ok, here we go again. > Galois Theory is a series of techniques concerning possible > combinations of simple radicals and the basic symbols +, -, and /, > which purportedly tells you something about underlying factors relying > on factors in the ring of algebraic integers. > OK, you have thoroughly made an ass of yourself > on that part. Clearly you have no concept of the > theory. Example: what role does group theory play > in Galois theory? I've forgotten so much of what you think is so important because I > know it's not. What's wrong with my description of Galois Theory? > It doesn't convey any of the essence of the theory. It's superficial, a Reader's Digest level kind of explanation which leaves out all the key ideas. Plus it does not indicate any relevance of Galois theory to what you are trying to do. > I have a question to test your knowledge, explain quickly how Galois > Theory proves there is no general solution for polynomials beyond > quartics. Remember for instance that the quadratic formula is a > general solution for quadratics. The Cardano equations work for > others, so why not quintics? > I was out of town for 3 days and did not have Internet access. Or, if you prefer, I spent the last 3 days frantically trying to figure out what Galois theory is so I could answer the question. Not. The essence of Galois theory for your purposes is the group of automorphisms of a decomposition field for a polynomial which leave the field of rationals pointwise fixed. Galois showed that this group had a certain group- theoretic property (solvability) if and only if the roots of the polynomial were expressible in terms of combinations of radicals. This was an astonishing insight, given that at that time, group theory was almost non-existent. Then he showed that for certain polynomials, the group was sufficiently complicated that it does not have the group-theoretic property in question. The smallest Galois group for which this is true is the alternating group of permutations of 5 things. This group corresponds to a certain 5th degree polynomial. The '5 things' are the roots of the polynomial. However this is not the part of Galois theory that is relevant to your problem. Suppose a_1 and a_2 are two roots of an irreducible polynomial with integer coefficients. There exists an automorphism A of the 'splitting field' of this polynomial which takes a_1 to a_2, that is, A(a_1) = a_2. Now if a_1 is divisible by an integer r, then because A(a_1/r) = (1/r)*A(a_1) = a_2/ r, you can conclude a_2 is also divisible by r in the ring of algebraic integers (yes, I am leaving out a little bit here, but I am sure you can fill it in if you know anything at all). > Relate that explanation to Abel's proof and show how Galois Theory > does more simply what Abel did in his highly creative way. > I'll let you do that, since this is not relevant to the discussion here. > Explain that way. And give it historical context, and then let's see > who is the ass. > Be my guest. > You know you reply a lot but I wonder how much of even established > mathematics you actually know. Here's a simple test. If he fails, anyone can answer. > The simple test for you was to explain why the equation 7*(x^2 + 3x + 2) = (7x + 7)*(x + 2) is the only possible 'valid' way to distribute '7' among the factors on the right side, in the complex plane. You have never explained that. But you keep saying it must be true. You haven't even given a definition of 'valid'. You have not explained why the following is not also a valid way to distribute '7' across the two parentheses on the right, 7*(x^2 + 3x + 2) = (s(x)*x + s(x))*(t(x)*x + 2t(x)), where s(x) = 7/(1 + x^2), t(x) = (1 + x^2). (Note that s(0) = 7 and t(0) = 1, just as in your preferred distribution.) Note also that s(x) and t(x) are functions of x. You have not explained either why the distribution of '7' on the right side must not be dependent on the value of x. Does the equation I gave above violate the distributive property in the complex plane in some way? Explain. Feel free to use Galois theory if it helps. Marcus. > James Harris === Subject: Re: Proof that the exclusive or is associative posting-account=EL3hgwoAAABtyRFrR2z7EBO1tnJeMiO7 Gecko/2008120122 Firefox/3.0.5,gzip(gfe),gzip(gfe) > Does anybody know how I can proof that the exclusive or is associative > in algebra terms? Is this how I start? (p xor q) xor r = p xor (q xor r) > ((p and not q) or (not p and q)) xor r = p xor ((q and not r) or > (not q and r)) I surmise you mean Boolean algebra. You might start a proof in the ordinary way of first unpacking the defintions, then looking for appropriate axioms and previously proven theorems to work on the material you just unpacked. In this case let: + be the join operation (union, or, whatever) * be the meet operation (intersection, and, whatever) ~ be the complement operation (negation, whatever) p xor q =df (p+q)*~(p*q). (By the way, this is sometimes called 'the symmetric difference of p and q.) So unpack (p xor q) xor r by the above definition, and unpack p xor (q xor r) by the above defintition. Work on identities of both unpacked expressions your axioms and previously proven theorems. Probably use at least distributive law and DeMorgan's. Eventually you'll get the two expressions to meet in an identity. MoeBlee === Subject: Which property of 'e'? posting-account=YujYHwoAAAAXW3Ays0tHQ43tjw57d7U_ 5.1),gzip(gfe),gzip(gfe) given an operator p: p=(h/(2*pi*i))*d/dx on a function f: f(x)=e^((2*pi*i/h)*C*x) This then equates to C*f(x). ie., placed all together: (h/(2*pi*i))*d(e^(2*pi*i*C*x/h))/dx = C*e^((2*pi*i/h)*C*x) (I re-arranged e's exponent here; multiplication and division should be commutative) where 'e' is the number such that de^(x)/'dx=e^x, 'h' is Planck's (non- reduced) constant (though what constant it is should be immaterial), 'pi' is 22/7, i is sqrt(-1), 'C' is some constant, and 'x' the independent variable. Here's my thought process so you can perhaps find the hole: First, the d/dx of e^(whatever) is just the e^(whatever), so we can eliminate that, then we have the (h/(2*pi*i)) times all that - but how does it disappear to just become C? I would guess that somehow we manipulate 'e' to get its exponent down so we can multiply its (2*pi*i/ through what trick or principle of 'e' that is unbeknownst to me? === Subject: Re: Which property of 'e'? posting-account=9QOSvAoAAACEOWJVSDuswW7dB_0wApQO Gecko/20070530 Fedora/1.5.0.12-1.fc5 Firefox/1.5.0.12,gzip(gfe),gzip(gfe) given an operator p: > p=(h/(2*pi*i))*d/dx on a function f: > f(x)=e^((2*pi*i/h)*C*x) This then equates to C*f(x). ie., placed all together: > (h/(2*pi*i))*d(e^(2*pi*i*C*x/h))/dx = C*e^((2*pi*i/h)*C*x) > (I re-arranged e's exponent here; multiplication and division should > be commutative) where 'e' is the number such that de^(x)/'dx=e^x, 'h' is Planck's (non- > reduced) constant (though what constant it is should be immaterial), > 'pi' is 22/7, i is sqrt(-1), 'C' is some constant, and 'x' the > independent variable. If you replace pi by 22/7 why not simply use zero instead of h? ;-) > Here's my thought process so you can perhaps find the hole: > First, the d/dx of e^(whatever) is just the e^(whatever), This is not true. For example, d/dx (e^(2x)) is different from e^(2x) > so we can eliminate that, > [...] so you can't really eliminate that... -- m === Subject: william nessler - Free posting-account=DG4DeQoAAABKgmR36q-qauGKpU8cnbxn iOpus-Web-Automation; MRA 5.2 (build 02400); MRSPUTNIK 2, 0, 1, 26 SW; .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) william nessler . . . *******CLICK HERE******** http://club247.cn/william-nessler ***************************** . . . . . . . . . . . . william nessler === Subject: william nesler - Free posting-account=DG4DeQoAAABKgmR36q-qauGKpU8cnbxn iOpus-Web-Automation; MRA 5.2 (build 02400); MRSPUTNIK 2, 0, 1, 26 SW; .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) william nesler . . . *******CLICK HERE******** http://club247.cn/william-nesler ***************************** . . . . . . . . . . . . william nesler === S === === Subject: Re: Tutte's theorem made easy? > I'm looking for a proof as elementary as possible of Tutte's theorem > stating that any vertically 4-connected planar graph is Hamiltonian. I > have tried to read Tutte's paper (the 1977 version of the proof) but > find it very dry. Maybe its wording doesn't help... > [...] >Sorry for my ignorance, what is a *vertically* 4-connected planar >graph? He means 4-vertex-connected, as opposed to 4-edge-connected. I haven't ever studied this result in detail myself, but there's a proof > at the end of Chapter 5 in Ore's book The Four-Color Problem. I'm > guessing that it's more readable than Tutte's proof, simply because Tutte > is almost always hard to read. > -- > Tim Chow tchow-at-alum-dot-mit-dot-edu > The range of our projectiles---even ... the artillery---however great, will > never exceed four of those miles of which as many thousand separate us from > the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences grab a copy of Ore's book. === Subject: attempt at faking math talk? > It's the way things are, and always will be. No one >can change it Goober...not Rupert....not his instructors... >not the boys in the math ngs....not you, Goo. It isn't. Then you try changing it, or Rupert, or his instructors, or your nurses Goo... Let's see the corrected equation(s). Go: >It is worthless cracker bull that describes nothing. It >wasn't math, it wasn't an equation; it was just a bunch of letters that >you thought looked like math. It considers basic existence and also the value of the life experienced. Your moral values do not apply Goob, nor do any of your obsessions with pre-existence. >e + N = -V and e + P = +V It calculates the value of life Goo. In order to calibrate it or whatever it would get more complex, but what we've got is too much for some people like all you misnomer advocates just as it is. >(correct prediction: Goo can't think of it being any other way, >and is lying when he pretends that he can) === Subject: Re: Goowit Harrison's attempt at faking math talk? stupid pig-ing cracker, cockfighting specialist - woke up and said, How can I be even *more* stupid today than I was yesterday?, and so he lied: > No pointing out. Stupid, illiterate, convicted felon crackers do not point out. > It's the way things are > It isn't. It was just stupid cracker fake math talk. It doesn't describe anything. Then you try changing it Nothing to change. It's obvious that it's cracker fake math talk. > It is worthless cracker bull that describes nothing. It > wasn't math, it wasn't an equation; it was just a bunch of letters that > you thought looked like math. It considers It's fake math talk. It's nothing. > e + N = -V and e + P = +V It calculates the value of life It calculates nothing. It's fake. It's complete bull. You just strung some letters and a couple of arithmetic operators together at random. It's bull - the usual cracker spew from an uneducated, stupid, low-IQ cracker. === Subject: Re: mathematiks -sbk +M[5[U[QT7xFN%^gR=tuJw%TXXR'Fp~W;(T1(739R%m0Yyyv*gkGoPA.$b,D.w:z+<'=-lV T?6 {T?=R^:W5g|E2#EhjKCa+nt:4b}dU7GYB*HBxn&Td$@f%.kl^:7X8rQWd[NTcPu6nkisze/ Q;8 9Z{peQF,w)7UjV$c|RO/mQW/NMgWfr5*$-Z%u46/00mx-,R'fLPe.)^ > the torque of the pork * the heat of the meat= the speed of the deed 1: TH=S > The mass of the ass / torque of the pork = the heat of the meat 2: M/T=H > the speed of the deed * the heat of the meat = the mass of the ass 3: SH=M M=SH (3) but H=M/T (2) therfore M=SM/T 1=S/T S=T but TH=S TH=T therfore H=1 2: M/T=H M/T=H (2) M=TH TH=S S=M S=T=M H=1 or S=T=M=0 so, either the heat of the meat is 1 and the torque of the pork is The mass of the ass and also the speed of the deed or torque of the pork,The mass of the ass and the speed of the deed is 0 and the heat of the meat cannot be determined === Subject: Re: JSH: Was never a factor argument > He did independently discover a prime-counting algorithm - Also more than just a few years ago. The Harris who did that looks like > a super genius compared to the Harris of today. > the fact that (as you have pointed out) equivalent to > Legendre's method Many pointed that out before me, although among all such I may have > spent the largest percentage of my life explaining exactly how it was > equivalent, in endless pedantic detail ;-) > says something positive, not negative, about his innate talent. Or the innate talent he /used/ to have. It's possible that relentless > years of seemingly cultivated laziness and bad practice have wholly > eroded whatever innate talent he once had. Does he display any talent now? I mean for math, not for ranting like a > deranged lunatic. I'm not sure independently discovering something equivalent to Legendre's method even indicates talent. Legendre's method is close to a triviality. Legendre was a genius, but he was also working at a time when mathematical knowledge was a lot less formalized and systematized than it is now. When a mathematician of that era used, as a small part of some great worksof genius, some fact or theorem that was trivial, there was a good chance he was the first to use that fact or theorem publicly or prominently, and so gets credit for it. ... > I only mentioned it because you seemed to show signs recently of not > /enjoying/ your futile exchanges with him. And if it's true that you're > bashing your head against the Harris Wall more but enjoying it less, it > might be helpful to be reminded that there's truly no need to continue > doing it -- indeed, it's hard to see where there's any benefit to it. OTOH, /I/ enjoy watching his lunatic responses, so please don't find > something better to do on my account :-) One benefit of following the JSH threads is that occasionally there is very interesting mathematics involved if you try to understand just how wrong he is. Consider, for example, his Diophantine equation chain approach to solving the Pell equation. It doesn't, in general, work. I believe it only works for a very small number of Pell equations. In trying to prove that, I ended up with a hypergeometric series that I needed to sum. That led to a fascinating diversion into learning something about summing hypergeometric series, which turns out to be a really cool area of mathematics, which I probably would not have looked into, if not for JSH. -- --Tim Smith === Subject: Re: JSH: Was never a factor argument > [David Bernier] > ... > For now, my working assumption is that James can > manipulate algebraic symbols, but he > hasn't mastered some fundamental concepts in > high school algebra. Maybe this includes > the conceptual difference between parameters > or coefficients and an indeterminate or unknown quantity, > as the x is in ax^2 + bx + c. agree also I agree that's part of the truth. James is a symbol pusher, endlessly > manipulating equations /as/ equations, with a spectacular lack of > /insight/. It's typical that he complicates the set of equations he > works with until it's such a mess he can talk himself into believing > there's a revolutionary breakthrough hiding in the parts of that mess > that have grown so complicated he can no longer understand them at all. disagree, he has failed to learn higher levels algebra, high school algebra, he does not know complex numbers at all. to save his ego he attacks, driven by NPD to its ultimate end, living in the woods alone, in a small plywood room, chasing rabbits in the snow, supreme and the God of all around him, and they all worship him. (whoever they are) In this respect, this JSH post from 2006 was revealing: http://mathforum.org/kb/message.jspa?messageID=4773926 ... As a hobby when I was a kid I was fascinated with parabolas. > I'd draw them, play with the equations for them. Trace out > tangent lines, and marvel over their properties--and I liked > to rotate them into hyperbolas. Just for fun. He later admitted this (rotating parabolas into hyperbolas) wasn't > not just a simple mistake, it reveals a mind with /no understanding > whatsover/ of plane geometry. It's an extreme symbol-pusher's brain, > prone to accepting /obviously/ wrong conclusions based on mistakes made > while manipulating equations mindlessly. That's our Jimmy ;-) === Subject: Re: JSH: No need for Galois theory Stated without proof. Prove if you can the statement that if a_1(x) is divisible > by 7 then so is d(x) and e(x), and give the ring. I know I deleted a statement where you say in any ring, > but you need to state that upfront if that is your > continued claim, as I'm clipping after anything unproven. I've seen this movie before. Isn't this the one where the hero (JSH, of course) demands to be spoon-fed every tiny, little detail; is forced (finally) to admit he was wrong; runs off and sulks for a while; then, comes back and continues to claim he was right all along (and mathematicians are evil for denying it)? No, wait... That one featured a simple (so-called) proof of Fermat's Last Theorem. Completely different movie. Carry on. Jim Burns === Subject: Re: JSH: No need for Galois theory <495A3965.7040108@osu.edu> posting-account=3WPJYgoAAAA55VjhzK9i07RN8h8u8eEs Gecko/2008092417 Firefox/3.0.3,gzip(gfe),gzip(gfe) I've seen this movie before. Isn't this the one where the hero (JSH, of course) demands > to be spoon-fed every tiny, little detail; is forced > (finally) to admit he was wrong; runs off and sulks for > a while; then, comes back and continues to claim he was > right all along (and mathematicians are evil for denying it)? No, wait... That one featured a simple (so-called) proof > of Fermat's Last Theorem. Completely different movie. Carry on. Jim Burns LOL! Yeah, well you know how most movies are these days: remakes and sequels. Most people probably enjoy them for the same reason they enjoy the JSH movie: it's easy to understand, predictable, and there's a doofus in the movie everyone can make fun of and feel superior to. M === Subject: Re: JSH: No need for Galois theory > On Dec 27, 11:23 am, William Hughes > Ok, your claim is that exactly one of a_1(x) and a_2(x) > should be divisible by 7. This claim contradicts simple algebra. > There is no need to even mention Galois theory. > - William Hughes > Then give the algebra, ok? > Consider the quadratic > a^2 - (7x-1)a + (49x^2 - 14x) = 0 > Then, if x is such that the quadratic is irreducible over > the rationals, then either both roots or neither > root is divisible by 7. > Let x be such that the quadaratic is irreducible over the rationals > and let a_1(x) and a_2(x) be the two roots. Then looking at the > quadratic formula, we see that a_1(x) = d(x) + e(x) where d(x) > is rational and e(x) is irrational or complex and that a_2(x) = > d(x) - > e(x). > If a_1(x) is divisible by 7 then so is d(x) and e(x) and therefore > a_2(x). > Stated without proof. > Prove if you can the statement that if a_1(x) is divisible by 7 then > so is d(x) and e(x), and give the ring. > Nope, I made a mistake. It's false in general. Yeah, I know. Oh, and I've already said that NEITHER of the a's can > have 7 as a factor in the ring of algebraic integers when non-rational > with rational x (note that requires integers for x to be in the ring). That's the wacky cool error! And readers keeping score should note that the poster DID eventually > run to the ring of algebraic integers. The region that provably has the error. Can't keep these little bastard in the field of complex numbers, now > can I? Guess they hate it. Why? Because in the field of complex numbers > they have no room to hold on to their delusion, that's why. Comfort. They're seeking comfort from the cold, hard mathematical > truth. So, NOT scientists, in any way shape or form. Oh yeah, a little more testy than normal as I just got an email from > the Bulletin. Not only did they reject my paper without explanation, > but the editor begged me not to send any more papers!!! I sent a nasty gram in reply. But she *deserved* it. Math people freaking go bonkers over this result. It's sad, but I > have to try to laugh so I don't cry. Next up is the Annals of Mathematics at Princeton. Then the New York > Journal of Mathematics as I begin to do the rounds, bringing in > journals so that later I can trash the entire modern academic system. Too bad Beckwith doesn't like you anymore and won't advise you on where to get crackpot papers published. (Beckwith, what a crackpot, a clampot!) I need to build up the potential energy to change it, as, um, it's > kind of big! (Oh, I forwarded her reply to Ribet and some other math dude. Thought > they needed the laugh.) Did you forward a copy to your daddy? James Harris === Subject: Primes of form x^2-ny^2, n > 0 (esp x^2-37y^2) posting-account=-ACVjwoAAAAVqSiDl929-Pe1jSK2zs-Q FunWebProducts; GTB5; .NET CLR 2.0.50727; .NET CLR 1.1.4322; .NET CLR 3.0.04506.30),gzip(gfe),gzip(gfe) Hello all, This is related to another post I made, summarized for convenience, with added info: Is it true the ff eqns x^2-py^2 = q have solns for ALL prime q of form: x^2-3y^2 = q; q = 12n+1 x^2-7y^2 = q; q = {28n+1, 28n+9, 28n+25} x^2-11y^2 = q; q = {44n+1, 44n+9, 44n+25, 44n+5, 44n+37} and, x^2-2y^2 = +/-q; q = 8n+/-1 x^2-5y^2 = +/-q; q = {20n+/-1, 20n+/-9} x^2-13y^2 = +/-q; q = {52n+/-1, 52n+/-9, 52n+/-25, 52n+/-49, 52n +/-29, 52n+/-17} as well as for other p? (Known to be true for p = 2,3, and for p>3 have been tested for the first few hundred examples for small p < 37. Counter-examples, pls, if any.) If there is none, then, CONJECTURE 1: For certain primes p of form 4n-1. There are integral solns to x^2-py^2 = q for ALL prime q when, (q-r) = mod(4p) and r is the smallest soln to s^2-v = mod(4p) for one v, v being all the odd numbers < p. Note 1: Violated by the smallest (?) p = 4n-1 = 79, 223, etc. CONJECTURE 2: For certain primes p of form 4n+1. There are integral solns to x^2-py^2 = +/-q for ALL prime q when, (q+/-r) = mod(4p) and r is the smallest soln to s^2-v = mod(4p) for one v, v being all the odd numbers < p. Note 2: Violated by the smallest (?) p = 4n+1 = 37, 101, etc. Question: Assuming the conjectures are true, for the exceptional primes (like 37) that don't obey it, is there a LINEAR form q=an+b, with constant {a,b}, such that whenever q is prime, it is expressible as x^2-37y^2? (For example, it seems all primes of form 20n+1 are expressible as x^2-5y^2.) P.S. I assume Cox discusses this, or does he focus on the case x^2+ny^2, n > 0? Tito === Subject: Re: Primes of form x^2-ny^2, n > 0 (esp x^2-37y^2) This is related to another post I made, summarized for convenience, > with added info: Is it true the ff eqns x^2-py^2 = q have solns for ALL prime q of > form: x^2-3y^2 = q; q = 12n+1 > x^2-7y^2 = q; q = {28n+1, 28n+9, 28n+25} === Subject: Re: JSH: Was never a factor argument days. My association with the Department is that of an alumnus. >Heh. This raises the question of which is the simplest explanation. The smallest explanation that has no proper nontrivial normal subexplanations, of course. -- It's not denial. I'm just very selective about what I accept as reality. --- Calvin (Calvin and Hobbes by Bill Watterson) Arturo Magidin magidin-at-member-ams-org === Subject: Re: JSH: Was never a factor argument posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif AppleWebKit/525.19 (KHTML, like Gecko) Chrome/1.0.154.36 Safari/525.19,gzip(gfe),gzip(gfe) > [JSH, spouting the usual JSH gibberish] > ... > [marcus bruck...@yahoo.com] > ... > It is NOT the case that the 7 can be distributed in only > one way across the two factors. You can deny that this > was your underlying goal, but clearly it was. Otherwise > you were just raving on about an utter trivial banality. > But even you are not that dumb. > I'm not sure about that. Give yourself a Christmas present :-) I > believe I replied to James a grand total of two times in 2008. In both > cases I simply presented 1-digit integer counterexamples to the goofy > claims he was making on those days. No arguments, no followups, no > attempts to reason with him. > And I learned something ;-) When arguing with him in previous years, I > made extraordinary efforts to try to make /any/ kind of coherent sense > out of the endless gibberish he spouted. But I now believe that, in > most cases, the sense I believed I found was my own construction, not > without twisting your head up your ass fifty different ways to try to > give him the benefit of the doubt, he really does appear to be that > dumb (at least when it concerns mathematics, in which he is profoundly > incompetent). > You had an ulterior motive. > False dichotomy there -- it's possible that he's both that dumb and > wallowing in ulterior motives. But, in this case, I think it more > likely that he doesn't understand the distinction you believe is dead > obvious here: that he believes his endlessly repeated > 7*(x^2 + 3x + 2) = (7x + 7)*(x + 2), I agree with that view, Tim. > I think James may be mixed up by what = means in math . > When using a calculator, pressing the = sign gives > the answer. So James could be thinking that > 7*(x^2 + 3x + 2) has *two* possible answers: > either > 7(x+1)(x+2) = (7x + 7)*(x+2) [Answer 1] > or > 7(x+1)(x+2) = (x + 1)*(7x + 14) [Answer 2] ; Nope. There are an INFINITY of ways to factor 7(x^2 + 3x + 2) on the complex plane. And ONE of those ways is 7(x^2 + 3x + 2) = (7x + 7)(x + 2). > but, to him, you choose one answer or the other, > but not both, because that's all about the > distributive property, which of course he thinks he > understands. I'm consistently saying the same thing. You and posters like you are making things up. > The = in math can be subtle [for A.I. purposes]. And I remind other readers who think it is about me. Clearly it's not. Given 7(x^2 + 3x + 2) = (7x + 7)(x + 2) you are looking at one factorization out of infinity, but it is a valid factorization, which does not shift dependent on the value of x. So 7x + 7 = 7(x+1), or to give the distributive property the straightforward way: 7(x+1) = 7x + 7, and it doesn't change dependent on the value of x. That is trivial algebra!!! What happens though if you follow mathematical logic is that now with 7*(175x^2 - 15x + 2) = (5a 1(x) + 7)(5a 2(x)+ 7) where the a's are roots of a^2 - (7x-1)a + (49x^2 - 14x) = 0 you get a weird situation if you normalize with a 1(x) = b 1(x), and a 2(x) = b 2(x) - 1, as then you have 7*(175x^2 - 15x + 2) = (5b 1(x) + 7)(5b 2(x)+ 2) where b 1(0) = 0, b 2(0) = 0, which is in key respects exactly like 7(x^2 + 3x + 2) = (7x + 7)(x+2) and it represents ONE factorization out of an infinite number of ways to factor: 7*(175x^2 - 15x + 2). So what's different then? Well, in one case you have 7x--a linear function. In the other you have b 1(x), a non-linear function defined in a fairly clever way using what I call a quadratic generator. Ergo, the argument then is over whether or not a*(f(x) + b) = a*f(x) + a*b varies because of the ***function*** as there is no argument that given 7(x^2 + 3x + 2) = (7x + 7)(x+2) it's ludicrous to claim that x=0 is different from x=1, or x equal any other value. So mathematical logic is firmly on my side, and it IS a case of people arguing against the distributive property, but of course, that is clearly nonsensical so they misrepresent what they are doing. What is more interesting though are those of you who may be confused!!! If so, you are confused for purely social reasons, which should show you how hard doing real mathematics can actually be. These people have gotten away with attacking the distributive property and claiming they are not doing so for over six years now. Most human beings simply are not cut out to do real mathematics, but lying to one's self is so easy that plenty of people around the world believe they are when with a simple test of a proof with huge social consequences where the linchpin is one of the most trivial of mathematical things---they fail, miserably. Most of you are not capable of being real mathematicians. In fantasy, yes, you can convince yourselves you are mathematicians. IN reality, no, you are cows who follow the herd. James Harris === Subject: Re: JSH: Was never a factor argument posting-account=wVv_VwoAAAAVTfUuyxLzug5SzYWCgHj1 5.1),gzip(gfe),gzip(gfe) > [JSH, spouting the usual JSH gibberish] > ... > [marcus bruck...@yahoo.com] > ... > It is NOT the case that the 7 can be distributed in only > one way across the two factors. You can deny that this > was your underlying goal, but clearly it was. Otherwise > you were just raving on about an utter trivial banality. > But even you are not that dumb. > I'm not sure about that. Give yourself a Christmas present :-) I > believe I replied to James a grand total of two times in 2008. In both > cases I simply presented 1-digit integer counterexamples to the goofy > claims he was making on those days. No arguments, no followups, no > attempts to reason with him. > And I learned something ;-) When arguing with him in previous years, I > made extraordinary efforts to try to make /any/ kind of coherent sense > out of the endless gibberish he spouted. But I now believe that, in > most cases, the sense I believed I found was my own construction, not > without twisting your head up your ass fifty different ways to try to > give him the benefit of the doubt, he really does appear to be that > dumb (at least when it concerns mathematics, in which he is profoundly > incompetent). > You had an ulterior motive. > False dichotomy there -- it's possible that he's both that dumb and > wallowing in ulterior motives. But, in this case, I think it more > likely that he doesn't understand the distinction you believe is dead > obvious here: that he believes his endlessly repeated > 7*(x^2 + 3x + 2) = (7x + 7)*(x + 2), > I agree with that view, Tim. > I think James may be mixed up by what = means in math . > When using a calculator, pressing the = sign gives > the answer. So James could be thinking that > 7*(x^2 + 3x + 2) has *two* possible answers: > either > 7(x+1)(x+2) = (7x + 7)*(x+2) [Answer 1] > or > 7(x+1)(x+2) = (x + 1)*(7x + 14) [Answer 2] ; Nope. There are an INFINITY of ways to factor 7(x^2 + 3x + 2) on the > complex plane. And ONE of those ways is 7(x^2 + 3x + 2) = (7x + 7)(x + 2). > Are all of infinitely many ways equally valid? > but, to him, you choose one answer or the other, > but not both, because that's all about the > distributive property, which of course he thinks he > understands. I'm consistently saying the same thing. > True. You are saying nothing, and trying to conclude something from it. > You and posters like you are making things up. > The = in math can be subtle [for A.I. purposes]. And I remind other readers who think it is about me. Clearly it's > not. Given 7(x^2 + 3x + 2) = (7x + 7)(x + 2) you are looking at one factorization out of infinity, but it is a > valid factorization, which does not shift dependent on the value of x. > What does valid mean? Are you saying that nonconstant factorizations are not valid? Why is that? Do you have a secret definition of valid? What is it? Do you have a secret proof that nonconstant factorizations are not valid? > So 7x + 7 = 7(x+1), or to give the distributive property the > straightforward way: 7(x+1) = 7x + 7, and it doesn't change dependent > on the value of x. > Is that forbidden? Why? > That is trivial algebra!!! > So far. But evidently something more than algebra. You appear to be ruling out nonconstant factorizations. Why ? Is there something wrong with them? Are they not valid ? Can you define valid? And then prove somehow that nonconstant factorizations are not valid ? > What happens though if you follow mathematical logic is that now with 7*(175x^2 - 15x + 2) = (5a 1(x) + 7)(5a 2(x)+ 7) where the a's are roots of a^2 - (7x-1)a + (49x^2 - 14x) = 0 you get a weird situation if you normalize with a 1(x) = b 1(x), and a 2(x) = b 2(x) - 1, as then you have 7*(175x^2 - 15x + 2) = (5b 1(x) + 7)(5b 2(x)+ 2) where b 1(0) = 0, b 2(0) = 0, which is in key respects exactly like 7(x^2 + 3x + 2) = (7x + 7)(x+2) > There are a lot of differences, and they are not trivial. In the 7x + 7 case, x is the polynomial variable. In the other case, 5b 1(x) is not even a polynomial function. Besides which, you are not factoring 7*(175x^2 - 15 x + 2) as a polynomial in x. You are factoring it as a polynomial in 5. The two situations are not parallel, or even close. You cannot generalize from the simplistic 7x + 7 thing to the more complex case. > and it represents ONE factorization out of an infinite number of ways > to factor: 7*(175x^2 - 15x + 2). So what's different then? Well, in one case you have 7x--a linear > function. In the other you have b 1(x), a non-linear function defined in a > fairly clever way using what I call a quadratic generator. > The fact that they have x in common is not enough. They are not even the same kinds of function. > Ergo, No. You say ergo only when what you are about to say is preceded by logical argument. That is far from the case here. > the argument then is over whether or not a*(f(x) + b) = a*f(x) + > a*b varies because of the ***function*** as there is no argument that > given 7(x^2 + 3x + 2) = (7x + 7)(x+2) > There IS an argument. You yourself just said there were infinitely many ways to factor 7(x^2 + 3x + 2) in the complex plane. You give no reason for selecting only one of those factorizations. Just your own preference? You give no reason for rejecting nonconstant factorizations. You imply they are not valid but you have no definition of valid, and no proof. Arguing by analogy cannot work here, because you have nothing on the easier side of the analogy, and the analogy is not even close anyway. Just some vague feeling, probably based on factorization-by-inspection. > it's ludicrous to claim that x=0 is different from x=1, or x equal any > other value. > Ludicrous is not a logical argument, not mathematics. I don't want ludicrous. I want RIGOROUS. You don't have it. > So mathematical logic is firmly on my side, and it IS a case of people > arguing against the distributive property, but of course, that is > clearly nonsensical so they misrepresent what they are doing. > No. You do NOT have logic on your side; just emotion, and ludicrous. Answer the questions above, give a rigorous proof rather than a hand-waving analogy which has no effect anyway since you have no proof for the simpler side of the analogy. > What is more interesting though are those of you who may be > confused!!! > Ah, the appeal to the Grandstand. All those innocent little undergrads out there. Maybe you can fool a few of them. How about answering some specific questions? 1. What is special about the factorization 7*(x^2 + 3x + 2) = (7x + 7)*(x + 2) in the complex plane? Is it better in some way than 7*(x^2 + 3x + 2) = (a(x)*x + a(x))*(b(x)*x + 2b(x)), where a(x) and b(x) are functions of x whose product is 7? For example, a(x) = 7/(1 + exp(x)), b(x) = 1 + exp(x) Does this nonconstant factorization violate the distributive property in some way? Can you PROVE that it does? Is this nonconstant factorization not valid? What do you mean when you say valid? What is the rigorous definition? Can you PROVE the nonconstant factorization is not valid ? Have you given such a proof? Where? 