== hey, the ten-year programme is perfectly on schedule, as far as I can see. I wonder if i can get a big prize, by solving the Perfect Box problem -- any offers, you dirty-rotten mathematicians? some other guy said taht he proved it (gave the thing on his site), but he made a dumb error on another problem, so, I didn't pursue it; I'm not very accomplished in mumbertheory (and the other problem was simple geometry). but, yeah: I've proven that there is no perfect box, whose edges and diagonals, including the interior one, are integral, with just the pyhtagorean theorem as the Air-hammer -- granite is tough stuff, y'know! that's a rectangular box or parallelipiped, all of whose 3 edge-lengths are different. > How many months do you think it would take Harris to find a correct --Dec.2000 'WAND' Chairman Paul O'Neill, reelected to Board. Newsish? http://www.rand.org/publications/randreview/issues/rr.12.00/ http://members.tripod.com/~american_almanac ==== > I've always wondered about Mathematical Olympics. Don't the judges have > to be smarter than any of the contestants, to be able to judge them > accordingly? Age (that is, experience) and time provide an advantage to the judges. The reviewed the problem are not as young and inexperienced (usually) as the typical math olympiad contestant. People get better at that kind of problem with practice. Moreover, developing model solutions for an olympiad problem can sometimes take weeks, while the contestants have at most hours to find a suitable solution. The judges have solutions at hand, so they can be spared the effort of devising a solution from scratch, and can simply do (what I acknowledge is still hard work) a comparison between the model answer and the answer submitted by each contestant. > But mathematics is different. Unlike athletics, it's not plain to see > who is better than who. Actually, to my eye it's often difficult to see which ice skater, for example, is better and the judging standards are sufficiently unclear even to the judges that most ice-skating competitions are judged by panels. Machines can tell who won a foot race, but fallible human beings have to make debatable decisions to decide, for example, how many points should be awarded for what level of performance in each event in the decathlon. > You have to be a mathematician yourself. Agreed that it takes one to know one at the highest level of mathematics. There is an interesting prize awarded every year by the Clay Mathematics Institute http://www.claymath.org/Education/Olympiad_Scholar/ for the student who displays the most original and mathematically correct solution to a problem in the USA Mathematical Olympiad. As you can imagine, the students who win this award are those who DON'T follow the model solution developed beforehand by the judges, but who come up with something unexpected. And I'm sure choosing the winner of that award each year is a difficult task in judging. P.S. I judge at a MUCH lower level of mathematical competitions, which exhausts my personal mathematical abilities. I admire the people who can judge at a higher level. -- Karl M. Bunday Christ has set us free. Galatians 5:1 Learn in Freedom (TM) http://learninfreedom.org/ ==== > What are actually good books or websites on calculus and algebra one > can recommend? Here's my FAQ-in-progress about studying calculus. Suggestions from onlookers for improvements in this FAQ would be much appreciated. [Rough draft of Calculus self-study FAQ begins here:] The best calculus textbook, at least in English, is Michael Spivak's book Calculus (Publish or Perish Press, third edition). This textbook is not specifically written to the AP Calculus syllabus and thus is unknown to many AP calculus teachers, but it is unanimously recommended by mathematicians. > What comes after calculus? What comes after a first course in calculus is a second try at learning calculus to really UNDERSTAND calculus. Hardly any universities use Michael Spivak's book Calculus (third edition, Publish or Perish Press) as a textbook for a first calculus course, but it is positively SCARY how unanimous mathematicians are in recommending that book for people who really want to understand calculus. Spivak's book also has good humor, as most good mathematical books do. A little while earlier, someone else on the same newsgroup asked a series of detailed questions about studying calculus. > Anyone got any idea as to good book on calculus? The