2. First you factor in the complex numbers. Then you want to jump to conclusions in the ring of algebraic integers. Is every theorem that is true in the complex plane also true in every subring of the complex plane? Can you prove that? If not, how do you transition from the complex plane to subrings of it? Stop shoveling smoke or whatever it is you are shoveling and give some definite answers! Marcus. === Subject: JSH: No need for Galois theory posting-account=1lE9SQkAAADFrJsDv61dh1YXcJ_ahy5I > where the a's are roots of a^2 - (7x-1)a + (49x^2 - 14x) = 0 > Then, if x is such that the quadratic is irreducible over the rationals, then either both roots or neither root is divisible by 7. You don't need the Galois sledgehammer to crack this walnut. Let x be such that the quadaratic is irreducible over the rationals and let a_1(x) and a_2(x) be the two roots. Then looking at the quadratic formula, we see that a_1(x) = d(x) + e(x) where d(x) is rational and e(x) is irrational or complex and that a_2(x) = d(x) - e(x). If a_1(x) is divisible by 7 then so is d(x) and e(x) and therefore a_2(x). So your claim that for all x, a_1(x) is divisible by 7 and a_2(x) is coprime to 7, breaks not only Galois theory but simple algebra. - William Hughes For extra credit identify where this proof breaks down if x is such that the quadratic is reducible over the rationals. Hint: look at e(x) is irrational or complex === Subject: Mach Projectile This introduces some of the math involved in predicting where a bullet will hit before it gets there. Three microphones on a helicopter pick up the conical shock wave. http://mypeoplepc.com/members/jon8338/math/id21.html === Subject: Re: Mach Projectile posting-account=c6T4LggAAACAqdk8Zx_zXI_oErOujh3M Gecko/20050915 Firefox/1.0.7,gzip(gfe),gzip(gfe) > This introduces some of the math involved in predicting where a bullet will > hit before it gets there. Three microphones on a helicopter pick up the > conical shock wave. http://mypeoplepc.com/members/jon8338/math/id21.html Man, with your brains, you could do some serious ultrasound engineering, for medical scanning. Ken === Subject: Re: Mach Projectile posting-account=42V-qwoAAABOAKkANAhMmpW4F3ZbRLXb Gecko/2008120122 Firefox/3.0.5,gzip(gfe),gzip(gfe) > This introduces some of the math involved in predicting where a bullet will > hit before it gets there. Three microphones on a helicopter pick up the > conical shock wave. http://mypeoplepc.com/members/jon8338/math/id21.html That's cute, but actual military application of this idea is used to retrodict the position of the gun that fired the shot. Mark L. Fergerson === Subject: Re: Mach Projectile > This introduces some of the math involved in predicting where a bullet will > hit before it gets there. Three microphones on a helicopter pick up the > conical shock wave. http://mypeoplepc.com/members/jon8338/math/id21.html Gun ballistics were solved about a century ago. The only thing new is what took days and a room full of people and calculators/math tables now takes seconds. -- Jim Pennino === Subject: Bochner's tube theorem On thinking about it more, there is a problem with this proof: http://www.journalarchive.jst.go.jp/jnlpdf.php?cdjournal=pjab1945&cdvol=26&n oissue=7&startpage=21&lang=en&from=jnlabstract The author shows that analytic functions on a cross-shaped tube domain can be extended to its convex hull. And that a domain that contains the convex hull of all crosses contained in it is convex. But when you're extending an analytic function on a domain by finding a cross contained in it and extending the function to the convex hull of the cross - how do you know this doesn't conflict with how the function is already defined? If the part of the domain that intersects the convex hull of the cross isn't connected, could you be on another branch of the function? A cross is two line segments at right angles, that intersect at their midpoints. All points in the line segments have real coordinates, so they're in the real part of the complex n-space. Is there maybe a biholomorphic map from a cross to two line segments intersecting, not at their midpoints? Laura === Subject: Re: Eight inches of snow, <95dc2$49526107$49e5d6b$24786@DIALUPUSA.NET> <6bq4l45nllpit0q8j4rfu51m0j0fuej191@4ax.com> <1825l49498c5niv5p6hjeugmrbjkeoikmh@4ax.com> posting-account=I3BSGAoAAADBa0hVQRltLB3YrdNlBH-l AppleWebKit/525.19 (KHTML, like Gecko) Chrome/1.0.154.36 Safari/525.19,gzip(gfe),gzip(gfe) >Daily rotation gives the Earth its 'tilt' - >http://www.robertreeves.com/star trails sept 18-9 2006 9pm-6am.jpg Nice image, but it has nothing to do with tilt. > Funny,funny,funny ! Rotational orientation (tilt) is a consequence of rotation so here I am now trying to explain the day and night cycle and having to produce time lapse footage.The reference for daily rotation is normally the central Sun and variations in the natural noon cycles which combines both the daily turning of the planet with the slow orbital change to alter the length of each noon cycle but the point here is that daily rotation keeps the Earth pointed in one direction in space and does nothing else - http://www.youtube.com/watch?v=XTTDWhky9HY I see the people from Mensa are included in the newsgroup header so how it comes to be that I am now reduced to explaining how daily rotation is related to the images of star trails and 'rotational orientation (tilt) is remarkable in itself. === Subject: Re: Eight inches of snow, > I see the people from Mensa are included in the newsgroup header so > how it comes to be that I am now reduced to explaining how daily > rotation is related to the images of star trails and 'rotational > orientation (tilt) is remarkable in itself. wreck.org.mensa has few of mensa caliber reading or posting. It's not much different from the make believe scientists posting so frequently to the sci newsgroups. Rather has to do with eternal September, I'm afraid. === Subject: Re: Eight inches of snow, <95dc2$49526107$49e5d6b$24786@DIALUPUSA.NET> <6bq4l45nllpit0q8j4rfu51m0j0fuej191@4ax.com> <1825l49498c5niv5p6hjeugmrbjkeoikmh@4ax.com> posting-account=I3BSGAoAAADBa0hVQRltLB3YrdNlBH-l AppleWebKit/525.19 (KHTML, like Gecko) Chrome/1.0.154.36 Safari/525.19,gzip(gfe),gzip(gfe) >Daily rotation gives the Earth its 'tilt' - >http://www.robertreeves.com/star trails sept 18-9 2006 9pm-6am.jpg Nice image, but it has nothing to do with tilt. >Daily rotation causes the day and night cycle and does nothing else so >the seasonal variartions have to be found elsewhere - try looking at >the orbital specifics of a planet and you will reach a satisfactory >conclusion. Well, that's exactly what everybody is telling you to do. Maybe you > should take your own advice! > Chris L Peterson > Cloudbait Observatoryhttp://www.cloudbait.com Maybe you are answering for 'everyone' but it still remains to be affirmed through direct observation by somebody else that there is a component to orbital motion,specifically a 360 degree turning of a location with respect to the central Sun that replaces the old explanation based on 'axial tilt'.The seasons require two 360 degree motions with respect to the central Sun and intrinsic to the planet itself and that is where the images of Uranus come in - http://astro.berkeley.edu/~imke/Infrared/UranusAo/ur time 2001 2005.jpg Maybe you can set the other Caltechies straight on this major modification for the seasonal daylight/darkness variation explanation but I would look for another institution with enough reknown to recognize what is been done.why it is enjoyable and fascinating first and why it is crucial for climate studies after that.You continue believing 'axial tilt' causes the seasons like a good child where you can do no harm. === Subject: Re: Eight inches of snow, Hey, this is a math discussion group. I haven't read all the posts to this string, so please forgive me if I am restating something already articulated with precision. I see global warming (T or F?) as a very difficult math problem. The global warming hypothesis is (in my opinion) a conjecture that the Earth's average temperature is increasing. That is not a local phenomenon, but in the truest sense a global one. To prove it, we would have to look at an integral, probably approximated by calculating the weighted average of millions of temperature readings simultaneously taken at more or less equally spaced points all over the World (and probably not just of the air). I will leave it up to the statisticians among us to determine how many that would be, and what the timing should be for reliable analysis. That could serve as a dissertation. When it's cold here, it's warmer somewhere else - adiabatic cooling (low pressure) here means compression heating (high pressure) somewhere else. Hell, when it's noon here it's midnight in the Philippines! Come to think of it, weren't there significant climate changes before man as we know ourselves came onto the scene? Weren't there warmer periods between the ice ages? There's a more or less constant number of air molecules, as the sources and sinks have more or less established equilibrium. The same can be said for sources and sinks of energy which would change their average kinetic energy. These include such things as Solar input and radiation back into space, and to lesser extent such things as friction, electrical devices (Joule heating), and endothermic and exothermic chemical reactions that make plastic containers for litter. One can gain information by comparing observable changes on other objects in our solar system. I don't think we can be blamed for reduction in size of the Martian polar icecaps; but also I don't know how to quantify the relationship in an attemtpt to apportion blame between Humankind and God! It is, I think, a problem of extracting very weak signals from very loud noise. The bottom line is that we do not to have the answer to know how, practically, to approach the problem. So, while the Government is in a generous mood, go out and get a huge grant to do the research. I would be interested in the results. === Subject: Re: kung fu mereotopology posting-account=euF15goAAACbw3KIqEWxZHCIPUc2KPmU .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) > First of all, I wonder precisely what word tommy1729 failed > to define, or redefined, in a way that would inspire Tonio > to compare it to redefining 1 as 2 in 1+1 = 3. > The 1 + 1 = 3 and etc. thing was NOT comparing to any definition, or > non-definition, Tommy did in his TST, but was used as a way to show > GALATHAEA's arguments' weakness...nothing to do with Tommy or his TST > at all! But what was galathaea discussing? TST, and MoeBlee's proposed proof of its inconsistency. > **Sigh**...read the whole damn thing again > In particular, the accusation of being focusing on the word set...in > a thread where someone explicitly tried to put forward a set theory of > his own...so ridiculous!! Like me talking of > politicians in a thread about politics: how could one dare?? So now we're in agreement that the person who made a redefinition akin to 1+1 = 3 is galathaea, and the word that she redefined that way is set. But first of all, what is the real definition of the word set, the definition that galathaea changed to suit her own purpose, anyway? The last time I checked, in ZFC, set is a undefined primitive . (Of course, in class theories such as NBG, class is the undefined primitive object, and a set is a class that is an element of another class.) So if tommy1729 has decided that the basic objects of his theory are sets, then no one, neither galathaea nor MoeBlee, can give a definition to the primitive concept of a set. Since you (Tonio) directed me to reread galathaea's post as well, let me do so: but your current tactic moeblee of focusing down on the word set well it's just showing off more of what you do not know because from the polish logicians to modern computer science lesniewski to scott and beyond mereologies have been used as foundations of set theories the use is very common What's going on here? Clearly galathaea and MoeBlee disagree on what a set is. Since we can't define the primitive set, let me take something which can be defined, empty set -- especially since MoeBlee used an empty set in his proposed proof that TST is inconsistent. To MoeBlee, an empty set cannot have any element, not even itself. This is, of course, how empty sets work in standard set theories such as ZFC. In MoeBlee's proof, he shows that tommy1729's x = [x] implies that the empty set does contain itself, [] = [[]], hence a contradiction. Then galathaea argued that in tommy1729's proposed theory, that's not how [] works in the flattened mereology. So MoeBlee countered that tommy1729 insisted that his was a set theory, which allegedly precludes it from having the flattened mereology. Then galathaea disagreed. So MoeBlee then accused her of redefining set to satisfy her own argument, and then Tonio compared her redefinition of set to 1+1 = 3. To galathaea, every set theory has a mereology -- even ZFC, but ZFC's mereology is not the flattened one. To MoeBlee, Tonio, and others, set theory and mereology are distinct concepts, and being a set theory precluding a theory from having mereology, and vice versa. To galathaea and tommy1729, the objects of a theory having flattened mereology may be called sets. To MoeBlee, Tonio, and others, the objects may be called something else, like fusions or heaps, but not sets -- and calling them sets is an arbitrary redefinition akin to 1+1 = 3. To galathaea and tommy1729, an empty object can contain itself (as a part). To MoeBlee, Tonio, and others, the empty set cannot contain itself (as an element), and anyone saying otherwise is an arbitratry redefinition akin to 1+1 = 3. I can go on and on. The Stanford Encyclopedia of Philosophy, which MoeBlee has suggested that I read earlier, does use different symbols and terms for the flattened mereology, such as fusion for set, part for element, bottom for empty set, top for universal set, and so on. To galathaea, these changes are merely cosmetic, and one can call them sets, elements, and empty set if one chooses to do so. To MoeBlee, Tonio, and others, these changes are necessarily to distinguish set theory from mereology. My own opinion? To me, galathaea is more of an expert on mereology than MoeBlee or Tonio, and so if she argues that the changes are cosmetic, than who am I to disagree? Still, I would use the Stanford notation, in order to avoid confusing posters like MoeBlee or Tonio who find the change in notation and terminology to be necessary. Notice that even tommy1729 made a cosmetic change -- replacing the braces {} of standard set theory to the [] of the flattened mereology. This could have alerted MoeBlee that tommy1729 doesn't intend [] to be an object such that no other object, not even [] itself, is part of it -- and if that did not, then galathaea's argument should have. If galathaea and tommy1729 had called [] Bottom, and if they had called it TMT (M = mereology) rather than TST, then MoeBlee might not have proposed what he had written as a proof of its inconsistency. To galathaea, tommy1729 can still call his theory a set theory despite having the flattened mereology. To me, maybe it would be less confusing if he didn't -- but nonetheless, I don't consider it a redefinition of set theory akin to 1+1 = 3. === Subject: Re: kung fu mereotopology posting-account=suWj4AkAAADE1IvGmj55Nmq3f98qb17e 2.0.50727),gzip(gfe),gzip(gfe) > First of all, I wonder precisely what word tommy1729 failed > to define, or redefined, in a way that would inspire Tonio > to compare it to redefining 1 as 2 in 1+1 = 3. > The 1 + 1 = 3 and etc. thing was NOT comparing to any definition, or > non-definition, Tommy did in his TST, but was used as a way to show > GALATHAEA's arguments' weakness...nothing to do with Tommy or his TST > at all! But what was galathaea discussing? TST, and MoeBlee's proposed > proof of its inconsistency. > **Sigh**...read the whole damn thing again > In particular, the accusation of being focusing on the word set...in > a thread where someone explicitly tried to put forward a set theory of > his own...so ridiculous!! Like me talking of > politicians in a thread about politics: how could one dare?? So now we're in agreement that the person who made a > redefinition akin to 1+1 = 3 is galathaea, and the > word that she redefined that way is set. > == No, we are not in agreement. In short, and to stop all this wondering and wandering of yours along all kinds of interpretations of theory and she told Moeblee, in her rather peculiar way, that what standard one that most standard mathematicans use, and that Moeblee was using the narrow definitions and notions that were given to him by authorities and etc., all this, imo, with lots of condescending, patronizing and, again imo, belittling phrases and descriptions. Among OTHER things, Galathaea mentioned the word set. In fact, these are her exact words: and what you see as a set theory is not what all people see as a set theory And from here my reaction. It's not G. defining the word set, is she saying that the above, so she thinks, Tommy meant with his TST. So there is no definition at all belonging to anybody akin to I even meant to insinuate ...can you NOW understand this? > But first of all, what is the real definition of > the word set, the definition that galathaea changed > to suit her own purpose, anyway? The last time I > checked, in ZFC, set is a undefined primitive . (Of > course, in class theories such as NBG, class is the > undefined primitive object, and a set is a class that > is an element of another class.) So if tommy1729 has decided that the basic objects of > his theory are sets, then no one, neither galathaea > nor MoeBlee, can give a definition to the primitive > concept of a set. > == Great! Thanx for clearifying my point: Tommy decided what to call sets to (disclaimer: I don't know whether this is actually true: I'm just assuming it is to go along with you in this), and then nobody can butt into his defining this, right? Unless, of course, someone points out, just as Moeblee did, that that definition, along with other stuff, leads us to a contradiction. > Since you (Tonio) directed me to reread galathaea's > post as well, let me do so: but your current tactic > moeblee > of focusing down on the word set > well > it's just showing off more of what you do not know > because > from the polish logicians to modern computer science > lesniewski to scott and beyond > mereologies have been used as foundations of set theories > the use is very common What's going on here? Clearly galathaea and MoeBlee > disagree on what a set is. > == Apparently so > Since we can't define the primitive set, let me take > something which can be defined, empty set -- especially > since MoeBlee used an empty set in his proposed proof that > TST is inconsistent. To MoeBlee, an empty set cannot have any element, not > even itself. This is, of course, how empty sets work in > standard set theories such as ZFC. In MoeBlee's proof, he > shows that tommy1729's x = [x] implies that the empty set > does contain itself, [] = [[]], hence a contradiction. Then galathaea argued that in tommy1729's proposed theory, > that's not how [] works in the flattened mereology. So > MoeBlee countered that tommy1729 insisted that his was a > set theory, which allegedly precludes it from having the > flattened mereology. > == Ok, this is going just fine: I agree so far! > Then galathaea disagreed. So MoeBlee then accused her of > redefining set to satisfy her own argument, and then Tonio > compared her redefinition of set to 1+1 = 3. == Too bad, we were advancing to nice! Read my first remark above, and please do pay attention to the fact that I do NOT mess at all with Galathaea's definitions, if any at all, but rather with her insistence in telling Moeblee that when he (Moeblee) reads the word set in TST, he's not to understand set as usual, but rather in a misterious, mistifying, foggy and, UNDEFINED (apparently) as far as I can see up to this moment, and unknown way. equation and then B says it is nonsense, then A retorting that for him a first 1 on the left of an equation is to be understood as a 2 because that's the way he likes is not a very intelligent and intellectually honest thing to do, since if for some reason he wants ALL the 1's in the first place of some equation to be read as 2's, then why the heck he did not define EXATLY that from the very beginning?! That is my point in this, and perhaps it was also Moeblee's, though I can't say for sure. To galathaea, every set theory has a mereology -- even ZFC, > but ZFC's mereology is not the flattened one. To MoeBlee, > Tonio, and others, set theory and mereology are distinct > concepts, and being a set theory precluding a theory from > having mereology, and vice versa. > == This is not true. As I alreadys stated before, I know mostly bananas about mereology, and my knowledge in set theory is a basic one. I just can't tell either way since I don't know enough. Period. This is also the reason I didn't mess in all the theoretical debate and consequent brawl, but ONLY in the way of explaining and understanding things: I think that if someone mentions set, we ALL are free to understand that she/he meant the overwhelmingly usual and standard thing, and NOT a new, undefined or ill-defined thing. > To galathaea and tommy1729, the objects of a theory having > flattened mereology may be called sets. To MoeBlee, Tonio, > and others, the objects may be called something else, like > fusions or heaps, but not sets -- and calling them > sets is an arbitrary redefinition akin to 1+1 = 3. > Again: no, and read prior remarks in this post > To galathaea and tommy1729, an empty object can contain > itself (as a part). To MoeBlee, Tonio, and others, the empty > set cannot contain itself (as an element), and anyone saying > otherwise is an arbitratry redefinition akin to 1+1 = 3. > No. Read above > I can go on and on. The Stanford Encyclopedia of Philosophy, > which MoeBlee has suggested that I read earlier, does use > different symbols and terms for the flattened mereology, > such as fusion for set, part for element, bottom > for empty set, top for universal set, and so on. To galathaea, these changes are merely cosmetic, and one can > call them sets, elements, and empty set if one chooses > to do so. To MoeBlee, Tonio, and others, these changes are > necessarily to distinguish set theory from mereology. > If Galathaea REALLY means the above, then I really wouldn't care to go along with this, though I think it may be rather confusing. Anyway, I think things must be crystal clear stated from the beginning to avoid misunderstandings Tonio === Subject: Re: kung fu mereotopology > First of all, I wonder precisely what word tommy1729 failed > to define, or redefined, in a way that would inspire Tonio > to compare it to redefining 1 as 2 in 1+1 = 3. > The 1 + 1 = 3 and etc. thing was NOT comparing to any definition, or > non-definition, Tommy did in his TST, but was used as a way to show > GALATHAEA's arguments' weakness...nothing to do with Tommy or his TST > at all! > But what was galathaea discussing? TST, and MoeBlee's proposed > proof of its inconsistency. > **Sigh**...read the whole damn thing again > In particular, the accusation of being focusing on the word set...in > a thread where someone explicitly tried to put forward a set theory of > his own...so ridiculous!! Like me talking of > politicians in a thread about politics: how could one dare?? > So now we're in agreement that the person who made a > redefinition akin to 1+1 = 3 is galathaea, and the > word that she redefined that way is set. == No, we are not in agreement. In short, and to stop all this > wondering and wandering of yours along all kinds of interpretations of > theory and she told Moeblee, in her rather peculiar way, that what > standard one that most standard mathematicans use, and that > Moeblee was using the narrow definitions and notions that were given > to him by authorities and etc., all this, imo, with lots of > condescending, patronizing and, again imo, belittling phrases and > descriptions. Among OTHER things, Galathaea mentioned the word set. In fact, these > are her exact words: and what you see as a set theory > is not what all people see as a set theory And from here my reaction. It's not G. defining the word set, is she > saying that the above, so she thinks, Tommy meant with his TST. So there is no definition at all belonging to anybody akin to > I even meant to insinuate ...can you NOW understand this? > But first of all, what is the _real_ definition of > the word set, the definition that galathaea changed > to suit her own purpose, anyway? The last time I > checked, in ZFC, set is a undefined _primitive_. (Of > course, in class theories such as NBG, class is the > undefined primitive object, and a set is a class that > is an element of another class.) > So if tommy1729 has decided that the basic objects of > his theory are sets, then no one, neither galathaea > nor MoeBlee, can give a definition to the primitive > concept of a set. == Great! Thanx for clearifying my point: Tommy decided what to call > sets to (disclaimer: I don't know whether this is actually true: I'm > just assuming it is to go along with you in this), and then nobody can > butt into his defining this, right? Unless, of course, someone points > out, just as Moeblee did, that that definition, along with other > stuff, leads us to a contradiction. > Since you (Tonio) directed me to reread galathaea's > post as well, let me do so: > but your current tactic > moeblee > of focusing down on the word set > well > it's just showing off more of what you do not know > because > from the polish logicians to modern computer science > lesniewski to scott and beyond > mereologies have been used as foundations of set theories > the use is very common > What's going on here? Clearly galathaea and MoeBlee > disagree on what a set is. == Apparently so > Since we can't define the primitive set, let me take > something which can be defined, empty set -- especially > since MoeBlee used an empty set in his proposed proof that > TST is inconsistent. > To MoeBlee, an empty set cannot have any element, not > even itself. This is, of course, how empty sets work in > standard set theories such as ZFC. In MoeBlee's proof, he > shows that tommy1729's x = [x] implies that the empty set > does contain itself, [] = [[]], hence a contradiction. > Then galathaea argued that in tommy1729's proposed theory, > that's not how [] works in the flattened mereology. So > MoeBlee countered that tommy1729 insisted that his was a > set theory, which allegedly precludes it from having the > flattened mereology. == Ok, this is going just fine: I agree so far! > Then galathaea disagreed. So MoeBlee then accused her of > redefining set to satisfy her own argument, and then Tonio > compared her redefinition of set to 1+1 = 3. > == Too bad, we were advancing to nice! Read my first remark above, and > please do pay attention to the fact that I do NOT mess at all with > Galathaea's definitions, if any at all, but rather with her insistence > in telling Moeblee that when he (Moeblee) reads the word set in TST, > he's not to understand set as usual, but rather in a misterious, > mistifying, foggy and, UNDEFINED (apparently) as far as I can see up > to this moment, and unknown way. equation and then B says it is nonsense, then A retorting that for him > a first 1 on the left of an equation is to be understood as a 2 > because that's the way he likes is not a very intelligent and > intellectually honest thing to do, since if for some reason he wants > ALL the 1's in the first place of some equation to be read as 2's, > then why the heck he did not define EXATLY that from the very > beginning?! That is my point in this, and perhaps it was also > Moeblee's, though I can't say for sure. > To galathaea, every set theory has a mereology -- even ZFC, > but ZFC's mereology is not the flattened one. To MoeBlee, > Tonio, and others, set theory and mereology are distinct > concepts, and being a set theory precluding a theory from > having mereology, and vice versa. == This is not true. As I alreadys stated before, I know mostly > bananas about mereology, and my knowledge in set theory is a basic > one. I just can't tell either way since I don't know enough. Period. > This is also the reason I didn't mess in all the theoretical debate > and consequent brawl, but ONLY in the way of explaining and > understanding things: I think that if someone mentions set, we ALL are > free to understand that she/he meant the overwhelmingly usual and > standard thing, and NOT a new, undefined or ill-defined thing. > To galathaea and tommy1729, the objects of a theory having > flattened mereology may be called sets. To MoeBlee, Tonio, > and others, the objects may be called something else, like > fusions or heaps, but not sets -- and calling them > sets is an arbitrary redefinition akin to 1+1 = 3. Again: no, and read prior remarks in this post My point of view is that to convey, illustrate, introduce, etc. a new set or collection theory, it would take several pages. Or, at the minimum, the more explanations, the better for the reader of sci.math . This would not be true if the theory is so simple as to be of no use to do analysis or algebra. (BTW.: I wish to add that when I reply in a thread with disagreements, I'm not necessarily disagreeing with what the person to whom I reply is writing.) David Bernier > To galathaea and tommy1729, an empty object can contain > itself (as a part). To MoeBlee, Tonio, and others, the empty > set cannot contain itself (as an element), and anyone saying > otherwise is an arbitratry redefinition akin to 1+1 = 3. No. Read above > I can go on and on. The Stanford Encyclopedia of Philosophy, > which MoeBlee has suggested that I read earlier, does use > different symbols and terms for the flattened mereology, > such as fusion for set, part for element, bottom > for empty set, top for universal set, and so on. > To galathaea, these changes are merely cosmetic, and one can > call them sets, elements, and empty set if one chooses > to do so. To MoeBlee, Tonio, and others, these changes are > necessarily to distinguish set theory from mereology. If Galathaea REALLY means the above, then I really wouldn't care to go > along with this, though I think it may be rather confusing. Anyway, I > think things must be crystal clear stated from the beginning to avoid > misunderstandings Tonio === Subject: Re: JSH: the Twelve Days of Harris > On the 12th day of Harris, Jimmy gave to me: QUESTIONS on Galois, > COMPLEX PLANE factoring, > the DEFINITION of a proof, > PRIME counting functions, > VENGENCE of the Hammer, > SEVEN as a factor, > P equals NP, FIVE...object...rings. A DEAD online journal, > THREE stupid blogs, > a NEW class viewer, > and a proof of F...L...T! I'll drink to that. -- Michael Press === Subject: Re: Carbon footprint questions posting-account=rsfFvAoAAADqHCqmunbjtmaKjfuP-pwP .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; InfoPath.1; .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) > [snips] > I was exploring carbon footprint issues, but then Mona made me clean > up the floor. > Yet, the anomolies remain. For touristic reasons, the Great Pyramid at > Giza > is the burial Chamber of an Egyptian King... . really? Read 'Dark > Mission: The Secret History of Nasa'. Try Anthony West - for a > somewhat better understanding of its history. God - so much to read, so little time. For sure: I gave up TV to for a bit - just to catch up with the books I'd bought, and hope to finish them before 2009, given Xmas reading. I am at it now, though booked out to go visiting on Boxing Day! IF, I stress IF, there is veridical evidence for OBE or NDE experiences outside one's body, then we shall need a theory of knowledge to account for it. Unfortunately, we seem to have only recent systematic data gathering and analysis in support of such an idea. On the other hand, we have means of recording experience unknown to our recent ancestors. IF, I stress IF, there is testable evidence for blind persons experiencing vision outside of their, not necessarily, dead bodies, then the epistemological role of one's body is called into question. Maybe bodies are like tools! Below, I comment on another view. -- foolsrushin. **************************************************************************** ************* d2ec- > (1) When people are technically dead, they often see their emergency > team operating on them and looking down on the team from up above > them, and can later describe the operation and remember some of the > words of the team. What senile bullcrap is this?!? (i) Your 'technically dead' merely refers (ineptly) to a useful medico- legal notion: its relevance to what 'absolutely and finally dead' might actually be is undefined (and all that is quite apart from the problems of making a correct diagnosis in difficult circumstances). Only an idiot would think otherwise. Doubters include a cousin, a doctor on my mother's side, who heard a number of NDE stories. (ii) 'People can remember stuff said in their presence' is far from being a world-shaking discovery, and only an idiot would think otherwise. *Good point, yet they often recall the operation being conducted upon them. (iii) A report of 'looking down on the team from above and describing an operation' is, for various reasons, not world-shaking either, and only an idiot would think otherwise. What *would* be world-shaking would be for someone in that alleged state *to read and report a message written on the top of a cupboard*. Get back to us when someone has. KF. Think: d2ec- > (1) When people are technically dead, they often see their emergency > team operating on them and looking down on the team from up above > them, and can later describe the operation and remember some of the > words of the team. What senile bullcrap is this?!? (i) Your 'technically dead' merely refers (ineptly) to a useful medico- legal notion: its relevance to what 'absolutely and finally dead' might actually be is undefined (and all that is quite apart from the problems of making a correct diagnosis in difficult circumstances). Only an idiot would think otherwise. (ii) 'People can remember stuff said in their presence' is far from being a world-shaking discovery, and only an idiot would think otherwise. (iii) A report of 'looking down on the team from above and describing an operation' is, for various reasons, not world-shaking either, and only an idiot would think otherwise. What *would* be world-shaking would be for someone in that alleged state *to read and report a message written on the top of a cupboard*. Get back to us when someone has. That is only true, I think you probably know, because surgeons and others became startled when patients, etc. reported seeing operations upon themselves. d2ec- > (1) When people are technically dead, they often see their emergency > team operating on them and looking down on the team from up above > them, and can later describe the operation and remember some of the > words of the team. Listen, mate, it happens all the time. . === Subject: Re: Sum to Infinity of a Geometric Progression > Suppose you have a function double powrep(r, k) > { > if (k == 1) return r; > if (k == 0) return 0; > return powrep(r, k - 1)*r; } > If you are a programmer you shouldn't have any problem with it as it is the > same thing as recursive functions only if you could carry out the recursive > and infinity number of times. That's written iteratively as: double r = 0.5; double answer = 0.5; for (long long k = 1; k++) { ....answer *= r; } isn't it? > k > ln(e)/ln(r) = log[r](e) (since 0 <= r < 1 k is positive assuming e is > small enough(e <= 1)) Could you explain what ln(e) means? I haven't encountered this yet. === Subject: Re: Sum to Infinity of a Geometric Progression > Suppose you have a function double powrep(r, k) > { > if (k == 1) return r; > if (k == 0) return 0; > return powrep(r, k - 1)*r; } > If you are a programmer you shouldn't have any problem with it as it is > the > same thing as recursive functions only if you could carry out the > recursive > and infinity number of times. That's written iteratively as: double r = 0.5; double answer = 0.5; for (long long k = 1; k++) { ....answer *= r; } isn't it? -------- yes, or just use pow which works for real exponents. > k > ln(e)/ln(r) = log[r](e) (since 0 <= r < 1 k is positive assuming e is > small enough(e <= 1)) Could you explain what ln(e) means? I haven't encountered this yet. --------- ln(e) means the natural logorithm(sometimes written log but log usually means base 10) basically if you have e^x = y and y is known, then what is x? well, ln is the function that returns the value of x. take ln of both sides(it is a function so it operates on the values) i.e. ln(e^x) and ln(y) must be the same since y is the same as e^x (BTW, e is a real number 2.7.... which is very special. It like Pi) or ln(e^x) = ln(y) but ln(e^x) is special in that it is just x. (it was created to do just that so e^x = y is the same as x = ln(y) the first is used if you don't know y and the second if you don't know x. but we can also have stuff like 10^x = y or 2^x = y the 10, 2 and e are called the base so you have log[base] and ln = log[e] it turns out that we can change from one base to any other quite easily. You need to realize that a large part of mathematics(and science in general) is trying to understand how to undo something that has been done. A procedure(or function) is applied to some input but we only have the output and the procedure and not the input... but we need the input for some reason. So we find another procedure that undo's the original... we call it the inverse function. So if f is a function/procedure and operates on x then we have f(x) which is the output(we might call it y and say y = f(x)). But suppose we just know y and f but not x, how can we get x? if f has an inverse, which we call f^(-1) then we can do f^(-1)(y) = f^(-1)(f(x)) but f^(-1) undo's what f does to x so we have f^(-1)(y) = x. Example: 3 = x^2 what is x? well, we take the sqrt of both sides! sqrt(3) = sqrt(x^2) but sqrt undo's the square. (think of it as undosquare(square(x)) so we have sqrt(3) = x and you can verify that 3 = (sqrt(3))^2 (this step is called a check since I got an x value and I plugged it back into the original equation to see if I got a true statement. If I didn't then something went wrong). Computer programming is very similar to mathematics and has many of the same abstract concepts. Mathematical functions are the same as computer algorithms but they are written using a different syntax and tend to be used a bit differently. Once you start thinking abstractly then it will all make sense. === Subject: The three magi and the religious proof of relativity. G_uv = GOD. See George Hammond. This is PHYSICS, not math or logic, and proof is completely irrelevant. See Tom Roberts. The speed of light from A to B is c-v, the speed of light from B to A is c+v, the time each way is the same. See Albert Einstein. ing nutters all. === Subject: Re: The three magi and the religious proof of relativity. reply-type=response > G_uv = GOD. > See George Hammond. This is PHYSICS, not math or logic, and proof is completely irrelevant. > See Tom Roberts. The speed of light from A to B is c-v, > the speed of light from B to A is c+v, > the time each way is the same. > See Albert Einstein. > See Albert Einstein to see what crap this statement is? === Subject: Re: The three magi and the religious proof of relativity. posting-account=Mjsi2gkAAAAWAGBcu6ms7lNq9TReSXcF Gecko/2008120122 Firefox/3.0.5,gzip(gfe),gzip(gfe) On Dec 24, 9:15pm, Peter Webb > G uv = GOD. > See George Hammond. > This is PHYSICS, not math or logic, and proof is completely irrelevant. > See Tom Roberts. > The speed of light from A to B is c-v, > the speed of light from B to A is c+v, > the time each way is the same. > See Albert Einstein. See Albert Einstein to see what crap this statement is? At testament to the brilliance of Einstein is how severely he vexes the extremely stupid. === Subject: Re: The three magi and the religious proof of relativity. > G uv = GOD. > See George Hammond. This is PHYSICS, not math or logic, and proof is completely irrelevant. > See Tom Roberts. The speed of light from A to B is c-v, > the speed of light from B to A is c+v, > the time each way is the same. > See Albert Einstein. ing nutters all. But, that's also true in Galilean transformations. Which is why the smarter people invented mid-points for both of them. Since they're both just a wank study in the conservation of linear momentum. === Subject: Re: The three magi and the religious proof of relativity. posting-account=2APXugoAAADkRMUHSY1XvGUVMY2N3xOK Gecko/20080410 SUSE/2.0.0.14-2.3 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) > G_uv = GOD. > See George Hammond. This is PHYSICS, not math or logic, and proof is completely irrelevant. > See Tom Roberts. The speed of light from A to B is c-v, > the speed of light from B to A is c+v, > the time each way is the same. > See Albert Einstein. ing nutters all. In your opinion, what compels the scientific community - an intellectual 'cream' of humanity'- to keep blindly following such 'nutters', like a herd of sheep? === Subject: Re: The three magi and the religious proof of relativity. > G_uv = GOD. > See George Hammond. > This is PHYSICS, not math or logic, and proof is completely irrelevant. > See