calculus book that I have seen most consistently get glowing reviews from professional mathematicians, with many calling it the best calculus book, is Calculus by Michael Spivak (3rd edition, Publish or Perish Press). I own Spivak's book, and know several people locally who think it is wonderful. However, Spivak's Calculus is not an EASY introduction to calculus--it's very useful to have for clear explanations and working through it would probably give you a deep understanding of calculus that would be difficult to forget, but it wouldn't be the fastest way to learn, for example, the calculus tested on the AP calculus exams. I second-source (actually, quintuple-source or more) calculus books, as I am also trying to learn calculus by self-study. In the end, the only way to learn calculus is to do A LOT of problems that build progressively on earlier understanding--on that, all teachers of calculus agree, whatever else they disagree on. And calculus is, indeed, one of the math courses for which there is the most varied assortment of textbooks, sometimes taking wildly differing approaches. > Can I learn calculus in the internet? There is a distance learning course on calculus for which you can get college credit (if you PAY for the college credit and keep up with your required homework) offered by the University of Illinois Urbana-Champaign http://www-cm.math.uiuc.edu/ called Calculus and Mathematica which some math professors like a lot, and others decry. I MAY just buy the book for that course through Amazon.com and work through it myself with a student copy of Mathematica, forgoing the college credit, but I'm still trying to decide. There is another distance learning course about calculus offered by the Education Program for Gifted Youth (EPGY) at Stanford University http://epgy.standford.edu/ but that course, as its name implies, is for gifted young people who haven't yet graduated from high school. That course uses a combination of the Anton textbook and innovative course software developed by Stanford. My oldest son is taking EPGY courses that are prerequisites for the calculus course right now, and may be taking calculus within two years. > Is there a web site to learn calculus? what amounts to a complete, FREE textbook by a famous mathematician in at least one case. Those include http://www.math.gatech.edu/~morley/1507/MeaninglessSymbolicManipulation.html (approaches to studying Calculus, including a recommendation of some of the books I just mentioned) http://www.math.washington.edu/~duchamp/124notes/k124-main.pdf http://www.math.washington.edu/~duchamp/125notes/k125-main.pdf (Two lengthy Adobe Acrobat .PDF files with a college calculus course, free for the downloading, by Professor Neal Koblitz of the University of Washington) http://www.math.hawaii.edu/~lee/calculus/ University of Hawaii) There is a lot more where these links came from; you could find good stuff about calculus on the Web for hours. Try Google http://www.google.com/ to run more searches of your own. homeschooled kids are looking for something like a high school calculus book. The first place to look is in your friendly local public library, where you may find several different calculus books aimed at high school students. Stewart's book is used here in Minnesota by the University of Minnesota Talented Youth Mathematics Program (UMTYMP) and the Anton book is used by EPGY; I can get both in my local library systems. How to Learn Calculus: A Streetwise Guide looks pretty good to me, although I would have your local library request it rather than buying it yourself. Calculus Made Easy is NOT a complete calculus course, but it is good for motivation and Calculus is a good introductory text; there are lots of high school cram books on calculus in good public libraries. There are many good calculus preparation sites for university students, for example, http://www.math.mun.ca/~apics/calculus/ The person I replied to on Usenet asked another useful question: > What about other books that would serve as backgrounders > along the same vein as the above point? There are LOTS of books for transition courses that bridge the gap between undergraduate calculus and math courses beyond calculus for math and science majors. Those books often have titles like Introduction to Proof, or Problem Solving or Introduction to Advanced Mathematics or Mathematical Thinking or phrases more or less like that. It is a good idea to start reading a