Tom Roberts. > The speed of light from A to B is c-v, > the speed of light from B to A is c+v, > the time each way is the same. > See Albert Einstein. > ing nutters all. In your opinion, what compels the scientific community - an > intellectual 'cream' of humanity'- to keep blindly following such > 'nutters', like a herd of sheep? In my opinion the scientific community consists of engineers, biochemists, chemists, biologists, geologists and medical professionals (my apologies to any specialist groups such as geneticists I've overlooked), and doesn't include mathematicians (who are intellectual artists) or theoretical physicists who are fruit cakes. In your opinion, what compels you to believe theoretical physicists are the intellectual 'cream' of the scientific community - and to keep blindly following such propaganda like a flock of Hawking wheel chairs chased by paparazzi? === Subject: Re: The three magi and the religious proof of relativity. > This is PHYSICS, not math or logic, and proof is completely irrelevant. > See Tom Roberts. > The speed of light from A to B is c-v, > the speed of light from B to A is c+v, > the time each way is the same. > See Albert Einstein. > ing nutters all. > In your opinion, what compels the scientific community - an > intellectual 'cream' of humanity'- to keep blindly following such > 'nutters', like a herd of sheep? In my opinion the scientific community consists of engineers, biochemists, > chemists, biologists, geologists and medical professionals (my apologies to > any specialist groups such as geneticists I've overlooked), and doesn't > include mathematicians (who are intellectual artists) or theoretical > physicists > who are fruit cakes. In your opinion, what compels you to believe theoretical physicists > are the intellectual 'cream' of the scientific community - and to keep > blindly following such propaganda like a flock of Hawking wheel chairs > chased by paparazzi? In my opinion, theoretical physicists are 'required' to be mathematicians, engineers and philosophers, 'all-in-one', scientists. I expect them to be the intellectual 'cream' of the scientific community because they are 'supposed' to be engaged in front-line fundamental research to explore the unknown and to unravel the mysteries of Nature. To err is human. Even if some of the assumptions or postulates of Albert Einstein are eventually proved to be wrong, it should not diminish his greatness. The turmoil in current scientific thought is a part of the evolution process. If someone is to be held to blame for the current mess in fundamental physics, it must be the 'blind followers', who, under the influence of excessive indoctrination, are unable to keep an open mind for the dissenting opinion. === Subject: Re: The three magi and the religious proof of relativity. > G_uv = GOD. > See George Hammond. > This is PHYSICS, not math or logic, and proof is completely > irrelevant. > See Tom Roberts. > The speed of light from A to B is c-v, > the speed of light from B to A is c+v, > the time each way is the same. > See Albert Einstein. > ing nutters all. > In your opinion, what compels the scientific community - an > intellectual 'cream' of humanity'- to keep blindly following such > 'nutters', like a herd of sheep? > In my opinion the scientific community consists of engineers, > biochemists, > chemists, biologists, geologists and medical professionals (my apologies > to > any specialist groups such as geneticists I've overlooked), and doesn't > include mathematicians (who are intellectual artists) or theoretical > physicists > who are fruit cakes. > In your opinion, what compels you to believe theoretical physicists > are the intellectual 'cream' of the scientific community - and to keep > blindly following such propaganda like a flock of Hawking wheel chairs > chased by paparazzi? In my opinion, theoretical physicists are 'required' to be > mathematicians, engineers and philosophers, 'all-in-one', scientists. > I expect them to be the intellectual 'cream' of the scientific > community because they are 'supposed' to be engaged in front-line > fundamental research to explore the unknown and to unravel the > mysteries of Nature. To err is human. Even if some of the assumptions or postulates of > Albert Einstein are eventually proved to be wrong, it should not > diminish his greatness. The turmoil in current scientific thought is a > part of the evolution process. If someone is to be held to blame for > the current mess in fundamental physics, it must be the 'blind > followers', who, under the influence of excessive indoctrination, are > unable to keep an open mind for the dissenting opinion. You humanly erred to answer my question. In your opinion, what compels *YOU* to believe theoretical physicists are the intellectual 'cream' of the scientific community - and to keep blindly following such propaganda like a flock of Hawking wheel chairs chased by paparazzi? And what do you mean by eventually proved to be wrong? Ref: http://www.fourmilab.ch/etexts/einstein/specrel/www/figures/img22.gif What kind of lunacy prompted Einstein to say the speed of light from A to B is c-v, the speed of light from B to A is c+v, the time each way is the same? Your answer goes here: ________________________________________________________ Other answers have been: According to the illiterate crank Peter Webb Its two equations. ________________________________________________________ According to the novice mitch sperkins@gmail.com (or mitchs perkins) ________________________________________________________ According to the Pillock Shawn Pollock (aka mathkills): Mikelzon Morrly, whatever. What Einstein does is basically modify Galilean relativity as follows X'=A(X-vt) yes you [Androcles] are an ass (presumably because I asked the question) ________________________________________________________ According to glird the tord: Both x and x' are in the domain of the function x |-> x' such that x' = ________________________________________________________ According to Idiot Ian Parker: We are not talking about the speed of light here we are talking classical stability theory. ________________________________________________________ According to Cretin harald.vanlintelButNotThis@epfl.ch Easy: he did NOT say that. According to cretin van lintel, Einstein did not write the equation he ________________________________________________________ According to xxein (not a true dingleberry): It is an artefactual/superficially imposed yin-yang of sorts. ________________________________________________________ According to Lamenting Shubert: Why do you want to know? ________________________________________________________ According to Imbecile Jimmy Black: In neither system (meaning frame of reference in modern-day terminology) is the speed of light c-v or c+v. In both systems the speed of light is c. According to Imbecile Jimmy Black, Einstein did not write the equation he ________________________________________________________ According to Cretin Dork Bruere ________________________________________________________ According to Lying Little Matthew Johnson And even the question is wrong! For he never said any such thing. This should be painfully obvious from what he _did_ say, namely, that the vacuum speed of light is a constant of nature, invariant under all admissable [sic] transformations between inertial reference frames. Apparently LLS Matthew Johnson has rewritten Einstein's paper. A team of scientists working under the direction of researchers from the University of Sussex have recently discovered that Einstein did not say inertial. According to LLS Matthew Johnson, Einstein did not write the equation he ________________________________________________________ According to Chief Wanker Uncle Stooopid Schwartz: c+v appears nowhere in the paper, nor could it. [sic] According to Chief Wanker Uncle Stooopid, Einstein did not write the ________________________________________________________ According to Dolt Spirit of Truth that math is correct but WRONG ________________________________________________________ Note: some names may be the aliases of a crank or cranks unknown. Further note: If Einstein/Mary-the-virgin had made his/her stupid claim on Usenet today, those very same cretins would be laughing uproariously. To err is chimpanzee. === Subject: Re: The three magi and the religious proof of relativity. posting-account=pwwnPQoAAAAIML5jwPIm9bxDc_8F50uT CLR 1.1.4322),gzip(gfe),gzip(gfe) > G uv = GOD. > See George Hammond. > This is PHYSICS, not math or logic, and proof is completely irrelevant. > See Tom Roberts. > The speed of light from A to B is c-v, > the speed of light from B to A is c+v, > the time each way is the same. > See Albert Einstein. > ing nutters all. > In your opinion, what compels the scientific community - an > intellectual 'cream' of humanity'- to keep blindly following such > 'nutters', like a herd of sheep? In my opinion the scientific community consists of engineers, biochemists, > chemists, biologists, geologists and medical professionals (my apologies to > any specialist groups such as geneticists I've overlooked), and doesn't > include mathematicians (who are intellectual artists) or theoretical > physicists > who are fruit cakes. In your opinion, what compels you to believe theoretical physicists > are the intellectual 'cream' of the scientific community - and to keep > blindly following such propaganda like a flock of Hawking wheel chairs > chased by paparazzi?- [Micro].9eÀå .81¯.bd.bc®¨ .bc.9e±.89±.89 - - [Micro].9eÀå .81¯.bd.bc®¨ .bcü±.89 - Emperical results have a some minimal quality, Only a small of those are important. When I read a journal of mathematical physcis. does not contain experimental result. In some aspect, Androcles is right. But Androcles' comments about theoritical science is only those of prosecutor. Prosecutor can not a judge. Androcles's viewpoint on science is narrow minded. === Subject: Re: The three magi and the religious proof of relativity. posting-account=rsfFvAoAAADqHCqmunbjtmaKjfuP-pwP .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; InfoPath.1; .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) > G_uv = GOD. > See George Hammond. > This is PHYSICS, not math or logic, and proof is completely irrelevant. > See Tom Roberts. > The speed of light from A to B is c-v, > the speed of light from B to A is c+v, > the time each way is the same. > See Albert Einstein. > ing nutters all. > In your opinion, what compels the scientific community - an > intellectual 'cream' of humanity'- to keep blindly following such > 'nutters', like a herd of sheep? In my opinion the scientific community consists of engineers, biochemists, > chemists, biologists, geologists and medical professionals (my apologies to > any specialist groups such as geneticists I've overlooked), and doesn't > include mathematicians (who are intellectual artists) or theoretical > physicists > who are fruit cakes. In your opinion, what compels you to believe theoretical > physicists are the intellectual 'cream' of the scientific > community - and to keep blindly following such propaganda like a > flock of Hawking wheel chairschased by paparazzi? Despite all our efforts proof is only relevant where it leads to empirically testable propositions capable in principle of being falsfied - or on the other hand, propositions that are not self- cotradictiory *and* true by definition. This leaves, in either case, a huge pile of propositions that may be satisfyingly true in Harry Potter Land, Line Land, etc. Merry Xmas and have a bountiful New Year, -- foolsrushin. === Subject: Re: Can someone help me with this permutation problem? > Here is a program in Python ... can run on > Mac, Linux, Windows, RISCOS, etc. > Wow, that totally rocks! Python is cool, and made me fall in love with programming again. It's simple, clean, and easy to write code. Using gmpy is also easy to do some very high-level stuff. I'm only just finding some of the library material available, and it's making my life a lot easier. > You made it look so easy! It's actually a simple problem when you have a language that supports lists, loops, co-routines, and other stuff like that, without syntactic noise getting in the way. > Of course, now I have to learn Python It will be worth it. === Subject: Proof that a Number is a Multiple of 3 If the Sum Of Its Digits in Decimal Notation Is a Multiple Of 3 posting-account=p0RNeQkAAAAfw70s8101WjGLhJhBEHo8 Gecko/2008120122 Firefox/3.0.5,gzip(gfe),gzip(gfe) What is the proof that if a the sum of the digits of a number's decimal representation is a multiple of 3, then the number is a multiple of 3? Michael === Subject: Re: Proof that a Number is a Multiple of 3 If the Sum Of Its Digits in Decimal Notation Is a Multiple Of 3 > What is the proof that if a the sum of the digits of a number's > decimal representation is a multiple of 3, then the number is a > multiple of 3? 10 == 1 mod 3, so sum_{j=0}^n a_j 10^j == sum_{j=0}^n a_j mod 3. Or mod 9, for that matter. -- Robert Israel israel@math.MyUniversitysInitials.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada === === Subject: JSH: No need for Galois theory posting-account=1lE9SQkAAADFrJsDv61dh1YXcJ_ahy5I > where the a's are roots of a^2 - (7x-1)a + (49x^2 - 14x) = 0 > Then, if x is such that the quadratic is irreducible over the rationals, then either both roots or neither root is divisible by 7. You don't need the Galois sledgehammer to crack this walnut. Let x be such that the quadaratic is irreducible over the rationals and let a_1(x) and a_2(x) be the two roots. Then looking at the quadratic formula, we see that a_1(x) = d(x) + e(x) where d(x) is rational and e(x) is irrational or complex and that a_2(x) = d(x) - e(x). If a_1(x) is divisible by 7 then so is d(x) and e(x) and therefore a_2(x). So your claim that for all x, a_1(x) is divisible by 7 and a_2(x) is coprime to 7, breaks not only Galois theory but simple algebra. - William Hughes For extra credit identify where this proof breaks down if x is such that the quadratic is reducible over the rationals. Hint: look at e(x) is irrational or complex === Subject: Re: JSH: Was never a factor argument posting-account=wVv_VwoAAAAVTfUuyxLzug5SzYWCgHj1 5.1),gzip(gfe),gzip(gfe) > [JSH, spouting the usual JSH gibberish] > ... > [marcus bruck...@yahoo.com] > ... > It is NOT the case that the 7 can be distributed in only > one way across the two factors. You can deny that this > was your underlying goal, but clearly it was. Otherwise > you were just raving on about an utter trivial banality. > But even you are not that dumb. > I'm not sure about that. Give yourself a Christmas present :-) I > believe I replied to James a grand total of two times in 2008. In both > cases I simply presented 1-digit integer counterexamples to the goofy > claims he was making on those days. No arguments, no followups, no > attempts to reason with him. > And I learned something ;-) When arguing with him in previous years, I > made extraordinary efforts to try to make /any/ kind of coherent sense > out of the endless gibberish he spouted. But I now believe that, in > most cases, the sense I believed I found was my own construction, not > without twisting your head up your ass fifty different ways to try to > give him the benefit of the doubt, he really does appear to be that > dumb (at least when it concerns mathematics, in which he is profoundly > incompetent). > You had an ulterior motive. > False dichotomy there -- it's possible that he's both that dumb and > wallowing in ulterior motives. But, in this case, I think it more > likely that he doesn't understand the distinction you believe is dead > obvious here: that he believes his endlessly repeated > 7*(x^2 + 3x + 2) = (7x + 7)*(x + 2), > I agree with that view, Tim. > I think James may be mixed up by what = means in math . > When using a calculator, pressing the = sign gives > the answer. So James could be thinking that > 7*(x^2 + 3x + 2) has *two* possible answers: > either > 7(x+1)(x+2) = (7x + 7)*(x+2) [Answer 1] > or > 7(x+1)(x+2) = (x + 1)*(7x + 14) [Answer 2] ; Nope. There are an INFINITY of ways to factor 7(x^2 + 3x + 2) on the > complex plane. And ONE of those ways is 7(x^2 + 3x + 2) = (7x + 7)(x + 2). > Are all of infinitely many ways equally valid? > but, to him, you choose one answer or the other, > but not both, because that's all about the > distributive property, which of course he thinks he > understands. I'm consistently saying the same thing. > True. You are saying nothing, and trying to conclude something from it. > You and posters like you are making things up. > The = in math can be subtle [for A.I. purposes]. And I remind other readers who think it is about me. Clearly it's > not. Given 7(x^2 + 3x + 2) = (7x + 7)(x + 2) you are looking at one factorization out of infinity, but it is a > valid factorization, which does not shift dependent on the value of x. > What does valid mean? Are you saying that nonconstant factorizations are not valid? Why is that? Do you have a secret definition of valid? What is it? Do you have a secret proof that nonconstant factorizations are not valid? > So 7x + 7 = 7(x+1), or to give the distributive property the > straightforward way: 7(x+1) = 7x + 7, and it doesn't change dependent > on the value of x. > Is that forbidden? Why? > That is trivial algebra!!! > So far. But evidently something more than algebra. You appear to be ruling out nonconstant factorizations. Why ? Is there something wrong with them? Are they not valid ? Can you define valid? And then prove somehow that nonconstant factorizations are not valid ? > What happens though if you follow mathematical logic is that now with 7*(175x^2 - 15x + 2) = (5a 1(x) + 7)(5a 2(x)+ 7) where the a's are roots of a^2 - (7x-1)a + (49x^2 - 14x) = 0 you get a weird situation if you normalize with a 1(x) = b 1(x), and a 2(x) = b 2(x) - 1, as then you have 7*(175x^2 - 15x + 2) = (5b 1(x) + 7)(5b 2(x)+ 2) where b 1(0) = 0, b 2(0) = 0, which is in key respects exactly like 7(x^2 + 3x + 2) = (7x + 7)(x+2) > There are a lot of differences, and they are not trivial. In the 7x + 7 case, x is the polynomial variable. In the other case, 5b 1(x) is not even a polynomial function. Besides which, you are not factoring 7*(175x^2 - 15 x + 2) as a polynomial in x. You are factoring it as a polynomial in 5. The two situations are not parallel, or even close. You cannot generalize from the simplistic 7x + 7 thing to the more complex case. > and it represents ONE factorization out of an infinite number of ways > to factor: 7*(175x^2 - 15x + 2). So what's different then? Well, in one case you have 7x--a linear > function. In the other you have b 1(x), a non-linear function defined in a > fairly clever way using what I call a quadratic generator. > The fact that they have x in common is not enough. They are not even the same kinds of function. > Ergo, No. You say ergo only when what you are about to say is preceded by logical argument. That is far from the case here. > the argument then is over whether or not a*(f(x) + b) = a*f(x) + > a*b varies because of the ***function*** as there is no argument that > given 7(x^2 + 3x + 2) = (7x + 7)(x+2) > There IS an argument. You yourself just said there were infinitely many ways to factor 7(x^2 + 3x + 2) in the complex plane. You give no reason for selecting only one of those factorizations. Just your own preference? You give no reason for rejecting nonconstant factorizations. You imply they are not valid but you have no definition of valid, and no proof. Arguing by analogy cannot work here, because you have nothing on the easier side of the analogy, and the analogy is not even close anyway. Just some vague feeling, probably based on factorization-by-inspection. > it's ludicrous to claim that x=0 is different from x=1, or x equal any > other value. > Ludicrous is not a logical argument, not mathematics. I don't want ludicrous. I want RIGOROUS. You don't have it. > So mathematical logic is firmly on my side, and it IS a case of people > arguing against the distributive property, but of course, that is > clearly nonsensical so they misrepresent what they are doing. > No. You do NOT have logic on your side; just emotion, and ludicrous. Answer the questions above, give a rigorous proof rather than a hand-waving analogy which has no effect anyway since you have no proof for the simpler side of the analogy. > What is more interesting though are those of you who may be > confused!!! > Ah, the appeal to the Grandstand. All those innocent little undergrads out there. Maybe you can fool a few of them. How about answering some specific questions? 1. What is special about the factorization 7*(x^2 + 3x + 2) = (7x + 7)*(x + 2) in the complex plane? Is it better in some way than 7*(x^2 + 3x + 2) = (a(x)*x + a(x))*(b(x)*x + 2b(x)), where a(x) and b(x) are functions of x whose product is 7? For example, a(x) = 7/(1 + exp(x)), b(x) = 1 + exp(x) Does this nonconstant factorization violate the distributive property in some way? Can you PROVE that it does? Is this nonconstant factorization not valid? What do you mean when you say valid? What is the rigorous definition? Can you PROVE the nonconstant factorization is not valid ? Have you given such a proof? Where? 2. First you factor in the complex numbers. Then you want to jump to conclusions in the ring of algebraic integers. Is every theorem that is true in the complex plane also true in every subring of the complex plane? Can you prove that? If not, how do you transition from the complex plane to subrings of it? Stop shoveling smoke or whatever it is you are shoveling and give some definite answers! Marcus. === Subject: Re: JSH: Was never a factor argument days. My association with the Department is that of an alumnus. >Heh. This raises the question of which is the simplest explanation. The smallest explanation that has no proper nontrivial normal subexplanations, of course. -- It's not denial. I'm just very selective about what I accept as reality. --- Calvin (Calvin and Hobbes by Bill Watterson) Arturo Magidin magidin-at-member-ams-org === Subject: Re: JSH: Was never a factor argument >Did he ? Was he not able to pick it somewhere ? In theory he could have. However given his reluctance to study any formal mathematics at all, it seems to be unlikely. He probably did arrive at the result on his own. His mathematical background is very patchy. rossum === Subject: Re: More tetration posting-account=-gYNIQoAAAD-MKGbMY_-Jpj1EqcOgRWx 3.0.2; .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) > Something that occurred to me in an idle moment... It seems to me that for a reasonable definition of iterated > exponentiation we ought to have exp^n(x) real for all real x and > nonnegative real n. Let z = -3*pi*i/2, then exp(z) = i. As n moves from 0 to 1, I'd expect > the plot of exp^n(z) on the complex plane to be a continuous line from > (0, -3*pi/2) to (0, 1), which means that for at least one value of n > in this range, say n = m, exp^m(z) must be real. Therefore, by the > initial assumption, exp^(1 - m)(exp^m(z)) must also be real. However, > exp^(1 - m)(exp^m(z)) = exp(z), which is not real. Is there any way to > resolve this? Is it possible that exp^n(z) has to go off to infinity > in the range 0 < n < 1? OK, let's look at a simpler example, say f(x) = x^3, so f^n(x) = x^ (3^n). We have, say, f(-2i) = 8i, so there ought to be at least one value of n between 0 and 1, say n = m, such that f^m(-2i) is real. In fact, here we can choose m = log(4)/log(3) - 1 and f^m(-2i) = 2^(4/3), so the expected real value of f^(1 - m)(f^m(-2i)) is (2^(4/3))^(3^(1 - m)) = 8. On the other hand, we also expect f^(1 - m)(f^m(-2i)) = f (-2i) = 8i. This seems to resolve itself through the fact that x^(3^n) is many- valued for non-integer n. One of the values of f^(1 - m)(f^m(-2i)) is indeed 8i, and another is indeed 8, so it all comes out OK provided you choose the right values at each stage. I'm wondering if the same principles apply to exp^n(x) in the complex realm -- in other words, it logically has to be many-valued for non- integer n. I guess this isn't so hard to believe; after all, we know it must be many-valued for negative integer n... === Subject: Re: More tetration posting-account=-gYNIQoAAAD-MKGbMY_-Jpj1EqcOgRWx 3.0.2; .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) > Something that occurred to me in an idle moment... > It seems to me that for a reasonable definition of iterated > exponentiation we ought to have exp^n(x) real for all real x and > nonnegative real n. > Let z = -3*pi*i/2, then exp(z) = i. As n moves from 0 to 1, I'd expect > the plot of exp^n(z) on the complex plane to be a continuous line from > (0, -3*pi/2) to (0, 1), which means that for at least one value of n > in this range, say n = m, exp^m(z) must be real. Therefore, by the > initial assumption, exp^(1 - m)(exp^m(z)) must also be real. Where do you get this from, exactly? How does the initial assumption > lead to this? The initial assumption is that exp^n(x) is real for all real x and nonnegative real n. In the case of exp^(1 - m)(exp^m(z)), we have x = exp^m(z), which is real, and n = 1 - m, which is nonnegative and real. Therefore exp^(1 - m)(exp^m(z)) is real. > However, exp^(1 - m)(exp^m(z)) = exp(z), which is not real. Is there any way to > resolve this? Is it possible that exp^n(z) has to go off to infinity > in the range 0 < n < 1?- Hide quoted text - - Show quoted text - === Subject: Re: More tetration Am 24.12.2008 03:21 schrieb Matt: > Something that occurred to me in an idle moment... It seems to me that for a reasonable definition of iterated > exponentiation we ought to have exp^n(x) real for all real x and > nonnegative real n. Let z = -3*pi*i/2, then exp(z) = i. As n moves from 0 to 1, I'd expect > the plot of exp^n(z) on the complex plane to be a continuous line from > (0, -3*pi/2) to (0, 1), which means that for at least one value of n > in this range, say n = m, exp^m(z) must be real. Ok, I see... > Therefore, by the > initial assumption, which one? > exp^(1 - m)(exp^m(z)) must also be real. ???? > However, > exp^(1 - m)(exp^m(z)) = exp(z), which is not real. Is there any way to > resolve this? Is it possible that exp^n(z) has to go off to infinity > in the range 0 < n < 1? Hmm, I didn't understand this where my question marks are. However I like the idea of filling up a compilation of interesting valid conclusions about tetration. What comes into mind is the fact, that in my diagonalization approach the powerseries for bases b>exp(exp(-1)) have complex coefficients. I was unable to derive whether/that their value for some real x and real heights should come out to be real. (not to mention a *continuous interval* of real values for the height-parameter)... Gottfried -- --- Gottfried Helms, Kassel === Subject: Re: More tetration posting-account=-gYNIQoAAAD-MKGbMY_-Jpj1EqcOgRWx 3.0.2; .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) > Am 24.12.2008 03:21 schrieb Matt: > Something that occurred to me in an idle moment... > It seems to me that for a reasonable definition of iterated > exponentiation we ought to have exp^n(x) real for all real x and > nonnegative real n. > Let z = -3*pi*i/2, then exp(z) = i. As n moves from 0 to 1, I'd expect > the plot of exp^n(z) on the complex plane to be a continuous line from > (0, -3*pi/2) to (0, 1), which means that for at least one value of n > in this range, say n = m, exp^m(z) must be real. Ok, I see... > Therefore, by the > initial assumption, which one? > exp^(1 - m)(exp^m(z)) must also be real. ???? > However, > exp^(1 - m)(exp^m(z)) = exp(z), which is not real. Is there any way to > resolve this? Is it possible that exp^n(z) has to go off to infinity > in the range 0 < n < 1? Hmm, I didn't understand this where my question marks are. Hmmm... mike3 asked the same; see my reply to him. === Subject: Mach Projectile This introduces some of the math involved in predicting where a bullet will hit before it gets there. Three microphones on a helicopter pick up the conical shock wave. http://mypeoplepc.com/members/jon8338/math/id21.html === Subject: Re: Mach Projectile posting-account=c6T4LggAAACAqdk8Zx_zXI_oErOujh3M Gecko/20050915 Firefox/1.0.7,gzip(gfe),gzip(gfe) > This introduces some of the math involved in predicting where a bullet will > hit before it gets there. Three microphones on a helicopter pick up the > conical shock wave. http://mypeoplepc.com/members/jon8338/math/id21.html Man, with your brains, you could do some serious ultrasound engineering, for medical scanning. Ken === Subject: Re: Mach Projectile posting-account=42V-qwoAAABOAKkANAhMmpW4F3ZbRLXb Gecko/2008120122 Firefox/3.0.5,gzip(gfe),gzip(gfe) > This introduces some of the math involved in predicting where a bullet will > hit before it gets there. Three microphones on a helicopter pick up the > conical shock wave. http://mypeoplepc.com/members/jon8338/math/id21.html That's cute, but actual military application of this idea is used to retrodict the position of the gun that fired the shot. Mark L. Fergerson === Subject: Re: Mach Projectile > This introduces some of the math involved in predicting where a bullet will > hit before it gets there. Three microphones on a helicopter pick up the > conical shock wave. http://mypeoplepc.com/members/jon8338/math/id21.html Gun ballistics were solved about a century ago. The only thing new is what took days and a room full of people and calculators/math tables now takes seconds. -- Jim Pennino === Subject: Re: General Relativity and the New Age Religion posting-account=rsfFvAoAAADqHCqmunbjtmaKjfuP-pwP .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; InfoPath.1; .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) > GOD = G_uv > Therefore your suspicion that > there is a relation between > RELATIVITY and RELIGION > is PROVEN TO BE ENTIRELY CORRECT. It is certainly true that you have properly identified the god of > religious relativists. And there is no doubt that your god is the god > that religious relativists worship. But you haven't proven anything. Please try to understand that you have merely defined your god > according to your demonic craving for a pantheistic religion. Shubeehttp://www.everythingimportant.org/physics/Hilbert.htm Of course I cannot support it in any seriously evidential way, yet I believe that bodies are possibly vehicles, and complex though they be, are no different in principle from unbilogical machines, such as computers or motor-cars. This is why I raised the question of blind person's OBEs and NDEs: something that is testable. What we share with computers and motor-cars is, on a shallow view, an aim. Look deeper, and then you will ask how do motor-cars know where to go or computers what to calculate! I think it silly, when we have really bright posters, even if we disagree with them on certain points, that we turn them away on the basis of shallow and abrasive attacks. [You'll do the same to the next lot! Ed.]. Not the way for wreck.org.mensa to go! Openess to experience is a critical part of the path to discovery, though we should the be willing rigorously to explore our hypotheses. -- foolsrushin. === Subject: Re: General Relativity and the New Age Religion > GOD = G_uv > Therefore your suspicion that > there is a relation between > RELATIVITY and RELIGION > is PROVEN TO BE ENTIRELY CORRECT. >[Shubee} > It is certainly true that you have properly identified the god of > religious relativists. And there is no doubt that your god is the god > that religious relativists worship. But you haven't proven anything. > Please try to understand that you have merely defined your god > according to your demonic craving for a pantheistic religion. > [Hammond] Utter horse ptukie. I haven't defined anything. I have DISCOVERED something, and PROVEN that it is the God of the Bible. [foolsrushin] >I think it silly, when we have really bright posters, even if we >disagree with them on certain points, that we turn them away on the >basis of shallow and abrasive attacks. > [Hammond] Bravo Foolsrushin! > http://geocities.com/scientific_proof_of_god mirror site: http://proof-of-god.freewebsitehosting.com GOD=G_uv (a folk song on mp3) http://interrobang.jwgh.org/songs/hammond.mp3 === Subject: Re: General Relativity and the New Age Religion posting-account=rsfFvAoAAADqHCqmunbjtmaKjfuP-pwP .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; InfoPath.1; .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) > GOD = G uv > Therefore your suspicion that > there is a relation between > RELATIVITY and RELIGION > is PROVEN TO BE ENTIRELY CORRECT. > It is certainly true that you have properly identified the god of > religious relativists. And there is no doubt that your god is the god > that religious relativists worship. But you haven't proven anything. > Please try to understand that you have merely defined your god > according to your demonic craving for a pantheistic religion. > Shubeehttp://www.everythingimportant.org/physics/Hilbert.htm Of course I cannot support it in any seriously evidential way, yet I > believe that bodies are possibly vehicles, and complex though they be, > are no different in principle from unbilogical machines, such as > computers or motor-cars. This is why I raised the question of blind > person's OBEs and NDEs: something that is testable. What we share with > computers and motor-cars is, on a shallow view, an aim. Look deeper, > and then you will ask how do motor-cars know where to go or computers > what to calculate! I think it silly, when we have really bright posters, even if we > disagree with them on certain points, that we turn them away on the > basis of shallow and abrasive attacks. [You'll do the same to the next > lot! Ed.]