book like that, and working through its exercises, BEFORE finishing a calculus course. Probably your local university has several book like this in the campus bookstore, and the math department could recommend whatever title is used where you go to school. [End of Calculus FAQ--revision suggestions eagerly sought] Hope this helps! -- Karl M. Bunday Christ has set us free. Galatians 5:1 Learn in Freedom (TM) http://learninfreedom.org/ ==== > > That's because I figure it may take me a few months to get everything > through a computerized proof check myself, and saving those months is > worth $100,000 US to me. > > You hate to work THAT much? Well, given what I've discovered over the past two years and how long I've waited $100,000 US is not a big deal. Besides, I have to admit that it'd be neat to share *something* with someone else, so we could party together, meet celebs, heads of state, and wonder about why math society fought for so long and hard. Then again, if no one is up to the challenge, I'll go ahead and do it all myself, like usual. Or that math journal will finish its review of my paper Advanced Polynomial Factorization in my favor. In any event, readers can be sure that the poster here doesn't have the skills needed to handle a computer check, or I'd think he wouldn't be wasting time, when there's money to be made. James Harris ==== > It doesnât matter how much time you might have, some things simply will not > happen in spite of all the faith you might have. For example, you will never > throw the number seven (the most common combination of two die), with a fair > pair of dice, 27 straight times. It is mathematically impossible. It will not > happen by random chance; it cannot happen! Faith or no faith, it will not > happen. It is certainly not mathematically impossible to get a roll of twenty-seven sevens in 27 rolls , just very unlikely. If it were impossible, the probability would be exactly equal to zero instead of being 1/6^27. ==== > It is certainly not mathematically impossible to get a roll of > twenty-seven sevens in 27 rolls , just very unlikely. > > If it were impossible, the probability would be exactly equal to > zero instead of being 1/6^27. -- In fact, given the number of times in the past that a pair of dice has been rolled 27 times in a row, it seems unlikely that it hasn't happened to someone. Have a tolerable existence. Eli ==== > In fact, given the number of times in the past that a pair of dice has been > rolled 27 times in a row, it seems unlikely that it hasn't happened to > someone. One of Littlewood's essays, contained in the collection A Mathematician's Miscellany, deals with seemingly unlikely events, and ocomputing how likely they really are. For example, he says it is not unreasonable that about once a year in England, someone receives a Bridge hand of thirteen of a suit. -- G. A. Edgar http://www.math.ohio-state.edu/~edgar/ ==== It is certainly not mathematically impossible to get a roll of > twenty-seven sevens in 27 rolls , just very unlikely. If it were impossible, the probability would be exactly equal to > zero instead of being 1/6^27. -- In fact, given the number of times in the past that a pair of dice has been > rolled 27 times in a row, it seems unlikely that it hasn't happened to > someone. Have a tolerable existence. Eli A very rough approximation gives around E 22 dice rolls in the last 200 years. this is the same order of magnitude as the inverse probability of 27 consecutive rolls of seven. I don't see however that the sample space of all connected throws of two dice would be anywhere this large. Does anyone know of actual events or legends where anyone broke the bank by a run of 27 sevens, or if it ever happened. (not to mention that supernatural things start to happen in the Casino's favor if doom is lurking!) Bob Pease ==== Dik T. Winter pushed briefly to the front of the door: ^ >The Open Court edition, which I own, was re-edited and published in ^ >Chicago, with additional notes by David Eugene Smith. It's possible ^ >that some of the spelling may have been altered to reflect american ^ >standards along the way... ^ > According to the OED, criticize is the preferred spelling. ^ Yes. I never know when to use 's' or 'z' in such words when writing ^ British English. I generally use 's', as many Brits also do because ^ they do not know the rules. It has to do with whether the origin is ^ Greek or Latin, if I remember correctly. 