. Not the way for wreck.org.mensa to go! Openess to experience is a critical part of the path to discovery, > though we should the be willing rigorously to explore our hypotheses. > -- > foolsrushin. I ought to have added that there is evidence to the effect that persons blind from birth do nevertheless see and can describe surgical operations being performed upon them or hover sightedly above a near-fatal accident involving them. Do I believe this to be the case? They might, for example, be halluciating, or trying to gain attention ... . Indeed. Also, and much more seriously, such reports appear to be mainly contemporary, at least in the case of the unsighted. Nevertheless, here we have something worth our attention and exploration. I wish you a merry Christmas - and a happy New Year! -- foolsrushin. === Subject: Finite Perfect Groups I have a question which comes from my autumn 2008 group theory final: A group G is perfect if it coincides with its commutator subgroup. Show that a finite group G is perfect if no maximal subgroup of G is normal. I proved the ==> implication first: if G is perfect, and M is a maximal subgroup of G which is normal, then G/M is simple. But then the commutator subgroup (G/M)' = G'M/M = GM/M = G/M so G/M is perfect! But a simple perfect group is trivial, so G = M, a contradiction. As for the converse, assume G is a finite group in which no maximal subgroup of G is normal. Let M be a maximal subgroup of G (which exists, since G is finite); then M is not normal, by assumption. If G is not perfect, then G'M is a proper subgroup of G (since G' is, too), so by maximality M = G'M, in which case G' is contained in M. I don't know whether this is the right approach, but it seems as though this could lead somewhere. The only trouble is, how do we arrive at a contradiction. I hope it is possible! I look forward to hearing from an expert soon! Charles. === Subject: Re: Finite Perfect Groups I have a question which comes from my autumn 2008 > group theory final: > A group G is perfect if it coincides with its > commutator subgroup. Show that a finite group G is perfect if no maximal > subgroup of G is normal. > I proved the ==> implication first: if G is perfect, and M is a maximal subgroup of G > which is normal, then G/M is simple. But then the > commutator subgroup (G/M)' = G'M/M = GM/M = G/M so G/M is perfect! But a simple perfect group is > trivial, so G = M, a contradiction. > As for the converse, assume G is a finite group in > which no maximal subgroup of G is normal. Here's a thought: G cannot be abelian, since a finite group always contains maximal subgroups, and subgroups of abelian groups are normal (though this much is true, I am not sure if these remarks are useful). Now, if G is not perfect, then G' is a proper (nontrivial, normal) subgroup. Since G is finite, G' is contained in some maximal subgroup H, hence H is normal, a contradiction. Does this work? C === Subject: Re: Finite Perfect Groups > Show that a finite group G is perfect if no > maximal subgroup of G is normal. > Here's a thought: G cannot be abelian, since a > finite group always contains maximal subgroups, > and subgroups of abelian groups are normal (though > this much is true, I am not sure if these remarks are > useful). Now, if G is not perfect, then G' is a proper > (nontrivial, normal) subgroup. Since G is finite, > G' is contained in some maximal subgroup H, hence > H is normal, a contradiction. Does this work? Yes, this shows that if G is not perfect, then G contains a maximal subgroup that is normal. === Subject: Re: Finite Perfect Groups > A group G is perfect if it coincides with its > commutator subgroup. Show that a finite group G is perfect if no maximal > subgroup of G is normal. > I proved the ==> implication first: if G is perfect, and M is a maximal subgroup of G > which is normal, then G/M is simple. Not only is it simple, but its only subgroups (normal or not) are M/M and G/M. This means that G/M is cyclic of order p, for some prime p. > But then the commutator subgroup (G/M)' = G'M/M = GM/M = G/M so G/M is perfect! But a simple perfect group is > trivial, so G = M, a contradiction. It is a perfect cyclic group, so trivial. > As for the converse, assume G is a finite group in > which no maximal subgroup of G is normal. Let M be a maximal subgroup of G (which exists, since > G is finite); then M is not normal, by assumption. > If G is not perfect, then G'M is a proper subgroup of This is not true. For instance the nonabelian group of order 6 has a commutator subgroup of order 3 and a maximal subgroup of order 2 that is not normal, but their product is the whole group. === Subject: Re: Finite Perfect Groups posting-account=9QOSvAoAAACEOWJVSDuswW7dB_0wApQO Gecko/2008111217 Fedora/3.0.4-1.fc9 Firefox/3.0.4,gzip(gfe),gzip(gfe) I have a question which comes from my autumn 2008 group theory final: A group G is perfect if it coincides with its commutator subgroup. Show that a finite group G is perfect if no maximal subgroup of G is normal. I proved the ==> implication first: if G is perfect, and M is a maximal subgroup of G which is normal, then G/M is simple. But then the commutator subgroup (G/M)' = G'M/M = GM/M = G/M so G/M is perfect! But a simple perfect group is trivial, so G = M, a contradiction. Why is a simple perfect group trivial? What is the first non-abelian non-trivial simple group you can name? Is it perfect? -- m === Subject: Re: Round curvature Einstein plagiarized David Hilbert's field equations of gravitation > and claimed them as his own. > Eugene, why do to keep up this nonsense! Certainly others made significant contribution to General Relativity as is well known. See: http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/General_relativity.ht m l However, the bulk of the credit really does belong to Einstein. Ref: http://www.scienceblog.com/community/older/1997/A/199700660.html According to the accepted view, the mathematician David Hilbert completed General Relativity five days before Albert Einstein in November 1915. Einstein may thus have copied crucial equations of this theory from Hilbert. Members of an international research group at the Max Planck Institute for the History of Science, Berlin, argue in their study, published in this week's issue of Science, that it was instead Hilbert who appropriated crucial results from Einstein and then published his paper under a misleading dateline. Albert Einstein submitted his conclusive paper on General Relativity on 25 November 1915. David Hilbert, one of the most eminent mathematicians of the 20th century, published a paper in March 1916 which also contains the correct field equations of General Relativity. Einstein came to know Hilbert's contribution in late November, even before he found his final equations. He immediately claimed that Hilbert had appropriated his results. The dateline of Hilbert's paper, 20 November 1915, however, suggests that it was submitted five days earlier than Einstein's contribution. Did Einstein even copy the correct field equations from Hilbert's paper, as has been argued? This possibility can now definitely be excluded. are dated 6 December 1915, that is after the submission of Einstein's conclusive contribution. Their detailed analysis of these proofs has revealed that they contain only an immature version of General Relativity, without the explicit field equations. These equations must have been inserted only later - after 6 December and before the published version appeared in 1916. Hilbert was, so the authors argue, still deeply ingrained in wrong assumptions about the physical meaning of his formalism, assumptions which Einstein had meanwhile painfully overcome. Einstein can hence definitively be freed from the charge of plagiarism. Hilbert's contribution, on the other hand, cannot even be considered as an independent alternative discovery of the field equations of General Relativity. Clearly, before he If Hilbert had only altered the dateline of this paper to the date when he inserted the correct equations into the proofs no later priority discussion could have arisen. Although disputes about priority and plagiarism can be crucially important to working scientists, they are not necessarily a key issue in the history of science. Historians of science are often less interested in who made an important new discovery but rather in how new insights become possible. In the case of Einstein's and Hilbert's struggle for establishing the field equations of a new, relativistic theory of gravitation the situation is, however, different since the approaches taken by the two scientists were dramatically distinct: Whereas Einstein combined mathematical strategies with a search for physical meaning, Hilbert very much relied on the power of his superior mathematical formalism. Clearly, in this case, the who of the discovery tells indeed much about the how. Since 1907 Einstein had attempted to carefully reconcile, step by step, tentative mathematical formulations of his heuristic goal to formulate a relativistic theory of gravitation with the then available physical knowledge. Hilbert, on the other hand, had only begun to work on General Relativity in the second half of 1915. He boldly aimed from the beginning at an axiomatic foundation of physics and at a kind of world formula, unifying gravitation with electromagnetism. This approach caused the wrong impression that the field equations of General Relativity could be found by pure mathematical reasoning. project dedicated to the history of General Relativity. The project is centered at the Max Planck Institute for the History of Science in Berlin and has produced in the last years several new insights into the development of this theory. === Subject: Re: Round curvature posting-account=5GUrzQkAAADun29oaK3p_W_saUVxxHUF Gecko/2008120122 Firefox/3.0.5,gzip(gfe),gzip(gfe) > Einstein plagiarized David Hilbert's field equations of gravitation > and claimed them as his own. Eugene, why do to keep up this nonsense! Certainly others made significant contribution to General Relativity as > is well known. See: > http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/General relati... However, the bulk of the credit really does belong to Einstein. Ref:http://www.scienceblog.com/community/older/1997/A/199700660.html According to the accepted view, the mathematician David Hilbert completed General > Relativity five days before Albert Einstein in November 1915. Einstein may thus have > copied crucial equations of this theory from Hilbert. Members of an international research group at the Max Planck Institute for the History of > Science, Berlin, argue in their study, published in this week's issue of Science, that it > was instead Hilbert who appropriated crucial results from Einstein and then published his > paper under a misleading dateline. Albert Einstein submitted his conclusive paper on General Relativity on 25 November 1915. > David Hilbert, one of the most eminent mathematicians of the 20th century, published a > paper in March 1916 which also contains the correct field equations of General Relativity. > Einstein came to know Hilbert's contribution in late November, even before he found his > final equations. He immediately claimed that Hilbert had appropriated his results. The > dateline of Hilbert's paper, 20 November 1915, however, suggests that it was submitted > five days earlier than Einstein's contribution. Did Einstein even copy the correct field > equations from Hilbert's paper, as has been argued? This possibility can now definitely be > excluded. are dated 6 December 1915, that is after the submission of Einstein's conclusive > contribution. Their detailed analysis of these proofs has revealed that they contain only > an immature version of General Relativity, without the explicit field equations. These > equations must have been inserted only later - after 6 December and before the published > version appeared in 1916. Hilbert was, so the authors argue, still deeply ingrained in > wrong assumptions about the physical meaning of his formalism, assumptions which Einstein > had meanwhile painfully overcome. Einstein can hence definitively be freed from the charge > of plagiarism. Hilbert's contribution, on the other hand, cannot even be considered as an independent > alternative discovery of the field equations of General Relativity. Clearly, before he > If Hilbert had only altered the dateline of this paper to the date when he inserted the > correct equations into the proofs no later priority discussion could have arisen. Although disputes about priority and plagiarism can be crucially important to working > scientists, they are not necessarily a key issue in the history of science. Historians of > science are often less interested in who made an important new discovery but rather in how > new insights become possible. In the case of Einstein's and Hilbert's struggle for > establishing the field equations of a new, relativistic theory of gravitation the > situation is, however, different since the approaches taken by the two scientists were > dramatically distinct: Whereas Einstein combined mathematical strategies with a search for > physical meaning, Hilbert very much relied on the power of his superior mathematical > formalism. Clearly, in this case, the who of the discovery tells indeed much about the how. Since 1907 Einstein had attempted to carefully reconcile, step by step, tentative > mathematical formulations of his heuristic goal to formulate a relativistic theory of > gravitation with the then available physical knowledge. Hilbert, on the other hand, had > only begun to work on General Relativity in the second half of 1915. He boldly aimed from > the beginning at an axiomatic foundation of physics and at a kind of world formula, > unifying gravitation with electromagnetism. This approach caused the wrong impression that > the field equations of General Relativity could be found by pure mathematical reasoning. project dedicated to the history of General Relativity. The project is centered at the Max > Planck Institute for the History of Science in Berlin and has produced in the last years > several new insights into the development of this theory. ----------------------- there was no need to dispue about plagiarism because all of them were wrong gravitation is a property of mass not of any stupid space got it master parrot ?? the rest was fraud methematical fiddling of impirical results to formulas got it parrot ?? Y.Porat --------------------------- === Subject: Re: Round curvature posting-account=PSw72goAAADTugQpI3-NCbn5m3k-KKO3 .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; WWTClient2),gzip(gfe),gzip(gfe) > Einstein plagiarized David Hilbert's field equations of gravitation > and claimed them as his own. > Eugene, why do to keep up this nonsense! > Certainly others made significant contribution to General Relativity as > is well known. See: > http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/General relati... > However, the bulk of the credit really does belong to Einstein. > Ref:http://www.scienceblog.com/community/older/1997/A/199700660.html > According to the accepted view, the mathematician David Hilbert completed General > Relativity five days before Albert Einstein in November 1915. Einstein may thus have > copied crucial equations of this theory from Hilbert. > Members of an international research group at the Max Planck Institute for the History of > Science, Berlin, argue in their study, published in this week's issue of Science, that it > was instead Hilbert who appropriated crucial results from Einstein and then published his > paper under a misleading dateline. > Albert Einstein submitted his conclusive paper on General Relativity on 25 November 1915. > David Hilbert, one of the most eminent mathematicians of the 20th century, published a > paper in March 1916 which also contains the correct field equations of General Relativity. > Einstein came to know Hilbert's contribution in late November, even before he found his > final equations. He immediately claimed that Hilbert had appropriated his results. The > dateline of Hilbert's paper, 20 November 1915, however, suggests that it was submitted > five days earlier than Einstein's contribution. Did Einstein even copy the correct field > equations from Hilbert's paper, as has been argued? This possibility can now definitely be > excluded. > are dated 6 December 1915, that is after the submission of Einstein's conclusive > contribution. Their detailed analysis of these proofs has revealed that they contain only > an immature version of General Relativity, without the explicit field equations. These > equations must have been inserted only later - after 6 December and before the published > version appeared in 1916. Hilbert was, so the authors argue, still deeply ingrained in > wrong assumptions about the physical meaning of his formalism, assumptions which Einstein > had meanwhile painfully overcome. Einstein can hence definitively be freed from the charge > of plagiarism. > Hilbert's contribution, on the other hand, cannot even be considered as an independent > alternative discovery of the field equations of General Relativity. Clearly, before he > If Hilbert had only altered the dateline of this paper to the date when he inserted the > correct equations into the proofs no later priority discussion could have arisen. > Although disputes about priority and plagiarism can be crucially important to working > scientists, they are not necessarily a key issue in the history of science. Historians of > science are often less interested in who made an important new discovery but rather in how > new insights become possible. In the case of Einstein's and Hilbert's struggle for > establishing the field equations of a new, relativistic theory of gravitation the > situation is, however, different since the approaches taken by the two scientists were > dramatically distinct: Whereas Einstein combined mathematical strategies with a search for > physical meaning, Hilbert very much relied on the power of his superior mathematical > formalism. Clearly, in this case, the who of the discovery tells indeed much about the how. > Since 1907 Einstein had attempted to carefully reconcile, step by step, tentative > mathematical formulations of his heuristic goal to formulate a relativistic theory of > gravitation with the then available physical knowledge. Hilbert, on the other hand, had > only begun to work on General Relativity in the second half of 1915. He boldly aimed from > the beginning at an axiomatic foundation of physics and at a kind of world formula, > unifying gravitation with electromagnetism. This approach caused the wrong impression that > the field equations of General Relativity could be found by pure mathematical reasoning. > project dedicated to the history of General Relativity. The project is centered at the Max > Planck Institute for the History of Science in Berlin and has produced in the last years > several new insights into the development of this theory. ----------------------- > there was no need to dispue about plagiarism > because all of them were wrong gravitation is a property of mass > not of any stupid space Mass generates space geometry outward from its center. That geometry is round So space is spherical. > got it master parrot ?? the rest was fraud methematical fiddling > of impirical results to formulas > got it parrot ?? Y.Porat > ---------------------------- Hide quoted text - - Show quoted text - === Subject: Re: Round curvature posting-account=42V-qwoAAABOAKkANAhMmpW4F3ZbRLXb Gecko/2008120122 Firefox/3.0.5,gzip(gfe),gzip(gfe) > Curvature emanates from the center of energy. Einstein first > discovered that space had to be curved around mass. But I say it has > an origin at concentrated energy center. Yeah, it's a decided improvement over old-fashioned square curvature. > Mitch Raemsch Hey, Mitch, what happened to your Nobel Prize announcements? Somehow I managed to miss them. Mark L. Fergerson === Subject: Re: Round curvature posting-account=vpv29woAAAAjASPtep1bSfPEIqZVH03h 4334.5003; Windows NT 5.0; .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) spider-mtc-ta01.proxy.aol.com[400C7001] (Prism/1.2.1), HTTP/1.1 cache-mtc-aa06.proxy.aol.com[400C740A] (Traffic-Server/6.1.5 [uScM]) > Curvature emanates from the center of energy. Einstein first > discovered that space had to be curved around mass. But I say it has > an origin at concentrated energy center. It's about time somebody straightened that out. Doug Chandler === Subject: Re: Round curvature posting-account=PSw72goAAADTugQpI3-NCbn5m3k-KKO3 .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; WWTClient2),gzip(gfe),gzip(gfe) > Curvature emanates from the center of energy. Einstein first > discovered that space had to be curved around mass. But I say it has > an origin at concentrated energy center. > Mitch Raemsch You are right but I have a feeling it is for the wrong reasons. It is > not so much at the center of the energy concentration but is due to > the mass energy relationship given by the famous E=mc^2. It is in > fact an experimentally confirmed prediction of general relativity. > Good insight, but it'salready been thought of. Patrick Energy is infinitely dense in the case of mass. It is masses definition. === Subject: Re: Fourier series expansion doubt posting-account=LChCFQoAAACR0FoxHzVn6GGERsr9zp8c Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) On Dec 25, 12:46am, Robert Israel > I've to expand any given polynomial of degree n i.e P(n) > as Fourier series, then I want the polynomial in purely > Cosine and sine terms > infinity > ------| > [ An cos (nx) + Bn Sin (nx) ] + ao/2 > / > ------| > n =3D 1 > and again transforming the series would bring back > My Original Polynomial. > To achieve this what conditions I've to follow. > Please help it in clear, I'll make out the notes > of it. > (a) How and what to select, interval values [ , ] or ( , ) The interval you select is up to you. But it may be slightly > simpler to use a symmetric interval such as [-pi,pi]. Then > for odd n, the Fourier series of x^n on this interval involves > only sines, and for even n only cosines. > (b) Problem with converges, and > ' > ' > ' > if there any conditions to achieve this > please provide them. As has been stated, the Fourier series will converge to the polynomial > on the open interval, and to the average of the two endpoint values at the > endpoints. If you use the interval [-pi,pi], then an even polynomial > has the same values at the two endpoints, an odd function does not. > However, convergence will be quite slow: the coefficients will be asymptotic > to constant/n in general (in which case the series will only converge > conditionally, not absolutely), or constant/n^2 for most even polynomials. > [ OR ] > Fourier integral transforms are any useful here. > F(x) =3D integral -infinity to +infinity P(n) (e)^-2pi ixE dx > P(n) =3D f(x) =3D integral -infinity to +infinity F(x)(e)^2pi ixE dx Polynomials have no Fourier transform in the usual sense, because they > are not square-integrable. They do have Fourier transforms in the > sense of distributions, but these involve Dirac deltas and their derivatives. > Thus the Fourier transform of x^n is 2 pi i^n Dirac^(n)(k), > corresponding to the fact that the n'th derivative of exp(i k x) > with respect to k at k = 0 is i^n x^n. > -- > Robert Israel isr...@math.MyUniversitysInitials.ca > Department of Mathematics http://www.math.ubc.ca/~israel > University of British Columbia Vancouver, BC, Canada ----------------------------------- I got Ur points recovering the original polynomial from Fourier expansion Series is going to be very hard and complicated, instead of that I'll go with comparing polynomail P(x) values, and Fourier expansion F[p(x)] values. ------------------------------------- Now the problem is like this, Part-I:- Let the polynomial be as P(x) and its degree is given by k. let k = 1500, 2000, 5000.....10,000.... I've to deal with extremely higher degree polynomials. Px(k=500), here if I provide x values I'll get f(x) or P(x) values for relative x value, up to here I hope everything is clear. Coming to Part-II I'm going to expand the polynomial as Fourier Series i.e F[Px(k=500)] = infinity ------| [ An cos (nx) + Bn Sin (nx) ] + ao/2 / ------| n = 1 Now how to get the same values of P(x) for x both in the polynomial form and Fourier expansion form. an error of -5 to +5 is OKAY for me, no problem with that. Now tell me, what precautions should I take into consideration ? (a) Selecting intervals = ? (b) Handling error = ? (c) dealing with even and odd function =? (d) if there are any more I've to consider,please provide them. Thnx === Subject: Re: Fourier series expansion doubt posting-account=PbSwTwgAAADCfhtjQF2Hq7jjSPSyO4QX Gecko/2008120122 Firefox/3.0.5,gzip(gfe),gzip(gfe) > On Dec 25, 12:46am,Robert Israel > (b) Problem with converges, and > ' > ' > ' > if there any conditions to achieve this > please provide them. > As has been stated, the Fourier series will converge to the polynomial > on the open interval, and to the average of the two endpoint values at the > endpoints. If you use the interval [-pi,pi], then an even polynomial > has the same values at the two endpoints, an odd function does not. > However, convergence will be quite slow: the coefficients will be asymptotic > to constant/n in general (in which case the series will only converge > conditionally, not absolutely), or constant/n^2 for most even polynomials. > I got Ur points recovering the original polynomial > from Fourier expansion Series is going to be very hard and > complicated, instead of that I'll go with comparing > polynomail P(x) values, > and Fourier expansion F[p(x)] values. I don't understand how that's supposed to be different. > ------------------------------------- > Now the problem is like this, > Part-I:- > Let the polynomial be as P(x) > and its degree is given by k. > let k = 1500, 2000, 5000.....10,000.... > I've to deal with extremely > higher degree polynomials. Polynomials of high degree, unless the high-degree coefficients are very small, can cause very severe numerical difficulties. Where do these polynomials come from? > Px(k=500), here if I provide x values > I'll get f(x) or P(x) values for relative x value, > up to here I hope everything is clear. No, it isn't. What is f? > Coming to > Part-II > I'm going to expand the polynomial as > Fourier Series i.e F[Px(k=500)] = infinity > ------| > [ An cos (nx) + Bn Sin (nx) ] + ao/2 > / > ------| > n = 1 Now how to get the same values of P(x) for x > both in the polynomial form and > Fourier expansion form. > an error of -5 to +5 is OKAY for me, no problem > with that. If your interval is symmetric and the polynomial is not even, then as I mentioned the series converges conditionally, not absolutely (and also not uniformly). So if you're using a finite truncation of the Fourier series, a large number of terms will be needed to get reasonable accuracy at a given point, and no single truncation of the series will work well everywhere (in particular, you'll have trouble near the ends of the interval). On the other hand, uniform convergence can be obtained using e.g. Cesaro means. Robert Israel israel@math.MyUniversitysInitials.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada === Subject: Re: Fourier series expansion doubt > If I expand a polynomial P(n) of degree n, as a fourier series > F [P(n)] = ao/2 + Sigma _n=1 to infinity [an cos(nx) + bn sin(nx)] > ao will be constant > remaining terms I'll get in cos and sin terms. > My_Question is: > Again how to get back to the original function i.e P(n) > Take this example: > P(n) = f(x) = X^2 > By expansion I got > F[p(n)] or F[f(x)]= > 4/3 pi^2 + 4( cosx + 1/2^2 cos2x+ 1/3^2 cos3x+....) - 4 pi > (sinx + 1/2 sin2x + 1/3 sin3x........) > So, I got X^2 in fourier series like this > Now, how to get back the original function by this series ? > If possible please write in Brief. > Thnx for the help. Your domain is bit hard, because your function as expanded to whole R >is not continuos(and smooth) at 0. If your domain would be [-pii,pii] >then the Fourier series would look something like >sum[n = 1][oo](-1)^n 4/(pii*n^2)*cos(nx). Now because your function >x^2 is continuosly diffrentiable it is absolutely convergent so you >can differentiate FS term by term. x^2 may be continuously differentiable, but the sum of the series isn't. In the [-pi, pi] case here, you have a_n = O(1/n^2) so you have uniform convergence and a continuous limit. The sum of the series has corners at the multiples of pi. Each time you differentiate the series you get another n in the numerator so the derived series coefficients are O(1/n), then next ones are O(1), O(n), etc. You don't get convergence like you would with a power series. --Lynn http://math.asu.edu/~kurtz === Subject: Re: Fourier series expansion doubt posting-account=iyXB5AkAAABPCtkDKhRJOsNWmafzHSRE Gecko/2008120122 Firefox/3.0.5,gzip(gfe),gzip(gfe) > If I expand a polynomial P(n) of degree n, as a fourier series > F [P(n)] = ao/2 + Sigma _n=1 to infinity [an cos(nx) + bn sin(nx)] > ao will be constant > remaining terms I'll get in cos and sin terms. > My_Question is: > Again how to get back to the original function i.e P(n) > Take this example: > P(n) = f(x) = X^2 > By expansion I got > F[p(n)] or F[f(x)]= > 4/3 pi^2 + 4( cosx + 1/2^2 cos2x+ 1/3^2 cos3x+....) - 4 pi > (sinx + 1/2 sin2x + 1/3 sin3x........) > So, I got X^2 in fourier series like this > Now, how to get back the original function by this series ? > If possible please write in Brief. > Thnx for the help. >Your domain is bit hard, because your function as expanded to whole R >is not continuos(and smooth) at 0. If your domain would be [-pii,pii] >then the Fourier series would look something like >sum[n = 1][oo](-1)^n 4/(pii*n^2)*cos(nx). Now because your function >x^2 is continuosly diffrentiable it is absolutely convergent so you >can differentiate FS term by term. x^2 may be continuously differentiable, but the sum of the series > isn't. I maybe well wrong, I had a quite a few beers tonight. But is it not sum of the FS in this case on the interior (-pii,pii) just the values of of f(x). So if it is a same function locally, I don`t quite understand your point. >In the [-pi, pi] case here, you have a_n = O(1/n^2) so you have > uniform convergence and a continuous limit. The sum of the series has > corners at the multiples of pi. Each time you differentiate the series > you get another n in the numerator so the derived series coefficients > are O(1/n), then next ones are O(1), O(n), etc. It is not the whole asymptic truth what`s in the numerator. Look at the Riemann series. >You don't get > convergence like you would with a power series. Are you sure? I calculated the FS of 2x on [-pii,pii] and I get just what I got with the differentiating term by term the original series. But I of course could now be making great mistakes. === Subject: Re: Fourier series expansion doubt > If I expand a polynomial P(n) of degree n, as a fourier series > F [P(n)] = ao/2 + Sigma _n=1 to infinity [an cos(nx) + bn sin(nx)] > ao will be constant > remaining terms I'll get in cos and sin terms. > My_Question is: > Again how to get back to the original function i.e P(n) > Take this example: > P(n) = f(x) = X^2 > By expansion I got > F[p(n)] or F[f(x)]= > 4/3 pi^2 + 4( cosx + 1/2^2 cos2x+ 1/3^2 cos3x+....) - 4 pi > (sinx + 1/2 sin2x + 1/3 sin3x........) > So, I got X^2 in fourier series like this > Now, how to get back the original function by this series ? > If possible please write in Brief. > Thnx for the help. >Your domain is bit hard, because your function as expanded to whole R >is not continuos(and smooth) at 0. If your domain would be [-pii,pii] >then the Fourier series would look something like >sum[n = 1][oo](-1)^n 4/(pii*n^2)*cos(nx). Now because your function >x^2 is continuosly diffrentiable it is absolutely convergent so you >can differentiate FS term by term. > x^2 may be continuously differentiable, but the sum of the series > isn't. I maybe well wrong, I had a quite a few beers tonight. But is it not >sum of the FS in this case on the interior (-pii,pii) just the values >of of >f(x). So if it is a same function locally, I don`t quite understand >your point. >In the [-pi, pi] case here, you have a_n = O(1/n^2) so you have > uniform convergence and a continuous limit. The sum of the series has > corners at the multiples of pi. Each time you differentiate the series > you get another n in the numerator so the derived series coefficients > are O(1/n), then next ones are O(1), O(n), etc. It is not the whole asymptic truth what`s in the numerator. Look at >the Riemann series. >You don't get > convergence like you would with a power series. Are you sure? I calculated the FS of 2x on [-pii,pii] and I get just >what I got with the differentiating term by term the original series. >But I of course could now be making great mistakes. It works once, but your original post talked about differentiating again. The series you get for 2x is only conditionally convergent. Your next series won't be convergent at all because the a_n won't go to zero. --Lynn http://math.asu.edu/~kurtz === Subject: Re: VEDIC TECHNOLOGY HAS NOT LOST ITS RELEVANCE Mudali posted: > . . . > Invaders used GUN POWDER which is a Chinese invention. . . . No, gunpowder was invented by Hindus in Bharat: The use of gunpowder-powered weapons is mentioned in the Ramaayan, which is dates around 7000 BCE -- see: Astronomical Dating of the Ramaayan Also, visit http://atributetohinduism.com which is the source of the following excerpt: [...] Military science - Gunpowder In regard to military science, the Raamaayan and the Puraan make frequent mention of Shataghnis, or canons, being placed on forts and used in times of emergency. A canon was called Shataghni because it meant the fire weapon that kills one hundred men at once. They ascribe these agniyastras, or weapons of fire, to Visvakarm, the architect of the Vedic epics. Rockets were also Indian inventions and were used in native armies when Europeans first came into contact with them. As per Dante's Inferno, Alexander mentioned in a letter to Aristotle, that terrific flashes of flame showered on his army in India. The Shukra Neeti is an ancient text that deals with the manufacture of arms such as rifles and guns. In The Celtic Druids (pp-115-116), Godfrey Higgins provides evidence that Hindus knew of gun powder from the remotest antiquity. [...] http://atributetohinduism.com/Hindu_Culture1.htm === [ Subject: VEDIC TECHNOLOGY HAS NOT LOST ITS RELEVANCE 'Vedic technology has not lost its relevance' By a Staff Reporter The Hindu Tuesday, November 08, 2005 Seminar focuses on rich Vedic heritage o Pure mathematics part of Vedas, says IIT professor o Forum opened to bring into relevance use of Vedic technology in modern science Vaishakhapatnam - ''You open any metallurgy book and it would state that steel was invented in the 19th century by an Englishman by name Henry Bessemer. But little do people know that the famous Damascus swords were made from steel imported from the southern part of India centuries ago. History traces that high quality steel like the one used in the swords was produced in India by 300 BC itself. That's the greatness of this land. The technological development that we see or hear today was written by our maharishis in the Vedic period itself,'' opined B.S. Murthy, professor of metallurgy and nanotechnology, IIT, Chennai, in his address at a seminar on Vedic technology organised by Maharshi Research Institute of Vedic Technology here on Sunday. The seminar was hosted by the institute to create awareness on the rich Vedic heritage and its application in modern science. According to A.B. Sudhakara Sastry, founder of the institute, every subject has its roots linked to the Vedas, especially the pure sciences like physics and chemistry. Part of Vedas Giving a power point presentation, Mr. Sastry showcased how pure mathematics formed an integral part of the Vedas. If one goes deep into the Vedas then he or she would find every aspect of modern applied mathematics like complex geometry and trigonometry mentioned somewhere in the Vedas. Subjects like astronomy, bio-technology, space technology, aeronautics, civil engineering, chemical engineering and atomic structures are discussed in detail by sages like Bharadwaja, Valmiki and Agastya under different chapters and texts. The only thing was that they talked of science with constructive ideas and we are now inching towards destruction by wrong usage of our modern knowledge,'' said Mr. Sastry. Forum inaugurated Apart from showcasing the use of science in Vedas, a forum, Maharshi Intellectual Forum, was also inaugurated to take up the task of bringing into relevance the use of Vedic technology in modern science. Speaking after inaugurating the forum, the chief guest, Sadguru Sivananda Murthy, said: It is now the duty of the young scientists to take this forum ahead. Professors and scientists have to guide young minds with logical and scientific interpretation of the Vedas. Our Vedas are an ocean of knowledge. One can find the mention of modern scientific topics like magnetic fields, anti-gravitational force and aerodynamics in the Vedas. Only thing is that one should take interest to learn and interpret the details rightly.'' Andhra University Rector L. Joga Rao and the correspondent of Gayatri Vidya Parishad, V. Soma Raju, also spoke. More at: http://www.hindu.com/2005/11/08/stories/2005110803440200.htm Jai Maharaj http://tinyurl.com/24fq83 http://www.mantra.com/jai http://www.mantra.com/jyotish Om Shanti Hindu Holocaust Museum http://www.mantra.com/holocaust Hindu life, principles, spirituality and philosophy http://www.hindu.org http://www.hindunet.org The truth about Islam and Muslims http://www.flex.com/~jai/satyamevajayate DISCLAIMER AND CONDITIONS o Not for commercial use. 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Section 107, the material on this site is distributed without profit to those who have expressed a prior interest in receiving the included information for research, comment, discussion and educational purposes by subscribing to USENET newsgroups or visiting web sites. For more information go to: http://www.law.cornell.edu/uscode/17/107.shtml your own that go beyond 'fair use', you must obtain permission from the copyright owner. === Subject: Re: Solve Equation for integer value > Given 2 positive integers A and B, what is the minimum value of > positive integer x > for which (A/x)^x -B >=0 is true ? > (a/x)^x >= b; a^x >= bx^x; bx^x <= a^x If b <= a, then x = 1. If a < b, let's consider some cases. If a = 1, then no solution. If a = 2, then 3x^x <= bx^x <= 2^x implies no solution. If a = 3, then 4x^x <= bx^x <= 3^x implies b = 4, x = 2 the only possibility ax^x < bx^x <= a^x implies x < a > If A=6, B=8, then x=2, A=10, B= 37 then x= 3. Substituting A/x= y, we get y^x -B >=0 , y^(A/y) - B >=0 , y^(1/y) >= > B^1/a , now integer y should be maximum for x to be minimum.The > problem is with y^(1/y) which increases then decreases. Now i don't know how to solve it ? I can draw graphs or do trial > error but any good ways. > Since the solution x cannot exceed a, an exhaustive search x = 1, 2,.. a-1 would tell you if there were an answer and what it would be for the cases involving a < b. For the cases b <= a, the answer is of course, x = 1. === Subject: Re: Solve Equation for integer value > Given 2 positive integers A and B, what is the minimum value of > positive integer x > for which (A/x)^x -B >=0 is true ? > (a/x)^x >= b; a^x >= bx^x; bx^x <= a^x If b <= a, then x = 1. Yes. And so, in what follows, I shall assume, as you did, that a < b. > If a < b, let's consider some cases. But if b is too large, then there will be no solution. Specifically, we must have b <= e^(a/e), the maximum value of the function (a/x)^x. > If a = 1, then no solution. > If a = 2, then 3x^x <= bx^x <= 2^x implies no solution. > If a = 3, then 4x^x <= bx^x <= 3^x > implies b = 4, x = 2 the only possibility b = 4 is too large since 4 > e^(3/e). Thus, if a = 3, there is no solution with a < b. Similarly, if a = 4, there is no solution with a < b. But if a = 5 and b = 6, then we have the solution x = 2. > ax^x < bx^x <= a^x implies x < a > If A=6, B=8, then x=2, A=10, B= 37 then x= 3. > > Substituting A/x= y, we get y^x -B >=0 , y^(A/y) - B >=0 , y^(1/y) >= > B^1/a , now integer y should be maximum for x to be minimum.The > problem is with y^(1/y) which increases then decreases. > > Now i don't know how to solve it ? I can draw graphs or do trial > error but any good ways. > Since the solution x cannot exceed a, an exhaustive search > x = 1, 2,.. a-1 would tell you if there were an answer and > what it would be for the cases involving a < b. To avoid such a search, the Lambert W function, mentioned here earlier by Rob Johnson, could be used. David > For the cases b <= a, the answer is of course, x = 1. === Subject: =?iso-8859-1?q?Re=3A_NEW_REPORT_=ABCANONICAL?= SCIENCE: =?iso-8859-1?q?ITS_HISTORY=2C_GOALS=2C_AND_FUTURE=BB?= > Keizer weems to have reputable publications in the literature, but I see > viturally nothing on your webblog. it is certainly news to me, that > Dirac was a reductionist, or that he solved the periodical table with > his mechanics; how > do *you* account for the allegedly missing antimatter? I have not studied this in detail still, because there is still problems with characterization of anti-matter: holes in Dirac sense? Or better the second quantization formalism? In my opinion none of those is still satisfactory. First I would find a complete and satisfactory characterization of anti-mmater and next re- examine data in the light of new formalism. > there is nothing wrong with the theory of strings, Some difficulties with string theory are noticed in the text, many other were left out by motives of space and because the report main theme is not an exhaustive analysis of string-brane-M theories. In a final box I also explain how new developments in gravity let us to predict the value of the cosmological constant in excellent agreement with observation. This is not possible using string theory. -- http://www.canonicalscience.org/ Usenet Guidelines: http://www.canonicalscience.org/en/miscellaneouszone/guidelines.html === Subject: water stream trajectory: parabolic or not? Many say that the format of a jet of water takes the form of a parabola: http://groups.physics.umn.edu/demo/mechanics/1D6065.html However, measurements show that the curve is not a parabola because the jet of water tends to disperse. Moreover: even a coherent and laminar stream of water, like that one http://www.flickr.com/photos/xinmincat/179006022/ is not a parabola (contrary to the caption of the flickr photo). The book Soap Bubbles - Their Colors and The Forces Which Mold Them by Boys gives a physical explanation for this behavior: vibration and interaction between the drops of water. Are there futher references about the shape of a water stream? === Subject: Re: water stream trajectory: parabolic or not? posting-account=504E-QkAAAA2v90r8nGnJKpfySa_yBSU 5.1),gzip(gfe),gzip(gfe) On Dec 25, 5:09am, humberto.bortolo...