19th century mathematician ^ De Morgan probably knew the rules. I always use 'z'. I get much better Scrabble scores that way. Andy -- Hell! - don't worry about old raving Dave Ullrich ... Basically he's a sociopath who can't see a red rag without regarding it as a personal insult. Bill Taylor, sci.math ==== > That's because I figure it may take me a few months to get everything > through a computerized proof check myself, and saving those months is > worth $100,000 US to me. You hate to work THAT much? Well, given what I've discovered over the past two years and how long > I've waited $100,000 US is not a big deal. You'll achieve something faster by working instead of waiting. Waiting usually worth nothing. > Besides, I have to admit that it'd be neat to share *something* with > someone else, so we could party together, meet celebs, heads of state, > and wonder about why math society fought for so long and hard. You already dreaming about parties? Then yes, you hate to work. :) > Then again, if no one is up to the challenge, I'll go ahead and do it > all myself, like usual. Start right now. Don't wait. > Or that math journal will finish its review of my paper Advanced > Polynomial Factorization in my favor. In any event, readers can be sure that the poster here doesn't have > the skills needed to handle a computer check, or I'd think he wouldn't > be wasting time, when there's money to be made. Oh, I have skills, but your writings are still too informal for successful conversion. These computers are unbelievable nitpickers - you just can't imagine! I asked you to rewrite your short explanation of the error in core without that non-math word should, but you refused. And I can't convert should to a formal logic statement. So ball's in your court right now. > James Harris ==== Is it your intention that JSH should take what you say about him seriously? If so I find it a rather cruel kind of sport. Gib ==== >> According to the OED, criticize is the preferred spelling. >What does the OED say about, say, generalize/generalise? They only have generalize. But about a third of their quotations use generalise. OED says this under -ize: This practice prob. began first in French; in mod.F. the suffix has become -iser, alike in words from Greek, as baptiser, .8evang.8eliser, organiser, and those formed after them from L., as civiliser, cicatriser, humaniser. Hence, some have used the spelling -ise in Eng., as in French, for all these words, and some prefer -ise in words formed in French or Eng. from L. elements, retaining -ize for those of Gr. composition. But the suffix itself, whatever the element to which it is added, is in its origin the Gr. -izein, L. -izare; and, as the pronunciation is also with z , there is no reason why in English the special French spelling should be followed, in opposition to that which is at once etymological and phonetic. In this Dictionary the termination is uniformly written -ize. Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada V6T 1Z2 ==== Would someone post a definition of the semi-direct product? OK. Let G and H be groups. A semidirect product of G by H involves a homomorphism phi: H -> Aut(G) - you can define a semidirect product for each such phi. So it should be denoted by G sd_phi H. (but the standard symbol for `sd' looks like ><| ). Fix such a phi. Then the elements of G sd_phi H are { (g,h) | g in G, h in H } and the multiplication is defined by (g1,h1) (g2,h2) = (g1 phi(h1)(g2), h1 h2). You can check that this defines a group - associativity needs checking, for example. The direct product is the special case in which phi(h) is the identity automorphism for all h in H. Any semidirect product has a normal subgroup { (g,1) | g in G } isomorphic to G and a subgroup H (which is normal only in the case of the direct product) { (1,h) | h in H }, so G sd_phi H = GH and G intersect H is trivial. So H is a complement of G. Coversely, if E is any group having a normal subgroup G and a subgroup H such that GH = E and G intersect H is trivial, then you can prove that E is isomorphic to a semidirect product G sd_phi H, where phi is defined by phi(h)(g) = h g h^-1. Semidirect products are extremely common, particularly among groups of small order, so it is important to understand them. But there are other important constructs as well, like central products. Derek Holt. <8765iqi5ee.fsf@phiwumbda.org> ==== According to the OED, criticize is the preferred spelling. What does the OED say about, say, generalize/generalise? They only have generalize. But about a third of their quotations > use generalise. OED says this under -ize: [...] Next time I co-author a paper, I will insist on -ize, then. I haven't done it previously because I thought -ize was just an American version, and here in Europe they prefer British misspellings. -- Jesse F. Hughes If anything is true in general about Usenet, it's that people can go on and on about just about anything. -- James Harris speaks the truth. ==== >Besides, I have to admit that it'd be neat to share *something* with >someone else, so we could party together, meet celebs, heads of state, >and wonder about why math society fought for so long and hard. You're doing *math* to party with people and meet celebs and heads of state? ==== > According to the OED, criticize is the preferred spelling. >>What does the OED say about, say, generalize/generalise? > They only have generalize. But about a third of their quotations >> use generalise. > OED says this under -ize: [...] >Next time I co-author a paper, I will insist on -ize, then. I haven't >done it previously because I thought -ize was just an American >version, and here in Europe they prefer British misspellings. -ize and -ise are acceptable alternatives in Britain, and the OED and Fowler prefer -ize. I think the -ise alternative crept in (under French influence) after English and US spelling had parted company, so the US spelling is more authentic in this case. But it is undoubtedly the case that the majority of British people use -ise and many people dislike -ize. I am afraid that I am inconsistent myself. One lazy reason for using -ise is that it becomes unnecessary to worry about those words like `revise' and `advise' which can only be spelt -ise. Derek Holt. ==== Besides, I have to admit that it'd be neat to share *something* with >>someone else, so we could party together, meet celebs, heads of state, >>and wonder about why math society fought for so long and hard. You're doing *math* to party with people and meet celebs and heads of >state? Some time ago he explained that the reason (or one reason) he was proving Fermat's Last Theorem was because it impressed women. Honest: >organization: Netcom >x-netcom-date: Fri Mar 15 10:37:28 PM CST 1996 >mime-version: 1.0 >newsgroups: sci.math >I haven't cut on my computer since I made the posting of the erroneous >proof that is that z(mod n)=1. I don't doubt that I'll have some choice >else. This seemed like a good time for a psychology (or I should say, >sociology) experiment because I'm almost through with Sci.Math. I've >posted my main result on FLT from the beginning. Although I've been told >that it's interesting but leads to nothing, I've got a couple more angles >to check out on it before I give up. Anyway, it's fun as a hobby and it >impresses women (yes, honest). ************************ David C. Ullrich <3c65f87.0310131913.3b561b84@posting.google.com> <5isnov0qlvfu38a71np60eenbecdqabcae@4ax.com> ==== >He also was apparently in gifted-talented programs as a >youngster and had a lot of people telling him how smart >he was. > Yes, I covered this in another post. It's Sesame Street >> all over. Tain't a damn thing wrong with Sesame Street. Well, yes there is, >now. The past year or two, the show has begun to completely suck, but >prior to that, tweren't a damn thing wrong with it. It destroyed childrens' natural long-term attention span abilities. /BAH ==== > I've always wondered about Mathematical Olympics. Don't the judges have > to be smarter than any of the contestants, to be able to judge them > accordingly? The judges have months in advance to prepare the questions. They can consult experts and books. They can re-write and revise until polished. The contestants have only 3 hours (or whatever) and no outside resources. ==== >> He also was apparently in gifted-talented programs as a >> youngster and had a lot of people telling him how smart >> he was. He seems unable to comprehend that a lot of the >> people in the newsgroups he frequents had the same life >> experiences, but managed to make the transition from big fish >> in little pond to little fish in big pond which, from >> all evidence, he did not. >Maybe he made a different transition. >Out of the water . . . >This is a serious problem and exclusive to JSH. Meant not exclusive, of course. Dammit! YES!!!! My deepest appreciation and thanks for making that