@gmail.com Many say that the format of a jet of water takes the form of a > parabola: http://groups.physics.umn.edu/demo/mechanics/1D6065.html However, measurements show that the curve is not a parabola because > the jet of water tends to disperse. Moreover: even a coherent and > laminar stream of water, like that one http://www.flickr.com/photos/xinmincat/179006022/ is not a parabola (contrary to the caption of the flickr photo). The book Soap Bubbles - Their Colors and The Forces Which Mold Them > by Boys gives a physical explanation for this behavior: vibration and > interaction between the drops of water. Are there futher references about the shape of a water stream? > A stream of water is not parabolic because it constantly is losing its horizontal component of velocity because of air resistance, while gravity continually acts to accelerate the vertical component. The flight of a cannon ball is similarly affected, but to an extent that is usually negligible. In either case, the path would be NEARLY [note the emphasis] parabolic in the absence of air resistance. It would be truly parabolic only if the gravity on earth was always perpendicular to a fixed reference plane. Such isn't the case. Harry C. === Subject: Re: water stream trajectory: parabolic or not? > On Dec 25, 5:09am, humberto.bortolo...@gmail.com > Many say that the format of a jet of water takes the form of a > parabola: > http://groups.physics.umn.edu/demo/mechanics/1D6065.html > However, measurements show that the curve is not a parabola because > the jet of water tends to disperse. Moreover: even a coherent and > laminar stream of water, like that one > http://www.flickr.com/photos/xinmincat/179006022/ > is not a parabola (contrary to the caption of the flickr photo). > The book Soap Bubbles - Their Colors and The Forces Which Mold Them > by Boys gives a physical explanation for this behavior: vibration and > interaction between the drops of water. > Are there futher references about the shape of a water stream? A stream of water is not parabolic because it constantly is losing its > horizontal component of velocity because of air resistance, while > gravity continually acts to accelerate the vertical component. The flight of a cannon ball is similarly affected, but to an extent > that is usually negligible. It is not negligible with any gun except at very short ranges. At the end of a trap/skeet range the shot is falling nearly vertically even with elevation angles approaching 45 degrees. High power rifle bullet trajectories aren't parabolic much past 100 yards. Don't get me started on artillery tables... > In either case, the path would be NEARLY [note the emphasis] parabolic > in the absence of air resistance. It would be truly parabolic only if > the gravity on earth was always perpendicular to a fixed reference > plane. Such isn't the case. Harry C. > -- Jim Pennino === Subject: Re: JSH: Questioning Galois Theory >My point is simple: I have simple proof of a massive error that >entered the mathematical field over a hundred years ago, so the error >has to be subtle. > So subtle that you cannot tell us what it is? It's easily demonstrated now but subtle in that it lasted for over a >hundred years and requires you do some things not intuitive for most >math students, for instance, who would have thought that 7(x^2 + 3x + 2) = (7x + 7)(x + 2) could be a matter of debate or show a crucial point for a major >mathematical proof? You have still not us what it is you are trying to show. We know that it is easily demonstrated, we know that it is subtle, we know that it lasted for over a hundred years, we know that it requires you do some things not intuitive for most math students, but we do to shout, but you do not seem to be getting the message. Please give us a statement of what it is you are trying to show. rossum === Subject: Re: JSH: Questioning Galois Theory My point is simple: I have simple proof of a massive error that > entered the mathematical field over a hundred years ago, so the error > has to be subtle. > So subtle that you cannot tell us what it is? > It's easily demonstrated now but subtle in that it lasted for over a > hundred years and requires you do some things not intuitive for most > math students, for instance, who would have thought that > 7(x^2 + 3x + 2) = (7x + 7)(x + 2) > could be a matter of debate or show a crucial point for a major > mathematical proof? > You have still not us what it is you are trying to show. We know that > it is easily demonstrated, we know that it is subtle, we know > that it lasted for over a hundred years, we know that it requires > you do some things not intuitive for most math students, but we do > to shout, but you do not seem to be getting the message. Please give > us a statement of what it is you are trying to show. rossum I agree. James: please explain this alleged goddamn error until we get it. Dave === Subject: Re: JSH: Questioning Galois Theory posting-account=wVv_VwoAAAAVTfUuyxLzug5SzYWCgHj1 Gecko/20081203 Firefox/2.0.0.19,gzip(gfe),gzip(gfe) > ... > > Counterexamples to what? In the complex plane the too simple result > > is as trivial as > > > 7(x^2 + 3x + 2) = (7x + 7)(x+2) > > > and there are no counterexamples. > > > Come on, I dare you, in the complex plane, give a counterexample. > Obviously in the complex plane there are no counterexamples because > everything is divisible by everything except 0. You have to restrict > yourself to somewhere where that is *not* the case. >Why? Because you say so? >My point is simple: I have simple proof of a massive error that >entered the mathematical field over a hundred years ago, so the error >has to be subtle. > So subtle that you cannot tell us what it is? It's easily demonstrated now but subtle in that it lasted for over a > hundred years and requires you do some things not intuitive for most > math students, for instance, who would have thought that 7(x^2 + 3x + 2) = (7x + 7)(x + 2) could be a matter of debate or show a crucial point for a major > mathematical proof? >To demonstrate that error I rely on a simple construction in the >complex plane. > So there is an error in the complex plane then. Is this a different No. The complex plane is the baseline to show the error. I prove something in the complex plane which indicates the error > elsewhere. > Let's stop being coy. Exactly what do you prove in the complex plane? Nice, crisp, clear statement, please. error from the one you claimed previously to have found in the > algebraic integers? >Math people indoctrinated in the error argue ad infinitum about >trivialities and try to crawl back to the region where the error holds >sway. > Which region is that? Be specific please. > rossum The ring of algebraic integers. Hey, I've very specific. No, you're not. You have not stated a theorem. > I've been explaining in detail, where for > readers wondering what's different, well, I'm holding posters to the > complex plane for the key construction and pointing out when they say > nonsensical things. > Like what? Here's the full argument again. Given 7(x^2 + 3x + 2) = (7x + 7)(x + 2) you are looking at one factorization out of infinity, but it is a > valid factorization, which does not shift dependent on the value of > x. Specifics: 1. What do you mean by 'valid factorization' ? 2. Are there any other 'valid factorizations' ? 3. Does a 'valid factorization' have to be independent of the values of x ? Why ? Can you prove that mathematically? > So 7x + 7 = 7(x+1), or to give the distributive property the > straightforward way: 7(x+1) = 7x + 7, and it doesn't change dependent > on the value of x. > Why is that significant? > That is trivial algebra!!! > So far. But you haven't said anything. > What happens though if you follow mathematical logic is that now with 7*(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x)+ 7) where the a's are roots of a^2 - (7x-1)a + (49x^2 - 14x) = 0 you get a weird situation if you normalize with a_1(x) = b_1(x), and a_2(x) = b_2(x) - 1, as then you have 7*(175x^2 - 15x + 2) = (5b_1(x) + 7)(5b_2(x)+ 2) where b_1(0) = 0, b_2(0) = 0, which is in key respects exactly like 7(x^2 + 3x + 2) = (7x + 7)(x+2) and it represents ONE factorization out of an infinite number of ways > to factor: > WHAT represents one factorization? You have not shown explicitly how 7 occurs on the right side of the equation. You have not given an explicit factorization! > 7*(175x^2 - 15x + 2). So what's different then? Well, in one case you have 7x--a linear > function. > NOT the only difference. In 7x + 7, you have one polynomial variable, x. In 5b_1(x) + 7, you have a nonpolynomial variable, 5b_1(x). In fact you are not even factoring your original polynomial, 7(175x^2 - 15x + 2) as a polynomial in x. You are factoring it as a polynomial in the symbol 5. Further, b_1(x) = a_1(x) is a root of an associated quadratic, a^2 - (7x - 1)a + (49x^2 - 14x) = 0. This is very different from your simplistic 7x + 7 example. The analogy is not close. You cannot use something that you believe to be true for 7x + 7 and apply it immediately to (5b_1(x) + 7). There are too many important dissimilarities. > In the other you have b_1(x), a non-linear function defined in a > fairly clever way using what I call a quadratic generator. Ergo, the argument then is over whether or not a*(f(x) + b) = a*f(x) > + > a*b varies because of the ***function*** as there is no argument that > given 7(x^2 + 3x + 2) = (7x + 7)(x+2) it's ludicrous to claim that x=0 is different from x=1, or x equal > any > other value. > Saying something is ludicrous is not a proof. You know that. > So mathematical logic is firmly on my side, You could not be more wrong. > and it IS a case of > people > arguing against the distributive property, but of course, that is > clearly nonsensical so they misrepresent what they are doing. > The basic messages here are: 1. State a DEFINITE THEOREM regarding your factorization of 7(x^2 + 3x + 2) in the complex plane. 2. Show how you transition this theorem from the complex plane to other rings. 3. True or false: a) In the complex plane, there is ONLY ONE way to distribute 7 among the linear factors on the right side of the equation: 7*(x^2 + 3x + 2) = 7(x + 1)*(x + 2). True or false? b) True or false: Any theorem that is true in the complex plane must also be true in any subring of the complex plane. True or false? c) True or false: You believe that your argument contradicts Galois theory and Dedekind's theorem regarding greatest common divisors in the ring of algebraic integers. True or false? d) True or false: You can always rely on factorization by inspection. It always works. True or false? e) True or false: when you distribute 7 among the two parentheses in the expression 7(x + 1)*(x + 2) it cannot be dependent on the value of x. True or false? Proof? f) True or false: The following distributions of 7 among the two factors are NOT valid in the complex plane: 7(x + 1)*(x + 2) = (x + 1)*(7x + 14) 7(x + 1)*(x + 2) = (sqrt(7)x + sqrt(7) * (sqrt(7)x + 2sqrt(7)) 7(x + 1)*(x + 2) = (a*x + a)*(b*x + b) where a*b = 7. 7(x + 1)(x + 2) = (a(x)*x + a(x))*(b(x)*b + 2b(x)) where a(x)*b(x) = 7 What does valid mean? You have been vague and nospecific in all your recent posts on this topic. It is time to stop that. Put it in the language of physics: state testable hypotheses; make testable statements. Otherwise we are just talking semantics and word games. Marcus. > James Harris === Subject: =?GB2312?Q?I_Isaac_Newton=A3=AC=A1=B6With_Israel_nation_in_Western_Eu?= =?GB2312?Q?rope_during_the_nation=A1=B7?= posting-account=ZlGCvQoAAAATD726Ltb7kS8_LJmQ9GM- Presto/2.1.1, DynaWeb http://www.dit-inc.us/disclaimer.php,gzip(gfe),gzip(gfe) This should be my last time in the voice of Radio Free Asia, the following information than the Dead Sea Scrolls, found that the more important, I have no doubt that the existence of a harbinger, allow me to get well prepared for the rapidly after the finish. I Birth to death as early as 500 years ago was full of prophecy, I do not think I have the ability to say here's a lie. Prophet predicted that the major Israeli history has occurred, they have all been in me all come true, I really Is that all Jews have been waiting for the Messiah, Jesus the son of evil aliens to take my name came to the use of high technology to deceive all the people, so that the Jewish nation cast a unredressed injustice, which as early as before Christ Written on after the Bible Code in the. I have never been a Christian, I do not believe in Jesus has always been, I am not a Muslim, I never Jiubu Xin Mohammed. I was discriminated against Jews because they Offended God, God abandoned the law in the near future to become the king of the Jews and I certainly will be in accordance with God's will you come back to correct. I like the psychological and moral England with a person exactly the same, but it is in the soul The result, it is entirely in religious beliefs other than. Jesus, Muhammad two big liar distorts the image of God and humanity and the contract, God is never to use intermediaries, God is there is no body of the supernatural With the strength of a miracle. Likely in the near future I am going to be a prophet, a great scholar and the king. I really was, Old Testament and all of the century and John Apocalypse and after the Bible Code by Prophecy, the prophets also predicted that in the future since ancient times to no one's reputation can be compared with me. Israel's many prophets have long predicted that the metaphorical to my life, the people of Israel, and so I surpass the 3000 , Who in the end I up to now, these four books, as predicted by the can, for my safety, I can only tell you all come true in me, and I was all century, predicted that into the grave again To the people, therefore, have to say that my life is totally your year. Prophets of Israel is usually around things metaphorical familiar with the way God communicated to us in the Old Testament by the book To see things are metaphorical. Dead Sea Scrolls, predicted that the Messiah is a very strong power of the Messiah, the facts have proven that Jesus is only so-called alien made out of a God, is Without thinking of the so- called alien in accordance with the literal interpretation of the creation of a big liar, by the so-called Virgin born and the bar is a serious departure from the hands and feet, the Dead Sea Scrolls, the so-called Christ's true, the Dead Sea Scrolls, predicted In fact metaphorical point to me, I will explain to you to listen to; in the Dead Sea Scrolls, predicted that will lead to all of the Jewish king was referring to me, Ma predicted to spend is the so-called The alien masterpiece, John Apocalypse, the authors we will never know his true identity, but he must not believe Jesus was a Jewish prophet, he is not written in Jesus before. In addition to the John Apocalypse , New is not credible, it repeats the Dead Sea Scrolls, a lot of content, should be John Apocalypse and all of the century and Where Paul Huang predicted that the first into the Dead Sea Scrolls, will be composed of books that they can be referred to as the Bible. Maya from the books, I think the so-called ancient alien is subject to the punishment of God, fled to the vicinity of the Earth, large- scale can not breed, can not be Re-adapt to the environments of the Earth's ancient humans, they must be back at the Earth from time to time to supply the needs of the Earth is the only supplies they needed, the extinction of species on Earth, they can not survive; it is not human They are the so-called build-out. Darwin once said, as long as there is a discovery of biological evolution in the body can not get the small parts, then his theory of evolution completely bankrupt, modern science has proven that the theory of evolution is wrong. Indeed, human Is created by God, God is there is no physical force and the supernatural miracle, because God promised in the universe formed a protein component, to land on Earth, to have had a wonderful variety of biological machine, and then miraculously To produce a variety of species of DNA, culminating in a variety of species; As this is miraculous, I can assure you that life on Earth in the universe is indeed unique. Reference from the Falun Gong cult Toru save the world poem. Zhu century in a poem: After 500 years of attention to the people of the world, his presence is an honor that era, the great moment of inspiration in the emergence of the century with the people who have been great to meet. Now that I do in the full do not know of any predictions that I said to you in the end who, while a few months later I found that as early as in a long time ago and I have long predicted would be his own regeneration, and all of my life long ago In my records, as defined under the Bible. Appearance from the point of view, I would definitely not a personal copy, I met the teachings of Judaism, I was absolutely out at the so-called alien unexpected. I advocate Fate by the day, into the subject, predicted the existence of what I did not constitute any impact. I just did not say what, in a long time ago I spent more than 50 years, to break the Old Testament and All the prophets predicted, I lost the memory of the past, now I really do not know what I[CapitalEth]«'è[CapitalEth][Copyrigh t].b2Ì«, I finally know that I was his, which took place from me as a miracle, and this Long hidden miracle in my writing, as defined under the Bible, I will explain to you listen to, no one is better qualified than I see before me in the I think, actually Adopted did not dare open a large number of these books, the Vatican's religious leaders have long known but Jesus was a liar and who I am. There is no doubt that faith in God is my whole life, in accordance with the Old Testament And so on, as provided for in the book of God, the Jews must enact cream for my King of the Jews, I have to be in accordance with God to the people of Israel to come back to correct; I am really looking forward to is that the Jews have been the Messiah, I must abide by God's will A strong Israel, all without leaving a Muslim expelled from the Palestinian land, and lead you to the upcoming terrorist deal with a major disaster. More than in October 7, 2008 in the world can listen to, but I was referring to Chinese, and with very large disturbance, as will be your king, who will have no power over the content does not Open,Otherwise, my father, the Lord God will punish him, I have to Easter in his capacity as the revived. === Subject: Re: D1 polytope posting-account=cvz5-QoAAABVNzogw177Plx_25TguPUZ .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; InfoPath.2),gzip(gfe),gzip(gfe) > Is a line segment considered a 1-dimensional polytope? Axel, A line segment is not a polytope in one dimension. The end points of a line segment is. Just as a triangle consists of its sides and not its interior, a 1-D polytope consists of the end points of a line segment, but not the points between those segments. - MO === Subject: Re: D1 polytope beeworks@hotmail.com a .8ecrit : > Is a line segment considered a 1-dimensional polytope? Axel, A line segment is not a polytope in one dimension. The end points of > a line segment is. Just as a triangle consists of its sides and not > its interior, a 1-D polytope consists of the end points of a line > segment, but not the points between those segments. > Perhaps you should check before answering (or read the whole thread)... > - MO === Subject: Re: D1 polytope <49536d92$0$28670$7a628cd7@news.club-internet.fr> posting-account=cvz5-QoAAABVNzogw177Plx_25TguPUZ .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; InfoPath.2),gzip(gfe),gzip(gfe) On Dec 25, 6:25am, Denis Feldmann Is a line segment considered a 1-dimensional polytope? > Axel, > A line segment is not a polytope in one dimension. The end points of > a line segment is. Just as a triangle consists of its sides and not > its interior, a 1-D polytope consists of the end points of a line > segment, but not the points between those segments. Perhaps you should check before answering (or read the whole thread)... > - MO- Hide quoted text - - Show quoted text - Perhaps. Mariano asked a question whose answer would indicate that a 1-D polytope is just two points. But then Axel responded by saying he was not a mathematician. Which indicated to me that he was looking for an intuitive answer to his question, rather than a formal one. David chimed in nicely by writing (allow me to paraphrase) that if Axel was using the term polytope he should know the definition of it. Well, that did not seem to me to be of much help, because it seemed that Axel was seeking to check on his understanding of the definition of polytope. Spudnik's third reply seem to offer some correct and more or less relavent information, but again, like Mariano's, it was steeped in formal mathematical jargon rather than offering an intuitive answer. In reply to Mariano's third reply, Axel reitierated that he is not a mathematician, and indicated that he was looking for an intuitive answer. So I offered an intuitive answer that was the Polytopes for Dummies version of Mariano's. - MO === Subject: Re: D1 polytope beeworks@hotmail.com a .8ecrit : > On Dec 25, 6:25 am, Denis Feldmann beewo...@hotmail.com a .8ecrit : > Is a line segment considered a 1-dimensional polytope? > Axel, > A line segment is not a polytope in one dimension. The end points of > a line segment is. Just as a triangle consists of its sides and not > its interior, a 1-D polytope consists of the end points of a line > segment, but not the points between those segments. > Perhaps you should check before answering (or read the whole thread)... > - MO- Hide quoted text - > - Show quoted text - Perhaps. Mariano asked a question whose answer would indicate that a > 1-D polytope is just two points. But then Axel responded by saying he > was not a mathematician. Which indicated to me that he was looking > for an intuitive answer to his question, rather than a formal one. > David chimed in nicely by writing (allow me to paraphrase) that if > Axel was using the term polytope he should know the definition of > it. Well, that did not seem to me to be of much help, because it > seemed that Axel was seeking to check on his understanding of the > definition of polytope. Spudnik's third reply seem to offer some > correct and more or less relavent information, but again, like > Mariano's, it was steeped in formal mathematical jargon rather than > offering an intuitive answer. In reply to Mariano's third reply, Axel > reitierated that he is not a mathematician, and indicated that he was > looking for an intuitive answer. So I offered an intuitive answer that was the Polytopes for Dummies > version of Mariano's. - MO Except your answer is wrong (or at least doesn't agree with the usual definition, which is anyway easier) : polytopes should be convex hulls , not skeletons, or more generally objects of the same dimension that the embedding space, not one lower. Otoh, it is hard to define, say, concave polyhedrons that way, and next, we enter the simplicial complex definitons, which are surely not appropriate for a beginner :-) === Subject: Re: D1 polytope <49537575$0$28669$7a628cd7@news.club-internet.fr> posting-account=cvz5-QoAAABVNzogw177Plx_25TguPUZ .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; InfoPath.2),gzip(gfe),gzip(gfe) On Dec 25, 6:58am, Denis Feldmann On Dec 25, 6:25 am, Denis Feldmann beewo...@hotmail.com a .8ecrit : > Is a line segment considered a 1-dimensional polytope? > Axel, > A line segment is not a polytope in one dimension. The end points of > a line segment is. Just as a triangle consists of its sides and not > its interior, a 1-D polytope consists of the end points of a line > segment, but not the points between those segments. > Perhaps you should check before answering (or read the whole thread)... > - MO- Hide quoted text - > - Show quoted text - > Perhaps. Mariano asked a question whose answer would indicate that a > 1-D polytope is just two points. But then Axel responded by saying he > was not a mathematician. Which indicated to me that he was looking > for an intuitive answer to his question, rather than a formal one. > David chimed in nicely by writing (allow me to paraphrase) that if > Axel was using the term polytope he should know the definition of > it. Well, that did not seem to me to be of much help, because it > seemed that Axel was seeking to check on his understanding of the > definition of polytope. Spudnik's third reply seem to offer some > correct and more or less relavent information, but again, like > Mariano's, it was steeped in formal mathematical jargon rather than > offering an intuitive answer. In reply to Mariano's third reply, Axel > reitierated that he is not a mathematician, and indicated that he was > looking for an intuitive answer. > So I offered an intuitive answer that was the Polytopes for Dummies > version of Mariano's. > - MO Except your answer is wrong (or at least doesn't agree with the usual > definition, which is anyway easier) : polytopes should be convex hulls > , not skeletons, or more generally objects of the same dimension that > the embedding space, not one lower. Otoh, it is hard to define, say, > concave polyhedrons that way, and next, we enter the simplicial complex > definitons, which are surely not appropriate for a beginner :-)- Hide quoted text - - Show quoted text - My understanding is that a triangle is three connected line segments and does not include its interior. You are telling me that a three- sided polygon is a triangle ~and~ its interior, rather than just the triangle. Is that right? === Subject: Re: D1 polytope posting-account=x5CZsAoAAADQB5YGnbi790y2igTGpwCe Gecko/20081216 Ubuntu/7.10 (gutsy) Firefox/2.0.0.19,gzip(gfe),gzip(gfe) > [ ... ] anyway, since a common definition of convex hull, > is just that any line between two points > of the space, is contained within the space, > the segment is just a trivial.degenerate case > of that. like that. As for the other two, thank you also but you could have responded less cattily. === Subject: Re: D1 polytope posting-account=9QOSvAoAAACEOWJVSDuswW7dB_0wApQO Gecko/2008111217 Fedora/3.0.4-1.fc9 Firefox/3.0.4,gzip(gfe),gzip(gfe) > [ ... ] > anyway, since a common definition of convex hull, > is just that any line between two points > of the space, is contained within the space, > the segment is just a trivial.degenerate case > of that. like that. As for the other two, thank you also > but you could have responded less cattily. One of the standard definitions of polytope is closed convex hull of a finite set of points in R^n. original question, are essentially irrelevant) If you understand the terms appearing in that definition, it is rather unlikely you will not know whether a segment is a polytope or not: on one hand, it is unthinkable that anyone can have been introduced to the definition of convex set and not know that a segment is convex, and it is unthinkable that anyone can have been introduced to the definition of convex hull and not know that a segment is the convex hull of the set of its endpoints. My first answer to you was the standard answer which essentially means you can answer the question yourself: simply check that the definition applies to the case at hand---the analogue of teaching how to fish---which is only of use, of course, if you know the definition. You then asked for clarification: but you did not specify if your need for clarification stemmed from your not knowing what the definition of a polytope is or from your not knowing how to check whether the definition of polytope applied to the specific case you had. Without knowing which of these two alternatives held, it was simply impossible to provide any amplification. Maybe you could be better at asking questions? -- m === Subject: Re: D1 polytope posting-account=x5CZsAoAAADQB5YGnbi790y2igTGpwCe Gecko/20081216 Ubuntu/7.10 (gutsy) Firefox/2.0.0.19,gzip(gfe),gzip(gfe) On Dec 25, 5:43 am, Mariano Su.87rez-Alvarez > [ ... ] > anyway, since a common definition of convex hull, > is just that any line between two points > of the space, is contained within the space, > the segment is just a trivial.degenerate case > of that. > like that. As for the other two, thank you also > but you could have responded less cattily. One of the standard definitions of polytope is > closed convex hull of a finite set of points in R^n. > original question, are essentially irrelevant) If you understand the terms appearing in that definition, > it is rather unlikely you will not know whether > a segment is a polytope or not: on one hand, it is > unthinkable that anyone can have been introduced to > the definition of convex set and not know that a > segment is convex, and it is unthinkable that anyone > can have been introduced to the definition of convex > hull and not know that a segment is the convex hull > of the set of its endpoints. My first answer to you was the standard answer which > essentially means you can answer the question yourself: > simply check that the definition applies to the case > at hand---the analogue of teaching how to fish---which > is only of use, of course, if you know the definition. > You then asked for clarification: but you did not > specify if your need for clarification stemmed from > your not knowing what the definition of a polytope is > or from your not knowing how to check whether the > definition of polytope applied to the specific case > you had. Without knowing which of these two alternatives > held, it was simply impossible to provide any amplification. Maybe you could be better at asking questions? -- m Mariano, you have to be aware of the difference between your technical vocabulary and that of an ordinary literate person. To me the word convex conveys absolutely nothing similar to a line segment. So I retract my comment. You are not catty; you are, however, too inflexible in your approach to the English lexicon. === Subject: Re: D1 polytope posting-account=jPnQ2goAAAA461y3QD0lbyw0oKeThma1 AppleWebKit/525.18 (KHTML, like Gecko) Version/3.1.2 Safari/525.20.1 FOH:R051,gzip(gfe),gzip(gfe) http://golem.ph.utexas.edu/category/2008/11/the_case_of_m_s_el_naschie.html http://xaravve.trentu.ca/330/Notes/notes.pdf > There are two possibilities: --only 24 hours to impeach Trickier Dick from the N.Admin, metaphorically typing, or Cheeny & Zbiggy, fo'mo' years; Good Morning, Afghanistan! ... Good Afternoon, Sudan! http://tarpley.net/bush12.htm http://wlym.com/campaigner/8011.pdf -- Brits hate Shakes, Why? http://www.wlym.com/~seattle/dynamis/ http://www.21stcenturysciencetech.com/current.html http://www.rwgrayprojects.com/synergetics/plates/plates.html http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=3163 http://wlym.com/campaigner/8011.pdf -- English, not! === === Subject: Re: it is the OUTER force that causes the INNER mass to accelerate > the first law says: subjected to zero outer force the weight tends to > preserve its uniform none accelerated motion i.e. travel with constant > velocity or rest. the second law says: when subjected to OUTER force > the weight accelerates proportionally to that force and reciprocally > to its INNER mass. the gravity law says: massive objects exert > gravity forces on each other proportional with the product of the > masses and reciprocal with the square distance between them. let me > go backwards: F1 R1 R1 / M1 = g M = F2 R2 R2 / M2 that is the gravity > . it splits on two equations: [(F1/F2=R2/R1) and (M2/M1=R2/R1)] > which can be unified in one double equation: F1/F2=M2/M1=R2/R1. so the > second flaw defends that: F1 = a2 M2 and F2 = a1 M1 cause it is the > OUTER force that makes the INNER mass accelerate not F1 = a1 M1 and F2 > = a2 M2 as it is widely practiced. but if it is so then the > elimination of them indexes requires that: (F1 a1 M1 = Constant = F2 a2 M2) so what will be the new formulation of the second ty flaw? the > product of force, mass and acceleration of every object is the same. > what a nonsense, but that is how it is with newton doing physics. go > baby... -------------------- there are a few possibilities to see it but you overlooked the best one!! it is not F=gamma xm it is F/gamma = m and m is constant!! (copyright Y.Porat long ago ) just stick it (you and all the other parrots) into your heads !! m remains constant and more important THERE IS JUST ONE KIND OF MASS! no matter how you will call it !! btw i dont think that in Newtons times anyone was thinking at all about any 'Gamma factor ' ie some magnifying factor . the gamma' can only at the 20 th century ATB Y.Porat ------------------------- === Subject: Re: it is the OUTER force that causes the INNER mass to accelerate posting-account=5GUrzQkAAADun29oaK3p_W_saUVxxHUF Gecko/2008120122 Firefox/3.0.5,gzip(gfe),gzip(gfe) > the first law says: subjected to zero outer force the weight tends to > preserve its uniform none accelerated motion i.e. travel with constant > velocity or rest. the second law says: when subjected to OUTER force > the weight accelerates proportionally to that force and reciprocally > to its INNER mass. the gravity law says: massive objects exert > gravity forces on each other proportional with the product of the > masses and reciprocal with the square distance between them. let me > go backwards: F1 R1 R1 / M1 = g M = F2 R2 R2 / M2 that is the gravity > . it splits on two equations: [(F1/F2=R2/R1) and (M2/M1=R2/R1)] > which can be unified in one double equation: F1/F2=M2/M1=R2/R1. so the > second flaw defends that: F1 = a2 M2 and F2 = a1 M1 cause it is the > OUTER force that makes the INNER mass accelerate not F1 = a1 M1 and F2 > = a2 M2 as it is widely practiced. but if it is so then the > elimination of them indexes requires that: > (F1 a1 M1 = Constant = F2 a2 M2) > so what will be the new formulation of the second ty flaw? the > product of force, mass and acceleration of every object is the same. > what a nonsense, but that is how it is with newton doing physics. go > baby... > -------------------- > there are a few possibilities to see it > but you overlooked the best one!! > it is not > F=gamma xm > it is > F/gamma = m > and m is constant!! > (copyright Y.Porat long ago ) > just stick it (you and all the other parrots) > into your heads !! > m remains constant > and more important > THERE IS JUST ONE KIND OF MASS! > no matter how you will call it !! > btw > i dont think that in Newtons times > anyone was thinking at all about any > 'Gamma factor ' > ie some magnifying factor . > the gamma' can only at the 20 th century > ATB > Y.Porat > ------------------------- F/gamma = m is no good cause F and m > don't belong to same object!!! > My(F)/Ur(M)=Ur(Accel); Ur(F)/My(M)=My(Accel) > the point of gravity is so as well: > My(F)/Ur(F)=Ur(M)/My(M)=Ur(R)/MY(R). > i cannot subject my own self to my own force > it would be ridiculous. if it is rediculous by you it is only for you fo rme youare rediculous because you could not understand what i presented to you and because you are not able to digest something that you never tought above before the formulaF=gamma m a is a mathematical formula andno one can tell me that i cannot present it in a different way than the common as long a sit is the same algebraic formula but here comes the physicist and i hope you got it at last that mathematics in mathematics and physics is physics and a mathematicsl formula can surprisingly have two PHYSICAL meanings it is the task of the good physicist todecide wich is closer to reality sometimes you need creative immaginationfor that sometimes you must have a much reacher physical experience and knowlwdge to make a revolutionary insight of a formula that no one could see it even if surprisingly simple (simplicity in physics is not a disadvantage) myinterpretation prevents the need as in your case TO INVENT A NEW AD HOCK KIND OF MASS !! (the simper the better said Occam s razor !!) got the difference between my suggestion and yours ???!!! ----------------- ------------ by the way: > what will be the mass of an oscillatory > weight? the Libra always shows the mass. > even when the weight is not resting on it. > or would you say the weight being naughty > turns the Libra off, so that case doesn't count btw just think about how forces are acting they act by force agents that attack the acted mass and keep in mind tha they might have A LIMITED VELOCITY ABILITY !! so in order to add more and more driving force you need more force agents untill no more force can help because the velocity of acted mass becones as the velocity of the acting force agents and the force agents cannot haunt their acted object (it seesm that you have never was old enough and poor enough to push an old car that does not ignite !! (:-). and at last starts to ignite so please have some respect to pld poor people (:-) they might have forgotten things that you have not been there yet . have you ever studies dynamics?? they know to handle the same mass in a dynamic situation it remains always the same mass yet the laws of dynamics are not always the laws of statics ATB Y.Porat ------------------------ === Subject: Re: E=MC**2 expressed as Venn Diagram (See Attached Graphic) > Math. Forum: I think I expressed the famous equation better this > time. C**2 is the intersecting event of the two > items; Matter and Energy. > The constant c does not have an independent existence; it is a mathematical artifact. The meaning of Einstein's equation is just E=M, i.e., (rest) mass and energy are equivalent. The constant explains the proportional relation between the states of matter, and sets an absolute limit on the velocity of mass. Tom > I use this same concept of expressing Items and > Events and their intersections giving a limited > Quantitative and Qualitative Constant, in other > general objects. Such as Apples, Pears, Oranges and > Fruit. See some more of my work at my site link at: http://www.zimmathematics.com/htm/application_Page_2.h > tm#ItemsEvents Zim Olson > Creative Mathematics > http://www.zimmathematics.com === Subject: x^2-py^2 = q, x^2-qy^2 = p posting-account=-ACVjwoAAAAVqSiDl929-Pe1jSK2zs-Q FunWebProducts; GTB5; .NET CLR 2.0.50727; .NET CLR 1.1.4322; .NET CLR 3.0.04506.30),gzip(gfe),gzip(gfe) Hi all, Let p and q be _positive_ integers, both _not_ squares. If x^2-py^2 = q has a solution in integers, then so does x^2-qy^2 = p. Is it true or not? Example: x^2-19y^2 = 5 has {x,y} = {9,2} x^2-5y^2 = 19 has {x,y} = {8,3} Background: I'm trying to solve a particular x^2-py^2 = q which has no soln with y < 10^5. This belongs to a family which conjecturally _has_ solns, so I'm supposing y is just large. However, x^2-qy^2 = p has relatively small solutions, so if the statement given earlier is true, then I'll know my original equation has a soln also. Tito === Subject: Re: x^2-py^2 = q, x^2-qy^2 = p Let p and q be positive integers, both not squares. If x^2-py^2 = q has a solution in integers, then so does x^2-qy^2 = p. Is it true or not? Check out quadratic reciprocity - that will get you started. -- GM === Subject: Re: Bochner's tube theorem >For any readers who haven't seen the paper: Actually those are >fairly thick line segements, aka rectangles. He shows that a domain that contains the convex hull of all crossed line segments contained in it is convex. But that's equivalent to containing the convex hull of all crossed rectangles contained in it. crossed rectangles being two rectangles crossing at right angles, with their centers at the same point. Maybe running into a conflicting definition when you're extending the function isn't a problem. Even if the intersection of the domain with the convex hull of a cross is disconnected, any two components are connected by a path in the domain. The path can be made simple. It's compact, so it's covered by a finite number of balls contained in the domain. So line segments between the centers of the balls are contained in the domain. And a tube of some radius around the simplified path, which is just joined line segments, is contained in the domain. So maybe an analytic function on the tube can be extended by this process of taking the convex hull of crossed rectangles. Then because an analytic extension is unique, you can't run into a conflicting definition when extending the original domain. Laura === === Subject: Question on expansion in differentiation I have been told in a physics class the following: ih*d/dx(x*f(x)) = f(x) + x*(df/dx)*ih That is, ih (or whatever) times the derivative of the product x times a function, expands to that function plus x times the derivative times ih. The first part I understand - we multiply d/dx by x and get dx/dx or one times the function. But then where does the + come from? When you multiply a*(b*c), isn't it as simple as a*b*c? Something special about the derivative d/dx that acts different than a number multiplying? === Subject: Re: Question on expansion in differentiation This is a long explanation that contains a lot of information. I've tried to explain this rule in a way that makes it fairly clear intuitively, and as a result easier to remember, but you need to follow each step. This does not read like a novel - you need to work on understanding it in detail. > I have been told in a physics class the following: ih*d/dx(x*f(x)) = f(x) + x*(df/dx)*ih That is, ih (or whatever) times the derivative of > the product x times a function, expands to that > function plus x times the derivative times ih. This is mostly true, although I think the ih term should be multiplied by the f(x) as well. However, let's leave that alone for the moment. Your basic misconception is that d/dx is simply a fraction. This misunderstanding is common and, in my opinion, understandable. The notation itself is almost designed to mislead, and is deeply unfortunate. However, history has given us the notation, and you will need to learn it. Think of d/dx as a single, indivisible symbol. In some areas of mathematics it is not used and a single symbol is used exactly for this reason. However ... d/dx represents a transformation of a function. It takes one function, say f(x), and in return gives you another that tells you how fast f(x) changes as x changes. In particular, you have the case of finding how much a product changes based on how much the parts of it change. The rule is simple when you can see where it comes from. Take a rectangle of size a by b. The area is ab. Now ask, if we vary a and b by small amounts, how much does the area change? The area to start is: A(a,b) = ab If we add a tiny amount, e, to a, then the area changes to (a+e)*b, which is an increase of e*b. If we add a tiny amount, f, to b, then the area changes to a*(b+f), which is an increase of a*f. If we add a tiny amount, e, to a, and we add a tiny amount, f, to b, the area is now: A(a,b,e,f) = (a+e)*(b+f) = ab + af + be + tiddly. As you can see, the amount of change from ab is af+be plus an amount that's really, really small, and we'll ignore it. So the change is effectively af + be. That's the value of a times the change in b, plus the value of b times the change in a. Read that again and again and again, and see how it follows from what I've written so far. Now let's put that into the context of calculus. Suppose we have f(x)*g(x). How does this change as we vary x by a small amount? Using the notation of CNG[.] to represent rate of change of something, we have: CNG[ f(x)*g(x) ] = f(x)*CNG[g(x)] + CNG[f(x)]*g(x) Now we can put that into the more usual notation: d/dx[ f(x).g(x) ] = f(x).