correction. We are breeding >>these types. It is the opinion of educators that correcting >>kids, when they're wrong, is damaging to their egos. They >>become adults never having been corrected. Then they get >>a job. >/BAH ************************ David C. Ullrich ==== > I am looking for some old HP calculators like HP 41CV, HP 41CX, HP > 71B, HP 15C, HP 16C, HP 67 and any others in the 1980's era...If you >I have an HP55 and no, I'm not selling. >>Bought it in 1975 and it still works :-) >> http://www.dotpoint.com/xnumber/hp55.htm > You can take my car; you can take my kids; you can take my >> freedom; but no way are you gonna get your hands on my HP-35. Ha... http://www.dotpoint.com/xnumber/hp35.htm >Those were the days when a nice design lasted for at least 3 years. >Pity they changed it after 1975 and went to the 25: > http://www.dotpoint.com/xnumber/hp25.htm >> [for those with a humor filter, drop it] Once upon a time, the battery died and thought that I'd just use this other calculator until I had time to get a new one. I could not function. RPN is so imbedded into my thinking that I could not use a regular calculator. I ended up doing the stuff on paper and the task of getting a new battery jumped to number 1 priority. /BAH ==== > Likewise, only 2 of the 3 involutions in the center of the > other non-abelian group with this distribution of element > orders are the squares of elements of order 4. This group is the > semidirect product Z_4 x| Z_4 with presentation b^4 = 1, a^b = a^-1>. Yes, I see this now. > The other one with three generators is the central >product of Z_4 and D_4, which is defined as the direct product of >Z_4 and D_4 but with their central elements of order 2 amalgamated. >This turns out to be isomorphic to the central product of Z_4 and Q >and is group number 13 in the GAP list. I also see now that this is true, though I am having some trouble with some of the details. There are 4 cyclic normal subgroups of order 4, with the elements of order 2 identified, but one of them is the center. But each element of order 4 which is not in the center (call them x_i, i = 1,2,3) has 4 elements of order 2, say y_j, such that y_j x_i y_j = x_i^(-1), as in D_4. There is certainly a lot of structure in groups of order 2^n which doesn't appear in in others. Perhaps it shows up in order p^n for any prime. Van Jacques ==== > I am looking for some old HP calculators like HP 41CV, HP 41CX, HP > 71B, HP 15C, HP 16C, HP 67 and any others in the 1980's era...If you >I have an HP55 and no, I'm not selling. >>Bought it in 1975 and it still works :-) >> http://www.dotpoint.com/xnumber/hp55.htm > You can take my car; you can take my kids; you can take my >> freedom; but no way are you gonna get your hands on my HP-35. Ha... http://www.dotpoint.com/xnumber/hp35.htm >Those were the days when a nice design lasted for at least 3 years. >Pity they changed it after 1975 and went to the 25: > http://www.dotpoint.com/xnumber/hp25.htm >> [for those with a humor filter, drop it] Once upon a time, the battery died and thought that I'd > just use this other calculator until I had time to get > a new one. I could not function. RPN is so imbedded > into my thinking that I could not use a regular calculator. > I ended up doing the stuff on paper and the task of getting > a new battery jumped to number 1 priority. Sounds all very familiar. Give me a =-calculator and I'm lost. I had my battery pack die so many times I stopped counting. Each time it had to be ordered and it took weeks. And it cost a fortune. So finally I decided to go out for some naked NiCd batteries, cut open the plastic packaging of the pack and replace the batteries myself. I was a mess (with aluminum paper contacts and such) but it worked and it was MUCH cheaper ;-) Dirk Vdm ==== > Is it your intention that JSH should take what you say about him > seriously? If so I find it a rather cruel kind of sport. > > Gib For those who wonder about posts like this one, where one of the regular attention parasites who tend to reply in my threads makes a comment having *deleted* out much of the pertinent information, my assessment is that it has to do with Google Groups. Google Groups brings a lot of readers to Usenet over the Internet, but its setup puts the *last* post forward, so that some posters have clearly adopted a strategy of trying to get in the last post, so that they are seen first by readers. Being seen first gets you guaranteed readership