[d/dx g(x)] + [d/dx f(x)].g(x) In your original we can define g(x)=x, so (ignoring the ih) then becomes: d/dx( f(x)*x ) = f(x).(d/dx x) + (d/dx f(x))*x I'm still ignoring the ih. Finally, the derivative of x is simply 1, and as a potentially confusing notational convenience, the derivative d/dx f(x) is often written as df/dx. That means you can see that this is what you were told. d/dx(x*f(x)) = f(x).(d/dx x) + (d/dx f(x))*x and that simplifies to f(x) + (df/dx)*x, as required. Another poster has commented about the ih and where it should go. I think you need to check your notes about that. I hope that helps. === Subject: Re: Question on expansion in differentiation posting-account=K5WE3woAAAAXArsybjkbN6LjMxWdHtbX Gecko/20081217 Firefox/2.0.0.20,gzip(gfe),gzip(gfe) > I have been told in a physics class the following: ih*d/dx(x*f(x)) = f(x) + x*(df/dx)*ih That is, ih (or whatever) times the derivative of the product x times > a function, expands to that function plus x times the derivative times > ih. The first part I understand - we multiply d/dx by x and get dx/dx or > one times the function. But then where does the + come from? When > you multiply a*(b*c), isn't it as simple as a*b*c? Something special > about the derivative d/dx that acts different than a number > multiplying? NO, absolutely not: the derivative, (d/dx)F(x) = dF(x)/dx of a function F(x) is defined as the limit of [F(x+r) - F(x)]/r when r ---> 0. Note that if you draw a graph of y = F(x) and look at the difference quotient [F(a+r) - F(a)]/r (for nonzero r), this is just the slope of the line through the two points (x1,y1) = (a,F(a)) and (x2,y2) = (a+r,F(a+r)) on the graph (one point at z = a on the graph, the other at x = a+r on the graph). In the limit as we take r --> 0, we get the slope of the tangent line to the graph y = F(x) at the point (a,F(a)). Anyway, the so-called product rule states that d[f(x) *g(x)]/dx = f(x)*dg(x)/dx + g(x)*df(x)/dx, and that is fairly easy to prove just from the definition of a derivative. So, you have (d/dx)(x*f (x)) = (dx/dx)*f(x) + x*df(x)/dx, and it is easy to see (from the definition) that dx/dx = 1. Note: this is NOT a ratio of two numbers dx and dx---there are no such numbers--- it is just a notation for the derivative. Anyway, as far as I can see you are missing a factor ih in the first term (that is, you should have ih*f(x), not f(x)). R.G. Vickson === Subject: Re: Question on expansion in differentiation > I have been told in a physics class the following: > > ih*d/dx(x*f(x)) = f(x) + x*(df/dx)*ih > > That is, ih (or whatever) times the derivative of the product x times > a function, expands to that function plus x times the derivative times > ih. Are you sure you were not told something slightly different, such as ih * d/dx(x * f(x)) = ih * (f(x) + x * d/dx(f(x))) === Subject: I really Newton, I will not be on this account and mailbox, or the Chinese government will absolutely kill me! posting-account=ZlGCvQoAAAATD726Ltb7kS8_LJmQ9GM- User-agent: Mozilla/4.0 (compatible; MSIE 6.0; Windows NT 5.1; SV1; http://bsalsa.com) ; .NET CLR 1.1.4322; TheWorld), DynaWeb http://www.dit-inc.us/disclaimer.php,gzip(gfe),gzip(gfe) John Apocalypse in the city of Babylon is referring to China, the so- called devil, evil dragon, Satan is referring to China and the Communist Party of China, I call for a whole year to Radio Free Asia, has exposed the dark side of the huge, Europe and the United States Government to force The Chinese government trade and industry and a comprehensive overhaul of the anti-corruption, because of my presence, to prevent the advent of World War III, otherwise the atomic bomb as early as the destruction of human beings, all have long records in the Apocalypse, Ezra book, All of the century , I will never again on this account and mailbox, I have the world number one Chinese government would like to kill people. Please keep in mind that the end of the world humanitarian cause by the Chinese government to launch Taiwan Caused by a missile! === Subject: Re: Bochner's tube theorem Also, if the tube domain is in n-dimensional complex space, n > 2, and you want to continue an analytic function on the domain to the convex hull of a cross contained within the base of the domain (the base is the subset of the domain with all real coordinates) - the analytic function had better be extended to an open set. Thus for n > 2, the cross has to have some thickness in the other dimensions also. He didn't show that you could extend the function analytically from a cross shaped domain that has thickness in n-space to its convex hull. You could extend it from each 2D slice, but how do you know the resulting function is analytic in n-space? Well I switched over to Hormander's book for right now, he has a proof of Bochner's tube theorem. Maybe this one works! Laura === Subject: Re: A Discrete Probability Distribution consider an urn containing N marbles, and suppose > that > m of them are white and N-m are black. Now imagine > to draw all the marbles without replacement. Define > a > random variable X as the place of the first white > marble in the sequence you obtained. It's quite > easy to find P(X=k), with k=1,...,N-m+1 P(X=k) = [(N-m)/N]*[(N-m-1)/(N-1)]*... > *[(N-m-k+2)/(N-k+2)]*[m/(N-k+1)] and it's easy to check that P(X=k) = [((N-k) choose (N-m-k+1))]/(N choose > (N-m)) The problem is: how to find the mean and the > variance > of X? > Do you know the name of the distribution of X? Let Y_j = 1 if the first j marbles are all black, 0 > otherwise, > so X = 1 + sum_{j=1}^{N-m} Y_j. > E[Y_j] = P(Y_j = 1) = (N-m choose j)/(N choose j) > E[X] = 1 + sum_{j=1}^{N-m} (N-m choose j)/(N choose > j) > = (N+1)/(m+1) according to Maple Similarly, > E[(X-1)^2] = sum_{i=1}^{N-m} sum_{j=1}^{N-m} E[Y_i > Y_j] > > Now Y_i Y_j = Y_j if i <= j. So this is sum_{i=1}^{N-m} (2i-1) E[Y_i] = > (2N-m)(N-m)/((m+2)(m+1) > again according to Maple. That makes E[X^2] = (2N-m+2)(N+1)/((m+2)(m+1)) > and Var(X) = E[X^2] - E[X]^2 = (N+1) m > (N-m)/((m+2)(m+1)^2) > -- > Robert Israel > israel@math.MyUniversitysInitials.ca > Department of Mathematics > http://www.math.ubc.ca/~israel > University of British Columbia Vancouver, > BC, Canada I found a proof of these relations using the induction principle, the identity (N-m choose j)/(N choose j) = (N-j choose N-m-j)/(N choose N-m) and the well known fact (n choose k) = (n-1 choose k) + (n-1 choose k-1) But I'm quite incredulous! How could Maple calculate the sums above? Anyhow, thank you very very ... much prof. Israel! Maury barbato === Subject: [ OT ] history of science: cases of mainstream in error I'm interested in compiling a list of cases in the history of science where the mainstream view was in error in a period when the mainstream was challenged, where mainstream means natural philosophers, physicists, biologists, etc. For example, in an other thread, I mentioned that physicists gave a low maximum age to the sun before radio-activity and nuclear reactions were discovered, which was in quite sharp disagreement with estimates from earth scientists for time needed to form of the Grand Canyon [ this may or may not have been a point of disagreement, because it depends on what geologists theorized or knew about its formation ] , and a large amount of fossil evidence, volcanoes, mountain formation and erosion, sedimentation, and all else that geologists study ]. Another case: in biology, Lamarck had a theory of spontaneous generation of life: so mold could form in a closed jar without any seed form of life, in this theory. Same for colonies of bacteria. Pasteur proved it false, if I've got the story right. David Bernier === Subject: Re: history of science: cases of mainstream in error posting-account=Z9v8GgkAAAB54xGwWI4tZlTl3U6kju-g Gecko/2008102920 Firefox/3.0.4,gzip(gfe),gzip(gfe) > I'm interested in compiling a list of cases in the history > of science where the mainstream view was in error in a period > when the mainstream was challenged, where mainstream means > natural philosophers, physicists, biologists, etc. David Bernier All the History of Science is the relate of the changes of paradigms. The immovility of the Earth, the impossibility of emptiness, the aristotelian concept of motion etc etc Ludovicus === Subject: Re: E=MC**2 expressed as Venn Diagram (See Attached Graphic) > Math. Forum: I think I expressed the famous equation better this > time. C**2 is the intersecting event of the two > items; Matter and Energy. I use this same concept of expressing Items and > Events and their intersections giving a limited > Quantitative and Qualitative Constant, in other > general objects. Such as Apples, Pears, Oranges and > Fruit. See some more of my work at my site link at: http://www.zimmathematics.com/htm/application_Page_2.h > tm#ItemsEvents Zim Olson > Creative Mathematics > http://www.zimmathematics.com . Zim is a time traveler !! on the above website he has a picture of himself titled : Zim Olson in 2009 whereas we are still in 2008 !! amazing guy ! tommy1729 -------------------------------------- Tommy1729: Guess I got ahead of myself. Just have a few days to go though. I took the photo a few days ago. You get the picture though. Zim Olson Creative Mathematics http://www.zimmathematics.com === Subject: Re: E=MC**2 expressed as Venn Diagram (See Attached Graphic) > Math. Forum: I think I expressed the famous equation better this > time. C**2 is the intersecting event of the two > items; Matter and Energy. I use this same concept of expressing Items and > Events and their intersections giving a limited > Quantitative and Qualitative Constant, in other > general objects. Such as Apples, Pears, Oranges and > Fruit. See some more of my work at my site link at: http://www.zimmathematics.com/htm/application_Page_2.h > tm#ItemsEvents Zim Olson > Creative Mathematics > http://www.zimmathematics.com The constant c does not have an independent existence; it is a mathematical artifact. The meaning of Einstein's equation is just E=M, i.e., (rest) mass and energy are equivalent. The constant explains the proportional relation between the states of matter, and sets an absolute limit on the velocity of mass. Tom --------------------------------------- Tom: I usually consider Items/Events as going together. What would you consider a lone Event to be in some other case? The speed of light can be considered an event and it is a factor or intersection of Enery and Matter? Your feed back is appreciated. Zim Olson Creative Mathematics http://www.zimmathematics.com === Subject: Re: E=MC**2 expressed as Venn Diagram (See Attached Graphic) > Math. Forum: I think I expressed the famous equation better > this > time. C**2 is the intersecting event of the two > items; Matter and Energy. I use this same concept of expressing Items and > Events and their intersections giving a limited > Quantitative and Qualitative Constant, in other > general objects. Such as Apples, Pears, Oranges > and > Fruit. See some more of my work at my site link at: http://www.zimmathematics.com/htm/application_Page_2.h tm#ItemsEvents Zim Olson > Creative Mathematics > http://www.zimmathematics.com The constant c does not have an independent > existence; > it is a mathematical artifact. The meaning of > Einstein's > equation is just E=M, i.e., (rest) mass and energy > are > equivalent. The constant explains the > proportional relation between the states of matter, > and > sets an absolute limit on the velocity of mass. Tom --------------------------------------- Tom: I usually consider Items/Events as going together. > What would you consider a lone Event to be in some > e other case? The speed of light can be considered an event and it > is a factor or intersection of Enery and Matter? Your > feed back is appreciated. > No, the speed of light is not an event. An event is immortal. As E=mc^2 states, energy and matter (mass) are not two different things that can intersect--they are the same thing. Tom > Zim Olson > Creative Mathematics > http://www.zimmathematics.com === Subject: Re: why does professor david c ullrich have to eat all his greens to lwalke3@lausd.net says... >starting to understand now. And happy holidays, Prof. McCullough! But for the record, I'm not a professor. I'm a knowledgeable amateur at mathematics and logic. -- Daryl McCullough Ithaca, NY === Subject: Re: An exact 1-D limit challenge - 39 (Merry Christmas sin/cos, EllipticF/E) > Ho! Ho! Ho! (<--- stolen from Roman Pearce ;) > u := (1-sqrt(2))*(1-cos(z))/sin(z): > v := EllipticF(I*u, 3 + 2*sqrt(2)): > w := EllipticE(I*u, 3 + 2*sqrt(2)): > f := -I*(-2*I*sqrt(2)*cos(z)^3-2*I*cos(z)^3+2*I*sqrt(2)*cos(z)^2 > +2*I*cos(z)^2+4*I*sqrt(2)*cos(z)+4*I*cos(z)+4*sqrt(sqrt(2)* > cos(z)-cos(z)+2-sqrt(2))*sqrt(4-2*sqrt(2)*cos(z)-2*cos(z)+2 > *sqrt(2))*v*sin(z)-4*I-sqrt(2)*sqrt(sqrt(2)*cos(z)-cos(z)+2 > -sqrt(2))*sqrt(4-2*sqrt(2)*cos(z)-2*cos(z)+2*sqrt(2))*w*sin > (z)-4*I*sqrt(2)+4*sqrt(2)*sqrt(sqrt(2)*cos(z)-cos(z)+2-sqrt > (2))*sqrt(4-2*sqrt(2)*cos(z)-2*cos(z)+2*sqrt(2))*v*sin(z))/ > sqrt(2-cos(z)^2)/sin(z): > limit(f, z = Pi, left); > ( = -18.4455466264368280559709220470526933146161141646893858...) > ? > Merry Christmas, > The most simple result is x ---> 0+ for +(4+2*2^(1/2))/x > -4*I*(2+2^(1/2))*EllipticF(c*I/x,k)+2*I*EllipticE(c*I/x,k), > c:=(2^(1/2)-1)*2^(1/2),k:=3+2*2^(1/2). > However MultiSeries:-series(%, x=0, 2) gives the wrong result Aha, nice to see! A bit of hint: 2*EllipticE(I)/................................ and there is something special in ................................ ;) My solution is w := 2*I*EllipticE(3+2*2^(1/2))+ (-6*I-4*I*2^(1/2))*EllipticE(3-2*2^(1/2)) + (-16+(8+8*I)*2^(1/2))*EllipticK(3-2*2^(1/2)) Using your hint w = 4*EllipticE(I) / q one identifies q as 1 - sqrt(2) (don't know why ...) === Subject: Re: E=MC**2 expressed as Venn Diagram (See Attached Graphic) > Math. Forum: I think I expressed the famous equation better this > time. C**2 is the intersecting event of the two > items; Matter and Energy. I use this same concept of expressing Items and > Events and their intersections giving a limited > Quantitative and Qualitative Constant, in other > general objects. Such as Apples, Pears, Oranges and > Fruit. See some more of my work at my site link at: http://www.zimmathematics.com/htm/application_Page_2.h > tm#ItemsEvents Zim Olson > Creative Mathematics > http://www.zimmathematics.com ---------------------------------------- > Tom: I usually consider Items/Events as going together. > What would you consider a lone Event to be in some > e other case? The speed of light can be considered an event and it > is a factor or intersection of Enery and Matter? Your > feed back is appreciated. > No, the speed of light is not an event. An event is immortal. As E=mc^2 states, energy and matter (mass) are not two different things that can intersect--they are the same thing. Tom ------------------------------------ Tom: Do you think any two objects or Items can have an intersecting Event? Take as example: Apple + Orange + Pear; could you say their intersecting event is maybe Fruit or maybe a Fruit function? Then would you say the Fruit or Fruit function does not exist here also? And is just a mathematical construct? Zim Olson Creative Mathematics http://www.zimmathematics.com === Subject: Re: Can You Handle The Truth? posting-account=suWj4AkAAADE1IvGmj55Nmq3f98qb17e 2.0.50727),gzip(gfe),gzip(gfe) > [snip crap] > The Jews are a dangerously out of control cult who need to be brought > to justice ASAP > The Manhattan Project had more Jews/m^2 than any Nazi concentration > camp. The Jews have always hated the Japanese since Moses led the > Children of Israel to the Far East, as described in the bible, This is more evidence Jews are not smart but a dangerously out of > control cult. Where did Jews get their blue eyes and white skin from? Why haven't Jews bothered to look at the archeological data gathered > from Ancient Egypt to see the Israelite slaves were CLEARLY DEPICTED > as a BLACK RACE from Africa? How smart can someone really be if their cultural belief system is > based on easily falsifiable mythology? Tales of a man Moses who parted a sea, following bizzare rules > imposed by rabbis, rituals of smearing blood on domicile walls from > freshly sacrificed goats on passover and other mythology, practiced > as reality, is CLEAR EVIDENCE of madness, not intelligence. Jews aren't victims, they are aggressors. [...] ************************************************************* Yeah, well....things get better with time, you know? Now it's used xtian children's blood to smear on houses' doors, and we then eat the little kid with fried potatoes and lots of garlic and onions: nothing goes to waste! Oy vey Hannuka Tonio === Subject: Re: Can You Handle The Truth? > The Jews bombed the USS Liberty and covered it up. The Jews framed the Arabs on 911. The Jews lied about the Holohoax and stole billions in fraudulent > compensation. The Jews own the banks and they just stole 9 trillion dollars from the > american sheeple. The monetary system is a gigantic pyramid scheme, where debt is > mathematically impossible to pay off. The Jews are buying up the world for pennies on the dollar now, just > after they crashed the world economy. The Jews are a fanatically racist and bigoted group of people with > deep occultic roots. However, let us not steep to their level by condemning all Jews and > becoming bigots ourselves. Most Jews REALLY BELIEVE they are victims of non-Jews, so they are not > so smart after all. Jews are creationists by definition, so they are not so smart after > all. Jews are totally brainwashed into following bizzare and regulated > rules set by paedophillic rabbis who suck the blood of circumsized > baby dicks during circumcision (THIS IS A FACT WHICH YOU CAN VERIFY). The Jews are a dangerously out of control cult who need to be brought > to justice ASAP Don't be afraid of the Jews, they need your help. Rescue the Jew from his own inbred madness and expose all of the above > to your fellow sheeple. If only The Jews would bomb your house, we wouldn't have to listen to your bigotry any more. Please Jews, bomb his house. === Subject: Re: Can You Handle The Truth? The Jews bombed the USS Liberty and covered it up. > The Jews are a fanatically racist and bigoted group of people > However, let us not steep to their level by condemning all Jews and > becoming bigots ourselves. > Most Jews REALLY BELIEVE they are victims of non-Jews, so they are not > so smart after all. If they stopped their constant whimpering about The Holocaust^tm, and looked at how many other holocausts, some even larger, that have occurred, then perhaps they'd stop their holocaust of the Gaza stript.. > The Jews are a dangerously out of control cult who need to be brought > to justice ASAP > US needs to stop them ASAP, from running and ruining US foreign policy in the mid-East. > Don't be afraid of the Jews, they need your help. Zionists are their own worse enemy. Even Einstein, the renown Jew, disapprove of Zionism. Therefor by their bigoted reasoning, he and all of us who don't approve of Zionism are anti-semitic. So be it. If disproval of Zionism is anti-semitic, then they've unfortunately converted another American to anti-semitism. > If only The Jews would bomb your house, we wouldn't have to listen to > your bigotry any more. Please Jews, bomb his house. > Sorry, open season for Jewish terrorism is only along the Gaza stript. Bombing however is not their style. They prefer bulldozing houses; it's so much more personal. === Subject: Re: Can You Handle The Truth? Yeah... ya got any? === Subject: Re: Can You Handle The Truth? posting-account=suWj4AkAAADE1IvGmj55Nmq3f98qb17e .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; InfoPath.2; .NET CLR 3.5.21022; Tablet PC 2.0),gzip(gfe),gzip(gfe) > The Jews bombed the USS Liberty and covered it up. The Jews framed the Arabs on 911. The Jews lied about the Holohoax and stole billions in fraudulent > compensation. The Jews own the banks and they just stole 9 trillion dollars from the > american sheeple. The monetary system is a gigantic pyramid scheme, where debt is > mathematically impossible to pay off. The Jews are buying up the world for pennies on the dollar now, just > after they crashed the world economy. The Jews are a fanatically racist and bigoted group of people with > deep occultic roots. However, let us not steep to their level by condemning all Jews and > becoming bigots ourselves. Most Jews REALLY BELIEVE they are victims of non-Jews, so they are not > so smart after all. Jews are creationists by definition, so they are not so smart after > all. Jews are totally brainwashed into following bizzare and regulated > rules set by paedophillic rabbis who suck the blood of circumsized > baby dicks during circumcision (THIS IS A FACT WHICH YOU CAN VERIFY). The Jews are a dangerously out of control cult who need to be brought > to justice ASAP Don't be afraid of the Jews, they need your help. Rescue the Jew from his own inbred madness and expose all of the above > to your fellow sheeple. ******************************************************************* Merry Hanukka to you too, my dear Tonio === Subject: Re: E=MC**2 expressed as Venn Diagram (See Attached Graphic) > Math. Forum: I think I expressed the famous equation better this > time. C**2 is the intersecting event of the two > items; Matter and Energy. I use this same concept of expressing Items and > Events and their intersections giving a limited > Quantitative and Qualitative Constant, in other > general objects. Such as Apples, Pears, Oranges and > Fruit. See some more of my work at my site link at: http://www.zimmathematics.com/htm/application_Page_2.h > tm#ItemsEvents Zim Olson > Creative Mathematics > http://www.zimmathematics.com ---------------------------------- Tom: Do you think any two objects or Items can have an > intersecting Event? Take as example: Apple + Orange + Pear; could you say their > intersecting event is maybe Fruit or maybe a Fruit > function? Then would you say the Fruit or Fruit function does > not exist here also? And is just a mathematical > construct? Zim Olson > Creative Mathematics > http://www.zimmathematics.com (apple * orange) - pear = ? tommy1729 --------------------------------------- tommy1729: Actualy I do have some thoughts on : (apple * orange) - pear = ? These involve 'System Transformations', 'System Relational Transformations', General System components of behavior etc. Covering basically how to add an Apples and an Oranges. I will get to this later, after resolving my proposed Intersecting Event of given Items. If anybody is still interested at that time? Merry XMas! Zim Olson Creative Mathematics http://www.zimmathematics.com === Subject: Re: Number of trayectories in a billiard board. posting-account=Z9v8GgkAAAB54xGwWI4tZlTl3U6kju-g Gecko/2008102920 Firefox/3.0.4,gzip(gfe),gzip(gfe) > Given a billiard board of dimensions m x n and a ball > tacked under an angle x / y from a corner. It is possible > to calculate the number of trayectories before it fall in > any other corner's pocket? Imagine grid points at each point (im,jn), where i,j are > any positive integers. Drawing the line of slope y/x from > the origin, assume that the first grid point it hits > is (am,bn). Then a,b is the minimum positive diaphontine > solution to x/y = (am)/(bn). The line will then cross (reflect off of) a-1 vertical > lines (cushions) and b-1 horizontal cushions, for a > total of a+b-2 trajectory changes. Did I interpret your > question as intended? your algorithm. Example: The grid 10 x 7 needs 25 trajectories when the ball starts from the left upper corner with slope 3/4 that is: 3 horizontal vs 4 vertical. The grid 5 x 3 needs 7 trajectories when the ball starts with slope 1/1 Ludovicus === Subject: Re: Eigenvalue distribution we know eigenvalue distribution of wishard martix A*A' where each > element of A is complex number with CN(0,mu). lets say we have each element of A, a+bi where a and b are taken from > S = {1,3,5,7,...,n} with equal probability 1/n. I suppose you mean 2/(n+1), and the real and imaginary parts of the entries are all independent. Also, I suspect your A' is the Hermitian conjugate of A, not the transpose, so A A' will be positive semidefinite. > could you give me a hint to find the eigenvalue distribution of this > problem... It must be very complicated, unless the matrix is very small. For example, if A is a 2 x 2 matrix and n = 5, there are some 338 possible pairs of eigenvalues. Some of which are quite common: 48 (+/-) 4 sqrt(131) and 40 (+/-) 10 sqrt(14)) each occur in 88 cases. Others are rare: ({0,200} and {0,8} each occur in only one case, namely [5+5i 5+5i] [5+5i 5+5i] for {0,200} and [1+i 1+i] [1+i 1+i] for {0,8}. A somewhat more tractable question would be to find the expected value of some particular function of the set of eigenvalues. For example, the sum of the k'th powers of the eigenvalues is trace((A A')^k), and it would be straightforward to evaluate the expected value of that, at least if k is a small integer. Thus if A is m x m, E[trace(A A')] = sum_i sum_j E[|A_{ij}|^2] = 2 m^2 n(n+2)/3 -- Robert Israel israel@math.MyUniversitysInitials.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada === Subject: Re: Bochner's tube theorem >Also, if the tube domain is in n-dimensional complex space, n > 2, and >you >want to continue an analytic function on the domain to the convex hull of >a cross contained within the base of the domain (the base is the subset of >the domain with all real coordinates) >- the analytic function had >better be extended to an open set. Thus for n > 2, the cross has to have >some thickness in the other dimensions also. He didn't show that you >could extend the function analytically from a cross shaped domain that has >thickness in n-space to its convex hull. You could extend it from each >2D slice, but how do you know the resulting function is analytic in >n-space? I doubt this is a problem, because his proof for the cross-shaped tube in 2D space can be extended to a tube with some thickness in other dimensions. But the other difficulty is still there. Laura === Subject: tetration, matrix^matrix, log(matrix)*matrix or matrix*log(matrix) Hi - just found -by accident- examples, meant to support the definition matrix^matrix = exp( log(matrix)*matrix) (1) instead of = exp( matrix*log(matrix)) (2) If we look at the lower-triangular binomialmatrix P, assumed having infinite dimension, then the tetrates in the following definition P^^2 = P^P = exp( log(P)*P) gives results which are meaningful in combinatorics. Examples taken from Online Encyclopedia of Integer Sequences, N.J.A.Sloane ------------------------------------------------------------ Example 1: X = P^P = P^^2 , definition (1) The first column of X contains 1,1,3,10,41,196,... This sequence has a combinatorical explanation: http://www.research.att.com/~njas/sequences/A000248 Number of forests with n nodes and height at most 1. Equivalently, number of idempotent mappings f from a set of n elements into itself (i.e. satisfying f o f = f). - E.g.f.: exp(x*exp(x)). Robert FERREOL (ferreol(AT)mathcurve.com), Oct 11 2007 Example 2: X = P^P^P = P^^3 , definition (1) The first column of X begins with 1,1,3,16,101,756,6607 This sequence has a combinatorical explanation: http://www.research.att.com/~njas/sequences/A000949 Number of forests with n nodes and height at most 2. E.g.f.: exp(x*exp(x*exp(x)) Example 3: X = P^(P^-1) // resembles e^(1/e) , definition (1) The first column of X begins with 1,1,-1,2,9,-4,-95 This sequence is known to OEIS: http://www.research.att.com/~njas/sequences/A003725 Expansion of exp(x e^-x ). --------------------------------------------------------- Additional remark: These coincidences also support another construction. If we try to determine the eigensystem of P we get a degenerate set of eigenvectors (since all eigenvalues=1) However, we can define another eigensystem-relation for P of infinite size. If the usual definition were, for instance, P~ = W * D * W^-1 // where D is diagonal then there is a non-invertible matrix W where P~ * W = W * E // E is diag(1,e,e^2,e^3,...) and W is the vandermonde-matrix W = matrix(r=0..inf,c=0..inf c^r/r! ) //r=rowindex,c=ol-index That the diagonal-matrix E occurs here seems another supporting argument for the meaningfulness of the P^P - definition (1) since this smoothes this context. ---- Just some accidental findings, I didn't do much more investigetions yet. Gottfried === Subject: Re: tetration, matrix^matrix, log(matrix)*matrix or matrix*log(matrix) Am 25.12.2008 22:00 schrieb Gottfried Helms: > > Example 3: X = P^(P^-1) // resembles e^(1/e) , definition (1) > The first column of X begins with > 1,1,-1,2,9,-4,-95 > > This sequence is known to OEIS: > http://www.research.att.com/~njas/sequences/A003725 > Expansion of exp(x e^-x ). > This means, that the entries of the first column combined with powers of x *and* reciprocal factorials, we get for x: y = 1 + 1 x/1! - 1 x^2/2! + 9 x^3/3! - 4 x^4/4! -95 x^5/5! +... and y = exp( x*exp(-x)) and for x=1 y= 1.44466786... = e^(1/e) Gottfried Helms === Cancel-Key: sha1:FahdBA2S9so1oRb/56Qs2Ut3TUw= === Subject: Odd and Even Exponents Cc: dlee753@yahoo.com posting-account=ffq-pAoAAAAWN8XUaOwbBbTrV981ne_q Trident/4.0; .NET CLR 1.0.3705; .NET CLR 1.1.4322; Media Center PC 4.0; IEMB3; IEMB3),gzip(gfe),gzip(gfe) Consider the following three equatins under the given conditions. x^2p + y^2p = z^2p (1) z^p + y^p = x^p (2) z^p - y^p = x^p (3) Conditions: (x, y, z) =1, y is even, prime p > 3. By FLT none of the three equations can have any integer solutions. (1) can be written as (x^2)^p + (y^2)^p = (z^2)^p (4) Since (2) has no integer solutions (1) also cannot have any integer solutions. Question: Is the reverse true? That is by knowing that (1) has no integer solutions is it possible to conclude that none of (2) or (3) also cannot have any integer solutions? A simple minded approach: By multiplying (2) by (3) one gets (1) Assertion: Since (1) has no integer solutions(FLT) then none of (2) or (3) also can have any integer solutions. Any comment upon the correctness of the Assertion based on my above reasoning will be appreciated. === Subject: Re: JSH: Questioning Galois Theory <21rtk411st2v8u1g6os5afsh0vbaqiu1io@4ax.com> posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif AppleWebKit/525.19 (KHTML, like Gecko) Chrome/1.0.154.36 Safari/525.19,gzip(gfe),gzip(gfe) > ... > Counterexamples to what? In the complex plane the too simple result > is as trivial as > > 7(x^2 + 3x + 2) = (7x + 7)(x+2) > > and there are no counterexamples. > > Come on, I dare you, in the complex plane, give a counterexample. > Obviously in the complex plane there are no counterexamples because > everything is divisible by everything except 0. You have to restrict > yourself to somewhere where that is *not* the case. >Why? Because you say so? >My point is simple: I have simple proof of a massive error that >entered the mathematical field over a hundred years ago, so the error >has to be subtle. So subtle that you cannot tell us what it is? It's easily demonstrated now but subtle in that it lasted for over a hundred years and requires you do some things not intuitive for most math students, for instance, who would have thought that 7(x^2 + 3x + 2) = (7x + 7)(x + 2) could be a matter of debate or show a crucial point for a major mathematical proof? >To demonstrate that error I rely on a simple construction in the >complex plane. So there is an error in the complex plane then. Is this a different No. The complex plane is the baseline to show the error. I prove something in the complex plane which indicates the error elsewhere. it if you don't know the story.) There I tried a paper over the ring of algebraic integers. Posters TOOK the error itself to claim the paper was wrong, and went after the journal, went after the paper, and then congratulated themselves for years. By relying on the complex plane where the error cannot hide, and where posters can't do that, I've defanged them. > error from the one you claimed previously to have found in the > algebraic integers? >Math people indoctrinated in the error argue ad infinitum about >trivialities and try to crawl back to the region where the error holds >sway. Which region is that? Be specific please. rossum The ring of algebraic integers. Hey, I've very specific. I've been explaining in detail, where for readers wondering what's different, well, I'm holding posters to the complex plane for the key construction and pointing out when they say nonsensical things. These people seem dedicated too! But remember what they are doing is a triumph of artifice over reason, using social tools to counter convincing through mathematical proof. So they are I like to say, anti-mathematicians. And they got away with it for six years so far. Six years of students learning bogus stuff, when that was avoidable. Here's the full argument again. Given 