in popular threads. Assuming that readers skim along checking out posts quickly, it's not necessarily the case that they'll bother to look back at previous posts, so a poster can try to influence the discussion without having to deal with other posts in the thread, knowing that a lot of readers will just see their post. If nothing else, it puts the spotlight on a particular poster, who might otherwise be drowned out, especially when they give very weak posts of little interest to others. James Harris ==== > That's because I figure it may take me a few months to get everything > through a computerized proof check myself, and saving those months is > worth $100,000 US to me. > You hate to work THAT much? Well, given what I've discovered over the past two years and how long > I've waited $100,000 US is not a big deal. > > You'll achieve something faster by working instead of waiting. > Waiting usually worth nothing. Readers, here's a funny post as it demonstrates to you how casually posters on sci.math lie, as at the end this poster makes a claim, which allows me to put forward the actual outline of the proof, yet again. Please pay careful attention. Many posters repeatedly lie in their posts depending on readers skimming through, with the assumption that I'm wrong. > Besides, I have to admit that it'd be neat to share *something* with > someone else, so we could party together, meet celebs, heads of state, > and wonder about why math society fought for so long and hard. > > You already dreaming about parties? Then yes, you hate to work. :) Work hard. Play hard. I'm talking about celebrating with someone who stepped up to the plate to make history. Celebration is not an indication of laziness. I find it interesting when posters attack normal social rituals. > Then again, if no one is up to the challenge, I'll go ahead and do it > all myself, like usual. > > Start right now. Don't wait. > > > Or that math journal will finish its review of my paper Advanced > Polynomial Factorization in my favor. Notice no commentary here from the poster. > In any event, readers can be sure that the poster here doesn't have > the skills needed to handle a computer check, or I'd think he wouldn't > be wasting time, when there's money to be made. > > Oh, I have skills, but your writings are still too informal for successful conversion. > These computers are unbelievable nitpickers - you just can't imagine! > > I asked you to rewrite your short explanation of the error in core without >that > non-math word should, but you refused. > And I can't convert should to a formal logic statement. So ball's in your >court right now. > Given the fact that I've repeatedly given the outline of the proof in this thread, it should be *extraordinary* to the reader that this poster make that claim, as, of course, I'll happily give it again. Notice there is no use of the word should. Is it extraordinary to anyone else that posters here lie so boldly, especially given that its mathematics under discussion. I mean sci.math is a *math* newsgroup, right? Or is it? Here's the current outline. PROOF OF CORE ERROR 1. Given P(m) = f^2((m^3 f^4 - 3m^2 f^2 + 3m) x^3 - 3(-1+mf^2 )x u^2 + u^3 f) Variables: m, f, x, u E Ring of Algebraic integers P(m) is a polynomial with m the key variable. 2. Let P(m) = (a_1(m) x + uf)(a_2(m) x + uf)(a_3(m) x + uf) Variables: a_1, a_2, a_3, roots of cubic defined as follows. Cubic: a^3 + 3(-1+mf^2)a^2-f^2(m^3 f^4 - 3m^2 f^2 + 3m) Solving for roots of P(m) by setting x = -uf/a will give cubic. 3. Let P(m) = g_1(m) g_2(m) g_3(m) Variables: g_1, g_2, g_3 defined as follows g_1(m) = (a_1(m) x + uf), g_2(m) = (a_2(m) x + uf), g_3(m) = (a_3(m) x + uf). Tautological base: Change in terms independent of m happens independent of m. My point is that concentrating on terms independent of m, will give me results independent of m. So I get terms independent of m. 4. List of independent terms. Independent terms are found by setting m=0. Doing so with cubic gives: a^3 - 3a^2 = 0, which gives a_1(0) = 0, a_2(0) = 0, a_3(0) = 3. (indices selected arbitrarily) Then from previous definitions: a. g_1 has value uf at m=0 indicating indepedent term uf b. g_2 has value uf at m=0 indicating independent term uf c. g_3 has value 3x + uf at m=0 indicating independent term 3x + uf So far so good, as now I have independent terms, which therefore will not change with m. CONDITION: f is coprime to 3, x and u This condition sets up the