7(x^2 + 3x + 2) = (7x + 7)(x + 2) you are looking at one factorization out of infinity, but it is a valid factorization, which does not shift dependent on the value of x. So 7x + 7 = 7(x+1), or to give the distributive property the straightforward way: 7(x+1) = 7x + 7, and it doesn't change dependent on the value of x. That is trivial algebra!!! What happens though if you follow mathematical logic is that now with 7*(175x^2 - 15x + 2) = (5a 1(x) + 7)(5a 2(x)+ 7) where the a's are roots of a^2 - (7x-1)a + (49x^2 - 14x) = 0 you get a weird situation if you normalize with a 1(x) = b 1(x), and a 2(x) = b 2(x) - 1, as then you have 7*(175x^2 - 15x + 2) = (5b 1(x) + 7)(5b 2(x)+ 2) where b 1(0) = 0, b 2(0) = 0, which is in key respects exactly like 7(x^2 + 3x + 2) = (7x + 7)(x+2) and it represents ONE factorization out of an infinite number of ways to factor: 7*(175x^2 - 15x + 2). So what's different then? Well, in one case you have 7x--a linear function. In the other you have b 1(x), a non-linear function defined in a fairly clever way using what I call a quadratic generator. Ergo, the argument then is over whether or not a*(f(x) + b) = a*f(x) + a*b varies because of the ***function*** as there is no argument that given 7(x^2 + 3x + 2) = (7x + 7)(x+2) it's ludicrous to claim that x=0 is different from x=1, or x equal any other value. So mathematical logic is firmly on my side, and it IS a case of people arguing against the distributive property, but of course, that is clearly nonsensical so they misrepresent what they are doing. James Harris === Subject: Re: JSH: Questioning Galois Theory >My point is simple: I have simple proof of a massive error that >entered the mathematical field over a hundred years ago, so the error >has to be subtle. > So subtle that you cannot tell us what it is? It's easily demonstrated now but subtle in that it lasted for over a >hundred years and requires you do some things not intuitive for most >math students, for instance, who would have thought that 7(x^2 + 3x + 2) = (7x + 7)(x + 2) could be a matter of debate or show a crucial point for a major >mathematical proof? You have still not us what it is you are trying to show. We know that it is easily demonstrated, we know that it is subtle, we know that it lasted for over a hundred years, we know that it requires you do some things not intuitive for most math students, but we do to shout, but you do not seem to be getting the message. Please give us a statement of what it is you are trying to show. rossum === Subject: Re: JSH: Questioning Galois Theory My point is simple: I have simple proof of a massive error that > entered the mathematical field over a hundred years ago, so the error > has to be subtle. > So subtle that you cannot tell us what it is? > It's easily demonstrated now but subtle in that it lasted for over a > hundred years and requires you do some things not intuitive for most > math students, for instance, who would have thought that > 7(x^2 + 3x + 2) = (7x + 7)(x + 2) > could be a matter of debate or show a crucial point for a major > mathematical proof? > You have still not us what it is you are trying to show. We know that > it is easily demonstrated, we know that it is subtle, we know > that it lasted for over a hundred years, we know that it requires > you do some things not intuitive for most math students, but we do > to shout, but you do not seem to be getting the message. Please give > us a statement of what it is you are trying to show. rossum I agree. James: please explain this alleged goddamn error until we get it. Dave === Subject: Re: JSH: Questioning Galois Theory posting-account=wVv_VwoAAAAVTfUuyxLzug5SzYWCgHj1 Gecko/20081203 Firefox/2.0.0.19,gzip(gfe),gzip(gfe) > ... > > Counterexamples to what? In the complex plane the too simple result > > is as trivial as > > > 7(x^2 + 3x + 2) = (7x + 7)(x+2) > > > and there are no counterexamples. > > > Come on, I dare you, in the complex plane, give a counterexample. > Obviously in the complex plane there are no counterexamples because > everything is divisible by everything except 0. You have to restrict > yourself to somewhere where that is *not* the case. >Why? Because you say so? >My point is simple: I have simple proof of a massive error that >entered the mathematical field over a hundred years ago, so the error >has to be subtle. > So subtle that you cannot tell us what it is? It's easily demonstrated now but subtle in that it lasted for over a > hundred years and requires you do some things not intuitive for most > math students, for instance, who would have thought that 7(x^2 + 3x + 2) = (7x + 7)(x + 2) could be a matter of debate or show a crucial point for a major > mathematical proof? >To demonstrate that error I rely on a simple construction in the >complex plane. > So there is an error in the complex plane then. Is this a different No. The complex plane is the baseline to show the error. I prove something in the complex plane which indicates the error > elsewhere. > Let's stop being coy. Exactly what do you prove in the complex plane? Nice, crisp, clear statement, please. error from the one you claimed previously to have found in the > algebraic integers? >Math people indoctrinated in the error argue ad infinitum about >trivialities and try to crawl back to the region where the error holds >sway. > Which region is that? Be specific please. > rossum The ring of algebraic integers. Hey, I've very specific. No, you're not. You have not stated a theorem. > I've been explaining in detail, where for > readers wondering what's different, well, I'm holding posters to the > complex plane for the key construction and pointing out when they say > nonsensical things. > Like what? Here's the full argument again. Given 7(x^2 + 3x + 2) = (7x + 7)(x + 2) you are looking at one factorization out of infinity, but it is a > valid factorization, which does not shift dependent on the value of > x. Specifics: 1. What do you mean by 'valid factorization' ? 2. Are there any other 'valid factorizations' ? 3. Does a 'valid factorization' have to be independent of the values of x ? Why ? Can you prove that mathematically? > So 7x + 7 = 7(x+1), or to give the distributive property the > straightforward way: 7(x+1) = 7x + 7, and it doesn't change dependent > on the value of x. > Why is that significant? > That is trivial algebra!!! > So far. But you haven't said anything. > What happens though if you follow mathematical logic is that now with 7*(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x)+ 7) where the a's are roots of a^2 - (7x-1)a + (49x^2 - 14x) = 0 you get a weird situation if you normalize with a_1(x) = b_1(x), and a_2(x) = b_2(x) - 1, as then you have 7*(175x^2 - 15x + 2) = (5b_1(x) + 7)(5b_2(x)+ 2) where b_1(0) = 0, b_2(0) = 0, which is in key respects exactly like 7(x^2 + 3x + 2) = (7x + 7)(x+2) and it represents ONE factorization out of an infinite number of ways > to factor: > WHAT represents one factorization? You have not shown explicitly how 7 occurs on the right side of the equation. You have not given an explicit factorization! > 7*(175x^2 - 15x + 2). So what's different then? Well, in one case you have 7x--a linear > function. > NOT the only difference. In 7x + 7, you have one polynomial variable, x. In 5b_1(x) + 7, you have a nonpolynomial variable, 5b_1(x). In fact you are not even factoring your original polynomial, 7(175x^2 - 15x + 2) as a polynomial in x. You are factoring it as a polynomial in the symbol 5. Further, b_1(x) = a_1(x) is a root of an associated quadratic, a^2 - (7x - 1)a + (49x^2 - 14x) = 0. This is very different from your simplistic 7x + 7 example. The analogy is not close. You cannot use something that you believe to be true for 7x + 7 and apply it immediately to (5b_1(x) + 7). There are too many important dissimilarities. > In the other you have b_1(x), a non-linear function defined in a > fairly clever way using what I call a quadratic generator. Ergo, the argument then is over whether or not a*(f(x) + b) = a*f(x) > + > a*b varies because of the ***function*** as there is no argument that > given 7(x^2 + 3x + 2) = (7x + 7)(x+2) it's ludicrous to claim that x=0 is different from x=1, or x equal > any > other value. > Saying something is ludicrous is not a proof. You know that. > So mathematical logic is firmly on my side, You could not be more wrong. > and it IS a case of > people > arguing against the distributive property, but of course, that is > clearly nonsensical so they misrepresent what they are doing. > The basic messages here are: 1. State a DEFINITE THEOREM regarding your factorization of 7(x^2 + 3x + 2) in the complex plane. 2. Show how you transition this theorem from the complex plane to other rings. 3. True or false: a) In the complex plane, there is ONLY ONE way to distribute 7 among the linear factors on the right side of the equation: 7*(x^2 + 3x + 2) = 7(x + 1)*(x + 2). True or false? b) True or false: Any theorem that is true in the complex plane must also be true in any subring of the complex plane. True or false? c) True or false: You believe that your argument contradicts Galois theory and Dedekind's theorem regarding greatest common divisors in the ring of algebraic integers. True or false? d) True or false: You can always rely on factorization by inspection. It always works. True or false? e) True or false: when you distribute 7 among the two parentheses in the expression 7(x + 1)*(x + 2) it cannot be dependent on the value of x. True or false? Proof? f) True or false: The following distributions of 7 among the two factors are NOT valid in the complex plane: 7(x + 1)*(x + 2) = (x + 1)*(7x + 14) 7(x + 1)*(x + 2) = (sqrt(7)x + sqrt(7) * (sqrt(7)x + 2sqrt(7)) 7(x + 1)*(x + 2) = (a*x + a)*(b*x + b) where a*b = 7. 7(x + 1)(x + 2) = (a(x)*x + a(x))*(b(x)*b + 2b(x)) where a(x)*b(x) = 7 What does valid mean? You have been vague and nospecific in all your recent posts on this topic. It is time to stop that. Put it in the language of physics: state testable hypotheses; make testable statements. Otherwise we are just talking semantics and word games. Marcus. > James Harris === Subject: Re: JSH: Was never a factor argument days. My association with the Department is that of an alumnus. >Heh. This raises the question of which is the simplest explanation. The smallest explanation that has no proper nontrivial normal subexplanations, of course. -- It's not denial. I'm just very selective about what I accept as reality. --- Calvin (Calvin and Hobbes by Bill Watterson) Arturo Magidin magidin-at-member-ams-org === Subject: Re: JSH: Was never a factor argument posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif AppleWebKit/525.19 (KHTML, like Gecko) Chrome/1.0.154.36 Safari/525.19,gzip(gfe),gzip(gfe) > [JSH, spouting the usual JSH gibberish] > ... > [marcus bruck...@yahoo.com] > ... > It is NOT the case that the 7 can be distributed in only > one way across the two factors. You can deny that this > was your underlying goal, but clearly it was. Otherwise > you were just raving on about an utter trivial banality. > But even you are not that dumb. > I'm not sure about that. Give yourself a Christmas present :-) I > believe I replied to James a grand total of two times in 2008. In both > cases I simply presented 1-digit integer counterexamples to the goofy > claims he was making on those days. No arguments, no followups, no > attempts to reason with him. > And I learned something ;-) When arguing with him in previous years, I > made extraordinary efforts to try to make /any/ kind of coherent sense > out of the endless gibberish he spouted. But I now believe that, in > most cases, the sense I believed I found was my own construction, not > without twisting your head up your ass fifty different ways to try to > give him the benefit of the doubt, he really does appear to be that > dumb (at least when it concerns mathematics, in which he is profoundly > incompetent). > You had an ulterior motive. > False dichotomy there -- it's possible that he's both that dumb and > wallowing in ulterior motives. But, in this case, I think it more > likely that he doesn't understand the distinction you believe is dead > obvious here: that he believes his endlessly repeated > 7*(x^2 + 3x + 2) = (7x + 7)*(x + 2), I agree with that view, Tim. > I think James may be mixed up by what = means in math . > When using a calculator, pressing the = sign gives > the answer. So James could be thinking that > 7*(x^2 + 3x + 2) has *two* possible answers: > either > 7(x+1)(x+2) = (7x + 7)*(x+2) [Answer 1] > or > 7(x+1)(x+2) = (x + 1)*(7x + 14) [Answer 2] ; Nope. There are an INFINITY of ways to factor 7(x^2 + 3x + 2) on the complex plane. And ONE of those ways is 7(x^2 + 3x + 2) = (7x + 7)(x + 2). > but, to him, you choose one answer or the other, > but not both, because that's all about the > distributive property, which of course he thinks he > understands. I'm consistently saying the same thing. You and posters like you are making things up. > The = in math can be subtle [for A.I. purposes]. And I remind other readers who think it is about me. Clearly it's not. Given 7(x^2 + 3x + 2) = (7x + 7)(x + 2) you are looking at one factorization out of infinity, but it is a valid factorization, which does not shift dependent on the value of x. So 7x + 7 = 7(x+1), or to give the distributive property the straightforward way: 7(x+1) = 7x + 7, and it doesn't change dependent on the value of x. That is trivial algebra!!! What happens though if you follow mathematical logic is that now with 7*(175x^2 - 15x + 2) = (5a 1(x) + 7)(5a 2(x)+ 7) where the a's are roots of a^2 - (7x-1)a + (49x^2 - 14x) = 0 you get a weird situation if you normalize with a 1(x) = b 1(x), and a 2(x) = b 2(x) - 1, as then you have 7*(175x^2 - 15x + 2) = (5b 1(x) + 7)(5b 2(x)+ 2) where b 1(0) = 0, b 2(0) = 0, which is in key respects exactly like 7(x^2 + 3x + 2) = (7x + 7)(x+2) and it represents ONE factorization out of an infinite number of ways to factor: 7*(175x^2 - 15x + 2). So what's different then? Well, in one case you have 7x--a linear function. In the other you have b 1(x), a non-linear function defined in a fairly clever way using what I call a quadratic generator. Ergo, the argument then is over whether or not a*(f(x) + b) = a*f(x) + a*b varies because of the ***function*** as there is no argument that given 7(x^2 + 3x + 2) = (7x + 7)(x+2) it's ludicrous to claim that x=0 is different from x=1, or x equal any other value. So mathematical logic is firmly on my side, and it IS a case of people arguing against the distributive property, but of course, that is clearly nonsensical so they misrepresent what they are doing. What is more interesting though are those of you who may be confused!!! If so, you are confused for purely social reasons, which should show you how hard doing real mathematics can actually be. These people have gotten away with attacking the distributive property and claiming they are not doing so for over six years now. Most human beings simply are not cut out to do real mathematics, but lying to one's self is so easy that plenty of people around the world believe they are when with a simple test of a proof with huge social consequences where the linchpin is one of the most trivial of mathematical things---they fail, miserably. Most of you are not capable of being real mathematicians. In fantasy, yes, you can convince yourselves you are mathematicians. IN reality, no, you are cows who follow the herd. James Harris === Subject: Re: JSH: Was never a factor argument posting-account=wVv_VwoAAAAVTfUuyxLzug5SzYWCgHj1 5.1),gzip(gfe),gzip(gfe) > [JSH, spouting the usual JSH gibberish] > ... > [marcus bruck...@yahoo.com] > ... > It is NOT the case that the 7 can be distributed in only > one way across the two factors. You can deny that this > was your underlying goal, but clearly it was. Otherwise > you were just raving on about an utter trivial banality. > But even you are not that dumb. > I'm not sure about that. Give yourself a Christmas present :-) I > believe I replied to James a grand total of two times in 2008. In both > cases I simply presented 1-digit integer counterexamples to the goofy > claims he was making on those days. No arguments, no followups, no > attempts to reason with him. > And I learned something ;-) When arguing with him in previous years, I > made extraordinary efforts to try to make /any/ kind of coherent sense > out of the endless gibberish he spouted. But I now believe that, in > most cases, the sense I believed I found was my own construction, not > without twisting your head up your ass fifty different ways to try to > give him the benefit of the doubt, he really does appear to be that > dumb (at least when it concerns mathematics, in which he is profoundly > incompetent). > You had an ulterior motive. > False dichotomy there -- it's possible that he's both that dumb and > wallowing in ulterior motives. But, in this case, I think it more > likely that he doesn't understand the distinction you believe is dead > obvious here: that he believes his endlessly repeated > 7*(x^2 + 3x + 2) = (7x + 7)*(x + 2), > I agree with that view, Tim. > I think James may be mixed up by what = means in math . > When using a calculator, pressing the = sign gives > the answer. So James could be thinking that > 7*(x^2 + 3x + 2) has *two* possible answers: > either > 7(x+1)(x+2) = (7x + 7)*(x+2) [Answer 1] > or > 7(x+1)(x+2) = (x + 1)*(7x + 14) [Answer 2] ; Nope. There are an INFINITY of ways to factor 7(x^2 + 3x + 2) on the > complex plane. And ONE of those ways is 7(x^2 + 3x + 2) = (7x + 7)(x + 2). > Are all of infinitely many ways equally valid? > but, to him, you choose one answer or the other, > but not both, because that's all about the > distributive property, which of course he thinks he > understands. I'm consistently saying the same thing. > True. You are saying nothing, and trying to conclude something from it. > You and posters like you are making things up. > The = in math can be subtle [for A.I. purposes]. And I remind other readers who think it is about me. Clearly it's > not. Given 7(x^2 + 3x + 2) = (7x + 7)(x + 2) you are looking at one factorization out of infinity, but it is a > valid factorization, which does not shift dependent on the value of x. > What does valid mean? Are you saying that nonconstant factorizations are not valid? Why is that? Do you have a secret definition of valid? What is it? Do you have a secret proof that nonconstant factorizations are not valid? > So 7x + 7 = 7(x+1), or to give the distributive property the > straightforward way: 7(x+1) = 7x + 7, and it doesn't change dependent > on the value of x. > Is that forbidden? Why? > That is trivial algebra!!! > So far. But evidently something more than algebra. You appear to be ruling out nonconstant factorizations. Why ? Is there something wrong with them? Are they not valid ? Can you define valid? And then prove somehow that nonconstant factorizations are not valid ? > What happens though if you follow mathematical logic is that now with 7*(175x^2 - 15x + 2) = (5a 1(x) + 7)(5a 2(x)+ 7) where the a's are roots of a^2 - (7x-1)a + (49x^2 - 14x) = 0 you get a weird situation if you normalize with a 1(x) = b 1(x), and a 2(x) = b 2(x) - 1, as then you have 7*(175x^2 - 15x + 2) = (5b 1(x) + 7)(5b 2(x)+ 2) where b 1(0) = 0, b 2(0) = 0, which is in key respects exactly like 7(x^2 + 3x + 2) = (7x + 7)(x+2) > There are a lot of differences, and they are not trivial. In the 7x + 7 case, x is the polynomial variable. In the other case, 5b 1(x) is not even a polynomial function. Besides which, you are not factoring 7*(175x^2 - 15 x + 2) as a polynomial in x. You are factoring it as a polynomial in 5. The two situations are not parallel, or even close. You cannot generalize from the simplistic 7x + 7 thing to the more complex case. > and it represents ONE factorization out of an infinite number of ways > to factor: 7*(175x^2 - 15x + 2). So what's different then? Well, in one case you have 7x--a linear > function. In the other you have b 1(x), a non-linear function defined in a > fairly clever way using what I call a quadratic generator. > The fact that they have x in common is not enough. They are not even the same kinds of function. > Ergo, No. You say ergo only when what you are about to say is preceded by logical argument. That is far from the case here. > the argument then is over whether or not a*(f(x) + b) = a*f(x) + > a*b varies because of the ***function*** as there is no argument that > given 7(x^2 + 3x + 2) = (7x + 7)(x+2) > There IS an argument. You yourself just said there were infinitely many ways to factor 7(x^2 + 3x + 2) in the complex plane. You give no reason for selecting only one of those factorizations. Just your own preference? You give no reason for rejecting nonconstant factorizations. You imply they are not valid but you have no definition of valid, and no proof. Arguing by analogy cannot work here, because you have nothing on the easier side of the analogy, and the analogy is not even close anyway. Just some vague feeling, probably based on factorization-by-inspection. > it's ludicrous to claim that x=0 is different from x=1, or x equal any > other value. > Ludicrous is not a logical argument, not mathematics. I don't want ludicrous. I want RIGOROUS. You don't have it. > So mathematical logic is firmly on my side, and it IS a case of people > arguing against the distributive property, but of course, that is > clearly nonsensical so they misrepresent what they are doing. > No. You do NOT have logic on your side; just emotion, and ludicrous. Answer the questions above, give a rigorous proof rather than a hand-waving analogy which has no effect anyway since you have no proof for the simpler side of the analogy. > What is more interesting though are those of you who may be > confused!!! > Ah, the appeal to the Grandstand. All those innocent little undergrads out there. Maybe you can fool a few of them. How about answering some specific questions? 1. What is special about the factorization 7*(x^2 + 3x + 2) = (7x + 7)*(x + 2) in the complex plane? Is it better in some way than 7*(x^2 + 3x + 2) = (a(x)*x + a(x))*(b(x)*x + 2b(x)), where a(x) and b(x) are functions of x whose product is 7? For example, a(x) = 7/(1 + exp(x)), b(x) = 1 + exp(x) Does this nonconstant factorization violate the distributive property in some way? Can you PROVE that it does? Is this nonconstant factorization not valid? What do you mean when you say valid? What is the rigorous definition? Can you PROVE the nonconstant factorization is not valid ? Have you given such a proof? Where? 2. First you factor in the complex numbers. Then you want to jump to conclusions in the ring of algebraic integers. Is every theorem that is true in the complex plane also true in every subring of the complex plane? Can you prove that? If not, how do you transition from the complex plane to subrings of it? Stop shoveling smoke or whatever it is you are shoveling and give some definite answers! Marcus. === Subject: JSH: No need for Galois theory posting-account=1lE9SQkAAADFrJsDv61dh1YXcJ_ahy5I > where the a's are roots of a^2 - (7x-1)a + (49x^2 - 14x) = 0 > Then, if x is such that the quadratic is irreducible over the rationals, then either both roots or neither root is divisible by 7. You don't need the Galois sledgehammer to crack this walnut. Let x be such that the quadaratic is irreducible over the rationals and let a_1(x) and a_2(x) be the two roots. Then looking at the quadratic formula, we see that a_1(x) = d(x) + e(x) where d(x) is rational and e(x) is irrational or complex and that a_2(x) = d(x) - e(x). If a_1(x) is divisible by 7 then so is d(x) and e(x) and therefore a_2(x). So your claim that for all x, a_1(x) is divisible by 7 and a_2(x) is coprime to 7, breaks not only Galois theory but simple algebra. - William Hughes For extra credit identify where this proof breaks down if x is such that the quadratic is reducible over the rationals. Hint: look at e(x) is irrational or complex === Subject: Topics on Electronics posting-account=i4ZM0AoAAACWOMo3oL7uBDjUklY1fpv3 Gecko/20081029 Firefox/2.0.0.18,gzip(gfe),gzip(gfe) Electronics is the field of manipulating electrical currents and voltages using passive and active components that are connected together to create circuits. Electronic circuits range from a simple load resistor that converts a current to a voltage, to computer central-processing units (CPUs) that can contain more than a million transistors. The following indices and documents provide a basic reference for understanding electronic components, circuits, and applications. http://electronicstopics.blogspot.com/2008/10/welcome-to-world-of-electronic s.html === === Subject: Re: JSH: Questioning Galois Theory >The error is the ability to demonstrate an apparent contradiction-- >anathema to mathematics. understanding what it is you think you have shown. In addition to the other things I know about whatever it is, I now know that it is an apparent contradiction. However I STILL DO NOT KNOW WHAT THE CONTRADICTION IS! Again my apologies for shouting, but you are not making yourself clear. Could you please give a clear short answer along the lines of: 1 Galois theory (or whatever) states ****************. 2 I have a proof that ###################. 3 ################### contradicts ****************. 4 Here is my proof of ###################: ... rossum === Subject: Re: JSH: Questioning Galois Theory <9eo6l49p6ecmfqijod79v51h9l8g0gaer9@4ax.com> posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif Gecko/2008120122 Firefox/3.0.5,gzip(gfe),gzip(gfe) >The error is the ability to demonstrate an apparent contradiction-- >anathema to mathematics. understanding what it is you think you have shown. In addition to the > other things I know about whatever it is, I now know that it is an > apparent contradiction. However I STILL DO NOT KNOW WHAT THE CONTRADICTION IS! Again my apologies for shouting, but you are not making yourself > clear. Could you please give a clear short answer along the lines of: 1 Galois theory (or whatever) states ****************. Ok, there was a request for an explanation which I'm giving, but you want the advanced stuff, which you haven't understood up until now, but ok, here we go again. Galois Theory is a series of techniques concerning possible combinations of simple radicals and the basic symbols +, -, and /, which purportedly tells you something about underlying factors relying on factors in the ring of algebraic integers. > 2 I have a proof that ###################. I can prove that factors in the ring of algebraic integers can actually be units masquerading as non-unit factors because they are non-units in the ring of algebraic integers which arbitrarily leaves out an infinity of necessary numbers because of the definition of algebraic integers as having to be roots of some monic polynomial with integer coefficients. > 3 ################### contradicts ****************. That shows that results found using Galois Theory or results from the ring of algebraic integers have no real meaning in terms of factors, so for instance, you can appear to prove that 7 is a factor of a number and prove that it cannot be a factor in the ring of algebraic integers. Further the entire class number machinery turns out to tell you-- nothing at all. So Galois Theory isn't wrong, it's just useless for telling you any important properties of numbers. > 4 Here is my proof of ###################: ... I'm able to show the problem easily enough with a distributive argument on the complex plane with a simple construction, which you've seen before. The distribution argument is brilliant in that it IS valid on the complex plane which de-fangs people who use the problem itself to claim there is no problem!!! rossum I really doubt you will understand much of the above, but you requested the explanation. My suggestion to you is that you start simple: think long and hard about what distributes means, and accept the result on the complex plane. James Harris === Subject: Re: JSH: Questioning Galois Theory <9eo6l49p6ecmfqijod79v51h9l8g0gaer9@4ax.com> posting-account=wVv_VwoAAAAVTfUuyxLzug5SzYWCgHj1 5.1),gzip(gfe),gzip(gfe) >The error is the ability to demonstrate an apparent contradiction-- >anathema to mathematics. > understanding what it is you think you have shown. In addition to the > other things I know about whatever it is, I now know that it is an > apparent contradiction. > However I STILL DO NOT KNOW WHAT THE CONTRADICTION IS! > Again my apologies for shouting, but you are not making yourself > clear. Could you please give a clear short answer along the lines of: > 1 Galois theory (or whatever) states ****************. Ok, there was a request for an explanation which I'm giving, but you > want the advanced stuff, which you haven't understood up until now, > but ok, here we go again. Galois Theory is a series of techniques concerning possible > combinations of simple radicals and the basic symbols +, -, and /, > which purportedly tells you something about underlying factors relying > on factors in the ring of algebraic integers. > OK, you have thoroughly made an ass of yourself on that part. Clearly you have no concept of the theory. Example: what role does group theory play in Galois theory? > 2 I have a proof that ###################. I can prove that factors in the ring of algebraic integers can > actually be units masquerading 'masquerading' is not a mathematical term. You may have your own private definition, but until you say what it is, you are not specifying what you think you can prove. So this answer is nonresponsive. Try again. > as non-unit factors because they are > non-units in the ring of algebraic integers This is just gibberish. You have no idea how to make a definite mathematical statement. > which arbitrarily leaves > out an infinity of necessary numbers Define 'necessary number'. > because of the definition of > algebraic integers as having to be roots of some monic polynomial with > integer coefficients. > 3 ################### contradicts ****************. That shows that results found using Galois Theory or results from the > ring of algebraic integers have no real meaning in terms of factors, > so for instance, you can appear to prove that 7 is a factor of a > number What does that mean, you can appear to prove that 7 is a factor of a number? Do you mean that YOU can appear to so prove? Why do you say appear? Can you prove it, or not? If you cannot, why do you think you have an apparent contradiction? Can't you make a definite statement about ANYTHING, even your own claims? > and prove that it cannot be a factor in the ring of algebraic > integers. Further the entire class number machinery turns out to tell you-- > nothing at all. > You want to make a stab at explaining class number theory? Never mind. Please don't. > So Galois Theory isn't wrong, it's just useless for telling you any > important properties of numbers. > 4 Here is my proof of ###################: ... I'm able to show the problem easily enough with a distributive > argument on the complex plane with a simple construction, which you've > seen before. > It has been thoroughly debunked. People here would not be asking this if you had actually given anything remotely close to a real proof. > The distribution argument is brilliant ... a little more modesty is warranted ... > in that it IS valid on the > complex plane State exactly a theorem which summarizes what you have proved in the complex plane. > which de-fangs people People don't have fangs. Dogs and snakes have fangs. Perhaps mutant aliens have fangs. Perhaps YOU have fangs. > who use the problem itself to > claim there is no problem!!! > rossum I really doubt you will understand much of the above, There is nothing to understand. You still have not stated a theorem or given a proof. > but you > requested the explanation. ... and you didn't get it. > My suggestion to you is that you start > simple: think long and hard about what distributes means, Good advice. Give it a shot. > and accept > the result on the complex plane. > What result? You have not stated a result. Marcus. > James Harris- Hide quoted text - - Show quoted text - === Subject: Re: JSH: Questioning Galois Theory <9eo6l49p6ecmfqijod79v51h9l8g0gaer9@4ax.com> posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif Gecko/2008120122 Firefox/3.0.5,gzip(gfe),gzip(gfe) >The error is the ability to demonstrate an apparent contradiction-- >anathema to mathematics. > understanding what it is you think you have shown. In addition to the > other things I know about whatever it is, I now know that it is an > apparent contradiction. > However I STILL DO NOT KNOW WHAT THE CONTRADICTION IS! > Again my apologies for shouting, but you are not making yourself > clear. Could you please give a clear short answer along the lines of: > 1 Galois theory (or whatever) states ****************. > Ok, there was a request for an explanation which I'm giving, but you > want the advanced stuff, which you haven't understood up until now, > but ok, here we go again. > Galois Theory is a series of techniques concerning possible > combinations of simple radicals and the basic symbols +, -, and /, > which purportedly tells you something about underlying factors relying > on factors in the ring of algebraic integers. OK, you have thoroughly made an ass of yourself > on that part. Clearly you have no concept of the > theory. Example: what role does group theory play > in Galois theory? I've forgotten so much of what you think is so important because I know it's not. What's wrong with my description of Galois Theory? I have a question to test your knowledge, explain quickly how Galois Theory proves there is no general solution for polynomials beyond quartics. Remember for instance that the quadratic formula is a general solution for quadratics. The Cardano equations work for others, so why not quintics? Relate that explanation to Abel's proof and show how Galois Theory does more simply what Abel did in his highly creative way. Explain that way. And give it historical context, and then let's see who is the ass. You know you reply a lot but I wonder how much of even established mathematics you actually know. Here's a simple test. If he fails, anyone can answer. James Harris === Subject: Re: JSH: Questioning Galois Theory > The error is the ability to demonstrate an apparent contradiction-- > anathema to mathematics. > understanding what it is you think you have shown. In addition to the > other things I know about whatever it is, I now know that it is an > apparent contradiction. > However I STILL DO NOT KNOW WHAT THE CONTRADICTION IS! > Again my apologies for shouting, but you are not making yourself > clear. Could you please give a clear short answer along the lines of: > 1 Galois theory (or whatever) states ****************. > Ok, there was a request for an explanation which I'm giving, but you > want the advanced stuff, which you haven't understood up until now, > but ok, here we go again. > Galois Theory is a series of techniques concerning possible > combinations of simple radicals and the basic symbols +, -, and /, > which purportedly tells you something about underlying factors relying > on factors in the ring of algebraic integers. > OK, you have thoroughly made an ass of yourself > on that part. Clearly you have no concept of the > theory. Example: what role does group theory play > in Galois theory? I've forgotten so much of what you think is so important because I > know it's not. What's wrong with my description of Galois Theory? I have a question to test your knowledge, explain quickly how Galois > Theory proves there is no general solution for polynomials beyond > quartics. Remember for instance that the quadratic formula is a > general solution for quadratics. The Cardano equations work for > others, so why not quintics? The groups A_5 and S_5 with 60 and 120 elements resp. are non-abelian and not solvable, because A_5 is simple. Non-abelian groups with fewer than 60 elements are solvable. I know that's a part of the explanation or proof. > Relate that explanation to Abel's proof and show how Galois Theory > does more simply what Abel did in his highly creative way. Explain that way. And give it historical context, and then let's see > who is the ass. You know you reply a lot but I wonder how much of even established > mathematics you actually know. Here's a simple test. If he fails, anyone can answer. > James Harris === Subject: Re: JSH: Questioning Galois Theory > The error is the ability to demonstrate an apparent contradiction-- > anathema to mathematics. > understanding what it is you think you have shown. In addition to the > other things I know about whatever it is, I now know that it is an > apparent contradiction. However I STILL DO NOT KNOW WHAT THE CONTRADICTION IS! Again my apologies for shouting, but you are not making yourself > clear. Could you please give a clear short answer No, he could not. It is not the nature of the beast. === Subject: Re: JSH: Questioning Galois Theory > My point is simple: I have simple proof of a massive error that > entered the mathematical field over a hundred years ago, so the error > has to be subtle. > So subtle that you cannot tell us what it is? > It's easily demonstrated now but subtle in that it lasted for over a > hundred years and requires you do some things not intuitive for most > math students, for instance, who would have thought that > 7(x^2 + 3x + 2) = (7x + 7)(x + 2) > could be a matter of debate or show a crucial point for a major > mathematical proof? > You have still not us what it is you are trying to show. We know that > it is easily demonstrated, we know that it is subtle, we know > that it lasted for over a hundred years, we know that it requires > you do some things not intuitive for most math students, but we do > to shout, but you do not seem to be getting the message. Please give > us a statement of what it is you are trying to show. > rossum > I agree. James: please explain this alleged goddamn error until > we get it. > Dave The error is the ability to demonstrate an apparent contradiction-- > anathema to mathematics. And it's kind of cool too how easy it is to show the bane of > mathematics (or what looks like it), as I can use a distributive > property argument to show how a trivial factor of 7 distributes > through a non-traditional factorization. Note I said distributes as I think for many of you the word > distributive in the distributive property was kind of a mysterious > thing, even though you probably thought before that a*(b+c) = a*b + > a*c was so meaninglessly trivial. Notice the distributive property is valid on the complex plane. So I prove a distribution on the complex plane! In the complex plane with 7*(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x)+ 7) where the a's are roots of a^2 - (7x-1)a + (49x^2 - 14x) = 0 you normalize: a_1(x) = b_1(x), and a_2(x) = b_2(x) - 1, as then you have 7*(175x^2 - 15x + 2) = (5b_1(x) + 7)(5b_2(x)+ 2) where b_1(0) = 0, b_2(0) = 0. And you have one factorization out of infinity and in THAT > factorization the 7 has distributed in one way, which is easily > verifiable at x=0, as then you it distributed through 5b_1(0) + 7, as that equals 7(0 + 1), so with the distributive > property you have a=7, b=0, c=1. The problem with an easy argument here is that it runs into bad > mathematical habits in other areas where people clearly think factor, > and an immediate impulse is to say 7 is a factor of one function, > which is true, but 7 is a factor of both functions on the complex > plane!!!!!!!!!! The argument is NOT a factor argument!!! It's a distributive argument. However, a factor problem emerges--the apparent contradiction, yeah!!! > weird cool!!!---in the ring of algebraic integers which can be > considered with a simpler factorization: 7(x^2 + 3x + 2) = (7x + 7)(x+2) Notice that it is impossible for x in the factor x+2 to spontaneously > have non-unit factors in common with 7, even in the ring of algebraic > integers, no matter what the value of x is. That's important. > (Ponder it.) The mainstream math. distinguishes factorizations of polynomials from factorizations in Z (the ordinary integers) Z[sqrt(-1)] and other rings of numbers. I'm not sure what you mean by: Notice that it is impossible for x in the factor x+2 to spontaneously have non-unit factors in common with 7, even in the ring of algebraic integers,[...] Suppose I let x = 7. Then gcd(x, 7) = 7. It's quite possible that I misunderstand what is meant above by spontaneously . But I think we can agree on this: if x is an algebraic integer, then 7(x^2 + 3x + 2) and (7x + 7) will always have 7 as a factor in the ring of algebraic integers. If x is an algebraic integer, then for infinitely many x, x + 2 will not have 7 as a factor in the ring of algebraic integers. HOWEVER, with 7*(175x^2 - 15x + 2) = (5b_1(x) + 7)(5b_2(x)+ 2) and non-linear functions that are non-rational with a rational x, you > CAN have a non-unit factor in common with 7 in the ring of algebraic > integers spontaneously generated. The same thing here with the word spontaneously; I'm not sure what you mean by that. David Bernier > It just emerges out of thin air. If you were able to keep up this far you may intuitively recoil from > that assessment, but remember, the 7 can be shown to have distributed > in a particular way on the complex plane. However, against the logic > of that distribution non-unit factors in common with 7 emerge in the > ring of algebraic integers!!! Some of you may be able to guess how or know from other postings I've > done. For the rest I'll leave that as a start to see how reasonable you > actually are here, after all, some of you asked me to explain and I > have given most of the explanation. > James Harris === Subject: Re: JSH: Questioning Galois Theory <9eo6l49p6ecmfqijod79v51h9l8g0gaer9@4ax.com> posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif Gecko/2008120122 Firefox/3.0.5,gzip(gfe),gzip(gfe) > My point is simple: I have simple proof of a massive error that > entered the mathematical field over a hundred years ago, so the error > has to be subtle. > So subtle that you cannot tell us what it is? > It's easily demonstrated now but subtle in that it lasted for over a > hundred years and requires you do some things not intuitive for most > math students, for instance, who would have thought that > 7(x^2 + 3x + 2) = (7x + 7)(x + 2) > could be a matter of debate or show a crucial point for a major > mathematical proof? > You have still not us what it is you are trying to show. We know that > it is easily demonstrated, we know that it is subtle, we know > that it lasted for over a hundred years, we know that it requires > you do some things not intuitive for most math students, but we do > to shout, but you do not seem to be getting the message. Please give > us a statement of what it is you are trying to show. > rossum > I agree. James: please explain this alleged goddamn error until > we get it. > Dave > The error is the ability to demonstrate an apparent contradiction-- > anathema to mathematics. > And it's kind of cool too how easy it is to show the bane of > mathematics (or what looks like it), as I can use a distributive > property argument to show how a trivial factor of 7 distributes > through a non-traditional factorization. > Note I said distributes as I think for many of you the word > distributive in the distributive property was kind of a mysterious > thing, even though you probably thought before that a*(b+c) = a*b + > a*c was so meaninglessly trivial. > Notice the distributive property is valid on the complex plane. > So I prove a distribution on the complex plane! > In the complex plane with > 7*(175x^2 - 15x + 2) = (5a 1(x) + 7)(5a 2(x)+ 7) > where the a's are roots of > a^2 - (7x-1)a + (49x^2 - 14x) = 0 > you normalize: > a 1(x) = b 1(x), and a 2(x) = b 2(x) - 1, as then you have > 7*(175x^2 - 15x + 2) = (5b 1(x) + 7)(5b 2(x)+ 2) > where b 1(0) = 0, b 2(0) = 0. > And you have one factorization out of infinity and in THAT > factorization the 7 has distributed in one way, which is easily > verifiable at x=0, as then you it distributed through > 5b 1(0) + 7, as that equals 7(0 + 1), so with the distributive > property you have a=7, b=0, c=1. > The problem with an easy argument here is that it runs into bad > mathematical habits in other areas where people clearly think factor, > and an immediate impulse is to say 7 is a factor of one function, > which is true, but 7 is a factor of both functions on the complex > plane!!!!!!!!!! > The argument is NOT a factor argument!!! > It's a distributive argument. > However, a factor problem emerges--the apparent contradiction, yeah!!! > weird cool!!!---in the ring of algebraic integers which can be > considered with a simpler factorization: > 7(x^2 + 3x + 2) = (7x + 7)(x+2) > Notice that it is impossible for x in the factor x+2 to spontaneously > have non-unit factors in common with 7, even in the ring of algebraic > integers, no matter what the value of x is. That's important. > (Ponder it.) The mainstream math. distinguishes factorizations of polynomials > from factorizations in Z (the ordinary integers) Z[sqrt(-1)] and > other rings of numbers. I'm not sure what you mean by: Notice that it is impossible for x in the factor x+2 to spontaneously > have non-unit factors in common with 7, even in the ring of algebraic > integers,[...] Good!!! If you understood everything before then there is progress. Let's do a simpler result, consider that the coefficient of x, with x +2, cannot change dependent on the value of x, with non-unit factors, even in the ring of algebraic integers. Notice that with *unit* factors it can change!!! 7(x^2 + 3x + 2) = (7u 1*x + 7*u 1)(u 2*x+2*u 2) where u 1*u 2 = 1 in the ring of algebraic integers, so now u 2 is the coefficient, so it changes while the 7 did NOT re-distribute. So the coefficient of x cannot transform into a non-unit factor in common with 7 dependent on the value of x, even in the ring of algebraic integers. > Suppose I let x = 7. Then gcd(x, 7) = 7. It's quite possible > that I misunderstand what is meant above by spontaneously . But I think we can agree on this: > if x is an algebraic integer, then > 7(x^2 + 3x + 2) and (7x + 7) will always have 7 as a factor > in the ring of algebraic integers. Irrelevant. > If x is an algebraic integer, then for infinitely many x, > x + 2 will not have 7 as a factor in the ring of > algebraic integers. Also irrelevant. Not important to worry about at all. > HOWEVER, with > 7*(175x^2 - 15x + 2) = (5b 1(x) + 7)(5b 2(x)+ 2) > and non-linear functions that are non-rational with a rational x, you > CAN have a non-unit factor in common with 7 in the ring of algebraic > integers spontaneously generated. The same thing here with the word spontaneously; I'm not sure > what you mean by that. David Bernier Well you know what despite the distribution proven on the complex plane where 7 distributes in this one particular way, in the ring of algebraic integers with an integer x you can get a non-unit factor of 7 from 5b 2(x)+ 2 while in contrast you cannot have that happen with x+2 from 7(x^2 + 3x + 2) = (7x + 7)(x + 2). So it's a mystery factor from out of thin air...where does it come from? Who sent it? What is its motivation? James Harris === Subject: Re: JSH: Questioning Galois Theory <9eo6l49p6ecmfqijod79v51h9l8g0gaer9@4ax.com> posting-account=wVv_VwoAAAAVTfUuyxLzug5SzYWCgHj1 Gecko/20081203 Firefox/2.0.0.19,gzip(gfe),gzip(gfe) > My point is simple: I have simple proof of a massive error that > entered the mathematical field over a hundred years ago, so the error > has to be subtle. > So subtle that you cannot tell us what it is? > It's easily demonstrated now but subtle in that it lasted for over a > hundred years and requires you do some things not intuitive for most > math students, for instance, who would have thought that > 7(x^2 + 3x + 2) = (7x + 7)(x + 2) > could be a matter of debate or show a crucial point for a major > mathematical proof? > You have still not us what it is you are trying to show. We know that > it is easily demonstrated, we know that it is subtle, we know > that it lasted for over a hundred years, we know that it requires > you do some things not intuitive for most math students, but we do > to shout, but you do not seem to be getting the message. Please give > us a statement of what it is you are trying to show. > rossum > I agree. James: please explain this alleged goddamn error until > we get it. > Dave The error is the ability to demonstrate an apparent contradiction-- > anathema to mathematics. > as the ability to do things. Yet again, you fail to state explicitly what you think you have proved. > And it's kind of cool too how easy it is to show the bane of > mathematics (or what looks like it), as I can use a distributive > property argument to show how a trivial factor of 7 distributes > through a non-traditional factorization. Note I said distributes as I think for many of you the word > distributive in the distributive property was kind of a mysterious > thing, even though you probably thought before that a*(b+c) = a*b + > a*c was so meaninglessly trivial. Notice the distributive property is valid on the complex plane. So I prove a distribution on the complex plane! In the complex plane with 7*(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x)+ 7) where the a's are roots of a^2 - (7x-1)a + (49x^2 - 14x) = 0 you normalize: a_1(x) = b_1(x), and a_2(x) = b_2(x) - 1, as then you have 7*(175x^2 - 15x + 2) = (5b_1(x) + 7)(5b_2(x)+ 2) where b_1(0) = 0, b_2(0) = 0. And you have one factorization out of infinity and in THAT > factorization the 7 has distributed in one way, which is easily > verifiable at x=0, as then you it distributed through 5b_1(0) + 7, as that equals 7(0 + 1), so with the distributive > property you have a=7, b=0, c=1. The problem with an easy argument here is that it runs into bad > mathematical habits in other areas where people clearly think factor, > and an immediate impulse is to say 7 is a factor of one function, > which is true, but 7 is a factor of both functions on the complex > plane!!!!!!!!!! > The same can be said of 2, or 3, or pi, or 1/i, or ANY OTHER NONZERO COMPLEX NUMBER!!!!. You have just stated a monumental triviality. > The argument is NOT a factor argument!!! It's a distributive argument. > State a theorem that has actual content. > However, a factor problem emerges--the apparent contradiction, yeah!!! > weird cool!!!---in the ring of algebraic integers which can be > considered with a simpler factorization: 7(x^2 + 3x + 2) = (7x + 7)(x+2) Notice that it is impossible for x in the factor x+2 to spontaneously > have non-unit factors in common with 7, even in the ring of algebraic > integers, no matter what the value of x is. Depends on x, doesn't it? For example, if x = 5, x + 2 very definitely does have non-unit factors in common with 7. It is NOT impossible for x in the factor x + 2 to spontaneously have non-unit factors in common with 7, even in the ring of INTEGERS. Any of course, in the ring of algebraic integers, it is trivial to show 7*(x^2 + 3x + 2) = (sqrt(7)*x + sqrt(7)*(sqrt(7)*x + 2sqrt(7)). Which again just contradicts what you just claimed. Hmmm. > That's important. > (Ponder it.) > Maybe you should do a little pondering first. > HOWEVER, with 7*(175x^2 - 15x + 2) = (5b_1(x) + 7)(5b_2(x)+ 2) and non-linear functions that are non-rational with a rational x, you > CAN have a non-unit factor in common with 7 in the ring of algebraic > integers spontaneously generated. It just emerges out of thin air. > Thin air or not, IT DOES EMERGE. If you said above were true, it would not. Your claim contradicts a brute arithmetical fact: when x = 1, the auxiliary quadratic equation is a^2 - 6a + 35 = 0, and neither root is divisible by 7, and both roots have nonunit factors in common with 7, in the ring of algebraic integers. To deny this - as you are doing when you say you have an apparent contradiction [see above] is exactly equivalent to saying that 2 + 2 is not equal to 4. But you keep saying it. Marcus. > If you were able to keep up this far you may intuitively recoil from > that assessment, but remember, the 7 can be shown to have distributed > in a particular way on the complex plane. However, against the logic > of that distribution non-unit factors in common with 7 emerge in the > ring of algebraic integers!!! Some of you may be able to guess how or know from other postings I've > done. For the rest I'll leave that as a start to see how reasonable you > actually are here, after all, some of you asked me to explain and I > have given most of the explanation. James Harris === Subject: Re: JSH: Questioning Galois Theory > In the complex plane with 7*(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x)+ 7) where the a's are roots of a^2 - (7x-1)a + (49x^2 - 14x) = 0 you normalize: a_1(x) = b_1(x), and a_2(x) = b_2(x) - 1, as then you have 7*(175x^2 - 15x + 2) = (5b_1(x) + 7)(5b_2(x)+ 2) where b_1(0) = 0, b_2(0) = 0. You should explicitly give a_1(x) and a_2(x), because otherwise there is a 50% chance that someone trying to check your work will first try for a_1 what you are using for a_2, and vice versa. This makes a difference. Someone who takes a_1(x) = -((sqrt(-147*x^2+42*x+1)-7*x+1)/2) a_2(x) = (sqrt(-147*x^2+42*x+1)+7*x-1)/2 will end up with b_1(0) = -1, b_2(0) = 1. Proper mathematical presentation should not require the reader to guess. -- --Tim Smith === Subject: JSH: Simple math but bad math habits posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif Gecko/2008120122 Firefox/3.0.5,gzip(gfe),gzip(gfe) It is hard to hear that you have been taught wrong, and harder still to confront dogma, because mathematical proof is just a phrase for most of you as you've never been put in a situation where you really did not wish to accept a result, so you avoid the mathematical proof but by rationalizing continue to *believe* yourselves to be mathematicians or real students of mathematics, when you no longer are. I defined mathematical proof. Don't believe me? Google it. Google: define mathematical proof I come up #2 now in most venues. Physics students *should* do better. Physicists know about resistance to results and hard to understand results which challenge accepted views, but the field has softened because of the dominance of mathematical techniques, so people who are really mathematicians get to pretend to be physicists, when they are not, and there is a worship as well of authority, so that when the math people say *false* physics students follow along because, what else can they do? Resist authority? But, but, but...how can they? All of that is a preamble for one of the simplest most powerful mathematical arguments in the history of human civilization which mathematicians have resisted for over 6 years now despite how easy it is to prove. It only requires you accept the distributive property and believe that proof is, well, proof. The distributive property is: a*(b + c) = a*b + a*c In the complex plane with 7*(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x)+ 7) where the a's are roots of a^2 - (7x-1)a + (49x^2 - 14x) = 0 you normalize: a_1(x) = b_1(x), and a_2(x) = b_2(x) - 1, as then you have 7*(175x^2 - 15x + 2) = (5b_1(x) + 7)(5b_2(x)+ 2) where b_1(0) = 0, b_2(0) = 0. And you have one factorization out of infinity and in THAT factorization the 7 has distributed in one way, which is easily verifiable at x=0, as then you it distributed through 5b_1(0) + 7, as that equals 7(0 + 1), so with the distributive property you have a=7, b=0, c=1. EASY. But remember 6 years of mathematicians arguing against this result!!! Now if we consider that a*(b+c) = a*b + a*c, is true if one of the elements is a function then I have a*(f(x) + b) = a*f(x) + a*b and the TYPE of the function does NOT MATTER; however, that challenges current mathematical intuition, so while with something like 7(x^2 + 3x + 2) = (7x + 7)(x + 2) math people found it hard to dispute the distributive property, hide the 7 away with: 7*(175x^2 - 15x + 2) = (5b_1(x) + 7)(5b_2(x)+ 2) and they disputed the result as they don't want to believe that with a^2 - (7x-1)a + (49x^2 - 14x) = 0 only one root should have 7 as a factor as that's what the distribution shows. (Remember the factorization is normalized and a_1(x) = b_1(x), and a_2(x) = b_2(x) - 1.) Now in case you forgot your algebra classes, it is NOT taught in them that only one of the roots of a^2 - (7x-1)a + (49x^2 - 14x) = 0 in general should have 7 as a factor. You can verify one case easily enough, x=0: a^2 + a = 0 as one root is 0, and 0, of course has 7 as a factor. But use x=1, and you get a^2 - 6a + 35 = 0 and only one of its roots actually has 7 as a factor, but you can prove in the ring of algebraic integers that NEITHER root has 7 as a factor as neither root does--IN THAT RING. The ring gives bad results. Techniques based on it give wrong results. So you have an advancement of human knowledge: it's now possible in this case to determine 7 is a factor of a root without being able to see it directly, where it's also not determined which root. There is an ambiguity which cannot be removed which means the solutions are paired or entangled in a way that cannot be beaten. You must take them by two's. With quarks you must take them by three's. Which may indicate some cubic function which controls some aspect of quark behavior, which cannot be probed without advanced analytical tools meaning some aspect of quark behavior may be beyond the vision of humanity with currently accepted mathematical tools, but possible to analytically study with the ones I've introduced. For perspective I used some of those tools to also generally solve binary quadratic Diophantine equations. Don't know what those are? Google it. I think I come up #1. So there may be a ceiling on what humanity can do in physics at this point because it is not using the full mathematical knowledge available, where mathematicians have been resisting this result as it overturns past beliefs, and they wrongly believe their field is immune from revolutionary upheavals. Their belief is holding back the scientific progress of our species. And THAT is how you go from a very simple quadratic argument which requires that you only believe the distributive property to understanding how math people could fight for belief for over 6 years against mathematical proof, and hurt the physics community and the progress of the entire human species in the process. James Harris === Subject: Re: JSH: Simple math but bad math habits > It is hard to hear that you have been taught wrong, and harder still > to confront dogma, because mathematical proof is just a phrase for > most of you as you've never been put in a situation where you really > did not wish to accept a result, so you avoid the mathematical proof > but by rationalizing continue to *believe* yourselves to be > mathematicians or real students of mathematics, when you no longer > are. You nailed it. [...] -- Michael Press === Subject: Re: JSH: Simple math but bad math habits posting-account=BVr-MgkAAABE4LRE1rHDnN9heo0IZZTk 2.0.50727; .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) > It is hard to hear that you have been taught wrong, and harder still > to confront dogma, because mathematical proof is just a phrase for > most of you as you've never been put in a situation where you really > did not wish to accept a result, so you avoid the mathematical proof > but by rationalizing continue to *believe* yourselves to be > mathematicians or real students of mathematics, when you no longer > are. I defined mathematical proof. Don't believe me? Google it. Google: > define mathematical proof I come up #2 now in most venues. Physics students *should* do better. Physicists know about resistance > to results and hard to understand results which challenge accepted > views, but the field has softened because of the dominance of > mathematical techniques, so people who are really mathematicians get > to pretend to be physicists, when they are not, and there is a worship > as well of authority, so that when the math people say *false* physics > students follow along because, what else can they do? Resist > authority? But, but, but...how can they? All of that is a preamble for one of the simplest most powerful > mathematical arguments in the history of human civilization which > mathematicians have resisted for over 6 years now despite how easy it > is to prove. It only requires you accept the distributive property and believe that > proof is, well, proof. The distributive property is: a*(b + c) = a*b + a*c In the complex plane with 7*(175x^2 - 15x + 2) = (5a 1(x) + 7)(5a 2(x)+ 7) where the a's are roots of a^2 - (7x-1)a + (49x^2 - 14x) = 0 you normalize: a 1(x) = b 1(x), and a 2(x) = b 2(x) - 1, as then you have 7*(175x^2 - 15x + 2) = (5b 1(x) + 7)(5b 2(x)+ 2) where b 1(0) = 0, b 2(0) = 0. And you have one factorization out of infinity and in THAT > factorization the 7 has distributed in one way, which is easily > verifiable at x=0, as then you it distributed through 5b 1(0) + 7, as that equals 7(0 + 1), so with the distributive property you have > a=7, b=0, c=1. EASY. But remember 6 years of mathematicians arguing against this > result!!! Now if we consider that a*(b+c) = a*b + a*c, is true if one of the > elements is a function then I have a*(f(x) + b) = a*f(x) + a*b and the TYPE of the function does NOT MATTER; however, that challenges > current mathematical intuition, so while with something like 7(x^2 + 3x + 2) = (7x + 7)(x + 2) math people found it hard to dispute the distributive property, hide > the 7 away with: 7*(175x^2 - 15x + 2) = (5b 1(x) + 7)(5b 2(x)+ 2) and they disputed the result as they don't want to believe that with a^2 - (7x-1)a + (49x^2 - 14x) = 0 only one root should have 7 as a factor as that's what the > distribution shows. (Remember the factorization is normalized and a 1(x) = b 1(x), and a 2(x) = b 2(x) - 1.) Now in case you forgot your algebra classes, it is NOT taught in them > that only one of the roots of a^2 - (7x-1)a + (49x^2 - 14x) = 0 in general should have 7 as a factor. You can verify one case easily > enough, x=0: a^2 + a = 0 as one root is 0, and 0, of course has 7 as a factor. But use x=1, > and you get a^2 - 6a + 35 = 0 and only one of its roots actually has 7 as a factor, but you can > prove in the ring of algebraic integers that NEITHER root has 7 as a > factor as neither root does--IN THAT RING. The ring gives bad results. Techniques based on it give wrong > results. So you have an advancement of human knowledge: it's now possible in > this case to determine 7 is a factor of a root without being able to > see it directly, where it's also not determined which root. There is an ambiguity which cannot be removed which means the > solutions are paired or entangled in a way that cannot be beaten. You > must take them by two's. With quarks you must take them by three's. Which may indicate some cubic function which controls some aspect of > quark behavior, which cannot be probed without advanced analytical > tools meaning some aspect of quark behavior may be beyond the vision > of humanity with currently accepted mathematical tools, but possible > to analytically study with the ones I've introduced. For perspective I used some of those tools to also generally solve > binary quadratic Diophantine equations. Don't know what those are? Google it. I think I come up #1. So there may be a ceiling on what humanity can do in physics at this > point because it is not using the full mathematical knowledge > available, where mathematicians have been resisting this result as it > overturns past beliefs, and they wrongly believe their field is immune > from revolutionary upheavals. Their belief is holding back the scientific progress of our species. And THAT is how you go from a very simple quadratic argument which > requires that you only believe the distributive property to > understanding how math people could fight for belief for over 6 years > against mathematical proof, and hurt the physics community and the > progress of the entire human species in the process. James Harris Where does that 7 really go? Given: P(x) = 175x^2 - 15x + 2 7*P(x) = 7*(175x^2 - 15x + 2) = (5a 1(x) + 7)(5a 2(x)+ 7) How does the 7 on the left distribute on the right? P(x) = 7 * 5^2 *x^2 - 3 * 5* x + 2 Rename the 7 and 5 Y = 7 Z = 5 Express the 2 and 3 in P(x) as functions of Y and Z Y - Z = 2 2 * Z - Y = 3 P(x) = Y * Z^2 * x^2 - (2 * Z - Y) * Z * x + (Y - Z) Name the 7 multiplier to be tracked Use lower case y because y = Y y = 7 y * P(x) = y * Y * Z^2 * x^2 - y * (2 * Z - Y) *Z * x + y * (Y - Z) to be factored as y * P(x) = (Z * a 1(x) + Y)*(Z * a 2(x) + Y) Find the a's as the roots of y * P(x) as a quadratic in Z y * P(x) = y * Y * Z^2 * x^2 - y * (2 * Z - Y) *Z * x + y * (Y - Z) Multiply out y * P(x) = y * Y * Z^2 * x^2 - 2 * y * Z^2 * x + y * Y * Z * x + y * Y - y * Z Collect terms of Z^2, y * Z, y * Y y*P(x) = (y * Y * Z^2 * x^2 - 2 * y * Z^2 * x) + (y * Y * Z * x - y * Z) + y * Y Factor out Z^2, y * Z, y * Y y*P(x) = (y * Y * x^2 - 2 * y * x) * Z^2 + (Y * x - 1) * y * Z + (y * Y) a^2 - (Y * x - 1) * a + (y * Y * x^2 - 2 * y * x) = 0 Using the quadratic formula to get a 1(x) and a 2(x) A = 1 B = - (Y * x - 1) C = (y * Y * x^2 - 2 * y * x) B^2 = ( - (Y * x - 1))^2 = (Y * x - 1)^2 B^2 = Y^2 * x^2 - 2 * Y * x + 1 4 * A * C = 4 * 1 * (y * Y * x^2 - 2 * y * x) 4 * A * C = 4 * y * Y * x^2 - 4 * 2 * y * x 4 * A * C = (4 * y * Y * x^2 - 8 * y * x) B^2 - 4 * A * C = Y^2 * x^2 - 2 * Y * x + 1 - (4 * y * Y * x^2 - 8 * y * x) B^2 - 4 * A * C = Y^2 * x^2 - 2 * Y * x + 1 - 4 * y * Y * x^2 + 8 * y * x B^2 - 4 * A * C = Y^2 * x^2 - 4 * y * Y * x^2 + 8 * y * x - 2 * Y * x + 1 B^2 - 4 * A * C = (Y^2 - 4 * y * Y)* x^2 + (8 * y - 2 * Y) * x + 1 B^2 - 4 * A * C = (Y^2 - 4 * y * Y)* x^2 - (-8 * y + 2 * Y) * x + 1 B^2 - 4 * A * C = (Y^2 - 4 * y * Y)* x^2 - (-4 * y + Y)* 2 * x + 1 B^2 - 4 * A * C = (Y^2 - 4 * y * Y)* x^2 - (Y - 4 * y)* 2 * x + 1 a(x) = [ Y * x - 1 +/- sqrt { (Y^2 - 4 * y * Y) * x^2 - (Y - 4 * y) * 2 * x + 1 } ] / 2 which occurs in y * P(x) = (Z * a 1(x) + Y)*(Z * a 2(x) + Y) Show the multiplier 7 of P(x) y * P(x) = (Z * a 1(x) + Y)*(Z * a 2(x) + Y) 7 * P(x) = (Z * a 1(x) + Y)*(Z * a 2(x) + Y) Show the multiplier 7 appearing in a 1(x) and a 2(x) a(x) = [ Y * x - 1 +/- sqrt { (Y^2 - 4 * y * Y) * x^2 - (Y - 4 * y) * 2 * x + 1 } ] / 2 a(x) = [ Y * x - 1 +/- sqrt { (Y^2 - 4 * 7 * Y) * x^2 - (Y - 4 * 7) * 2 * x + 1 } ] / 2 The 7 multiplier distributes only into the square root part of both a 1 (x) and a 2(x) The 7's visible in the right hand side of y * P(x) = (Z * a 1(x) + Y)*(Z * a 2(x) + Y) like this y*(175x^2 - 15x + 2) = (5a 1(x) + 7)(5a 2(x)+ 7) are from Y = 7 contained in 175x^2 - 15x + 2 and have nothing to do with the 7 multiplier on the left hand side. Enrico Quick check at x = 1 (y = 7, Y = 7, Z = 5) a(1) = [ 7 * 1 - 1 +/- sqrt { (7^2 - 4 * 7 * 7) * 1^2 - (7 - 4 * 7) * 2 * 1 + 1 } ] / 2 a(1) = [ 6 +/- sqrt { (49 - 196) * 1 - (7 - 28) * 2 + 1 } ] / 2 a(1) = [ 6 +/- sqrt { (-147) - (-21) * 2 + 1 } ] / 2 a(1) = [ 6 +/- sqrt { (-147) - (-21) * 2 + 1 } ] / 2 a(1) = [ 6 +/- sqrt { (-147) + 43 } ] / 2 a(1) = [ 6 +/- sqrt { -104 } ] / 2 a(1) = 3 +/- sqrt { -104 / 4 } a(1) = 3 +/- sqrt { - 26 } Which matches James' Let x=1, then you have a^2 - 6a + 35 = 0, which you can solve using the quadratic formula to get a = (6 +/- sqrt(-104))/2 = 3 +/- sqrt(-26) Quick check at x = 0 (y = 7, Y = 7, Z = 5) a(0) = [ 7 * 0 - 1 +/- sqrt { (7^2 - 4 * 7 * 7) * 0^2 - (7 - 4 * 7) * 2 * 0 + 1 } ] / 2 a(0) = [ - 1 +/- sqrt { 0^2 - 0 + 1 } ] / 2 a(0) = [ - 1 +/- sqrt { 1 } ] / 2 a(0) = [ - 1 +/- 1 ] / 2 a(0) = [-1 + 1]/2 , [-1 -1]/2 a(0) = 0, -1 === Subject: Re: JSH: Simple math but bad math habits posting-account=rIfu6QoAAAD5nXG3h9QEE0J3dZn1U45R Gecko/2008120122 Firefox/3.0.5,gzip(gfe),gzip(gfe) > It is hard to hear that you have been taught wrong [...] WHAT have be been taught wrong, James? === Subject: JSH: Mathematicians cheating is kind of weird posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif Gecko/2008120122 Firefox/3.0.5,gzip(gfe),gzip(gfe) Ok, so I have a simple proof of a massive problem in number theory and even got a more complicated cubic version published in a formally peer reviewed mathematical journal which is now dead. It died about a month after it pulled my paper after publication after some math people sent a bunch of emails claiming it was wrong. To see the archives of the now dead, dead, dead math journal, Google: No other journal would touch that paper and a physicist I had shopping it around told me he got the answer back that they just weren't going to touch it, not that it was wrong. I personally sent the paper finally to the Annals of Mathematics at Princeton, and was never told it was wrong, or anything else for months. After six months I contacted them asking what was its status and was told the database had been noted that a rejection had been sent by email. I never received a rejection. I asked if I could be told why, and was told that was all the info in the database, so no reviewers report. I have recently greatly simplified my presentation of the problem, and written another paper. It can be found at a math group I recently created: (Hope that works if it doesn't, well, um, hope it works.) If they reject it will go to the Annals. If they reject I will work my way down and work journals around the world as this time I am very serious. If necessary later I will pursue prosecutions for academic fraud and have no problems with pushing government agencies to issue subpoenas for people at Princeton or wherever. I have no respect for any institution in the world. I have no problem with having any academic at any level brought before a jury. So you grad students know you have no protection here. I may need any number of you to testify about what your professors were saying. But what's more interesting to me is this weird behavior from academics who should be terrified about not only losing their careers by ignoring this result, but dealing with massive humiliation along the way, so it occurs to me that they do not believe that proof will matter! Like I can talk about Barry Mazur at Harvard as a little twerp who got a look at my earlier paper, but so far to my knowledge has done nothing. Of course there is no way if the result gets accepted I would just sit still about him remaining at his position, so he never believed that it would be accepted. And he will not be at Harvard much longer. I guarantee it. I can go on and on. There is Andrew Granville who infamously told me his grad students often found something like my prime counting function, who also looked over the paper. Kenneth Ribet is safe as he never commented on my work and actually helped me a while back with a stupid bet I made (and lost). I can rip through a Who's Who of academics at institutions around the world. So, then, they never expected anyone to accept mathematical proof. Now isn't that odd? What do they think they know that I don't. Some of you have been remarkably arrogant as well, especially considering the massive hits you are going to take in the public eye as it will be very public and none of you will be anonymous any longer. Your faces will be of interest as will be your living circumstances, especially certain ones of you like Uncle Al and mensanator who seems to have the delusion that he can hide when the world is actually looking for him. This issue is of great importance to me as I've been very curious about why people would act against their own self-interests on such a scale when the end was not really in doubt. It has always been just a matter of time. James Harris === Subject: Re: JSH: Mathematicians cheating is kind of weird posting-account=rIfu6QoAAAD5nXG3h9QEE0J3dZn1U45R Gecko/2008120122 Firefox/3.0.5,gzip(gfe),gzip(gfe) > Ok, so I have a simple proof of a massive problem in number theory and > even got a more complicated cubic version published in a formally peer > reviewed mathematical journal which is now dead. It died about a > month after it pulled my paper after publication after some math > people sent a bunch of emails claiming it was wrong. the obvious criticism that it is in error. [...] === Subject: Re: JSH: Mathematicians cheating is kind of weird > I can go on and on. On this point you will meet no argument. You do go on, and on, and on. Like the crackling of thorns under the pot Full of sound and fury Signifying ... nothing. === Subject: Re: JSH: Mathematicians cheating is kind of weird posting-account=HaopWgoAAADs72-s8RQYwP_-ruRUuNzX .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; InfoPath.1),gzip(gfe),gzip(gfe) > Ok, so I have a simple proof of a massive problem in number theory and > even got a more complicated cubic version published in a formally peer > reviewed mathematical journal which is now dead. It died about a > month after it pulled my paper after publication after some math > people sent a bunch of emails claiming it was wrong. To see the archives of the now dead, dead, dead math journal, Google: No other journal would touch that paper and a physicist I had shopping > it around told me he got the answer back that they just weren't going > to touch it, not that it was wrong. I personally sent the paper finally to the Annals of Mathematics at > Princeton, and was never told it was wrong, or anything else for > months. After six months I contacted them asking what was its status > and was told the database had been noted that a rejection had been > sent by email. I never received a rejection. I asked if I could be > told why, and was told that was all the info in the database, so no > reviewers report. I have recently greatly simplified my presentation of the problem, and > written another paper. It can be found at a math group I recently > created: > (Hope that works if it doesn't, well, um, hope it works.) > If they reject it will go to the Annals. If they reject I will work my way down and work journals around the > world as this time I am very serious. If necessary later I will pursue prosecutions for academic fraud and > have no problems with pushing government agencies to issue subpoenas > for people at Princeton or wherever. I have no respect for any institution in the world. I have no problem > with having any academic at any level brought before a jury. So you grad students know you have no protection here. I may need any > number of you to testify about what your professors were saying. But what's more interesting to me is this weird behavior from > academics who should be terrified about not only losing their careers > by ignoring this result, but dealing with massive humiliation along > the way, so it occurs to me that they do not believe that proof will > matter! Like I can talk about Barry Mazur at Harvard as a little twerp who got > a look at my earlier paper, but so far to my knowledge has done > nothing. Of course there is no way if the result gets accepted I would just sit > still about him remaining at his position, so he never believed that > it would be accepted. And he will not be at Harvard much longer. I > guarantee it. I can go on and on. There is Andrew Granville who infamously told me his grad students > often found something like my prime counting function, who also looked > over the paper. Kenneth Ribet is safe as he never commented on my work and actually > helped me a while back with a stupid bet I made (and lost). I can rip through a Who's Who of academics at institutions around the > world. So, then, they never expected anyone to accept mathematical proof. Now isn't that odd? What do they think they know that I don't. Some of you have been remarkably arrogant as well, especially > considering the massive hits you are going to take in the public eye > as it will be very public and none of you will be anonymous any > longer. Your faces will be of interest as will be your living circumstances, > especially certain ones of you like Uncle Al and mensanator who > seems to have the delusion that he can hide when the world is actually > looking for him. This issue is of great importance to me as I've been very curious > about why people would act against their own self-interests on such a > scale when the end was not really in doubt. It has always been just a matter of time. James Harris You are so full of . You are a liar, cheat, charlatan and snake oil salesman. You continue to try and perpetuate your lies - and deciet. You are a narcissist! You are wrong! You have nothing! You will amount to nothing! You are a super troll, crank and are crazy! Liar - liar - liar! LIAR!!!!!