coprimeness results. PRIMARY ARGUMENT 5. Divide off f^2 from P(m). P(m)/f^2 = (m^3 f^4 - 3m^2 f^2 + 3m) x^3 - 3(-1+mf^2 )x u^2 + u^3 f Now I'm forcing a change by dividing off f^2, but again, I'm doing things independent of the value of m. 6. List resultant independent term P(0)/f^2 = u^2(3x + uf) Note that P(0)/f^2 is coprime to f given the condition above. which is P(0)/f^2 = u^2 g_3(0) which is P(0)/f^2 = g_1(0)/f g_2(0)/f g_3(0) Here the proof is basically complete as I've determined that f is a factor of two of the g's which may seem obvious, but remember, I'm setting up for a machine to check. Detail is necessary. a. g_1(0)/f is coprime to f b. g_2(0)/f is coprime to f c. g_3(0) is coprime to f Preliminary Finding: Independent terms of resultants are coprime to f. That sets up for the finale. 7. Backwards Theorem: Reverse use of distributive property proves g_1, g_2 have factor that is f. I find it interesting that no comments from others have been made here at the heart of the proof. g_1(m) = a_1(m) x + uf g_2(m) = a_1(m) x + uf so to remove factor f from independent term uf, f must divide g_1(m) and g_2(m), from reverse use of distributive property: g_1(m)/f = a_1(m)/f x + u. That is, I found that the independent term changes by a factor of f when I divide P(m) by f^2, and I made that finding *independent* of m, so now I use it without concern about the value of m, i.e. in general. Then by a reverse use of the distributive property, it follows that a_1 and g_1 have f as a factor. (Note to readers: The point of using independent terms is that they are *independent* of the value of m.) 8. Verification: Determine independent term of g_1(m)/f, by setting m=0. g_1(0)/f = a_1(0)/f x + u = u. Confirmed factor f for g_1. Now maybe you see why posters have ignored the full outline in their replies. Determine independent term of g_2(m)/f, by setting m=0. g_2(0)/f = a_2(0)/f x + u = u. Confirmed factor f for g_1. You see, there's no room for reasonable doubt. 9. Core error determination 10. Conclusion Core error, of course. ==== >Next time I co-author a paper, I will insist on -ize, then. But note that the OED's comment refers only to words where the suffix represents the Greek -izein. There are some words (e.g. advertise) where -ise is the generally accepted spelling. -- Richard -- FreeBSD rules! ==== > Is it your intention that JSH should take what you say about him > seriously? If so I find it a rather cruel kind of sport. Gib For those who wonder about posts like this one, where one of the > regular attention parasites who tend to reply in my threads makes a > comment having *deleted* out much of the pertinent information, my > assessment is that it has to do with Google Groups. Google Groups brings a lot of readers to Usenet over the Internet, but > its setup puts the *last* post forward, so that some posters have > clearly adopted a strategy of trying to get in the last post, so that > they are seen first by readers. Being seen first gets you guaranteed readership in popular threads. Assuming that readers skim along checking out posts quickly, it's not > necessarily the case that they'll bother to look back at previous > posts, so a poster can try to influence the discussion without having > to deal with other posts in the thread, knowing that a lot of readers > will just see their post. If nothing else, it puts the spotlight on a particular poster, who > might otherwise be drowned out, especially when they give very weak > posts of little interest to others. James Harris look to you for guidance about these matters. -- A fool and his proof are soon refuted. -- Democracy: The triumph of popularity over principle. -- http://www.crbond.com <5isnov0qlvfu38a71np60eenbecdqabcae@4ax.com> <585ab5d8.0310141203.4589c1bb@posting.google.com> <87he2aihf0.fsf@phiwumbda.org> ==== >Tain't a damn thing wrong with Sesame Street. Well, yes there is, >now. The past year or two, the show has begun to completely suck, but >prior to that, tweren't a damn thing wrong with it. It destroyed childrens' natural long-term attention span abilities. Yeah, but Mr. Rogers got it back. -- There are two things you must never attempt to prove: the unprovable -- and the obvious. -- Democracy: The triumph of popularity over principle. -- http://www.crbond.com ==== > but, yeah: I've proven that there is no perfect box, > whose edges and diagonals, including the interior one, are integral, > with just the pyhtagorean theorem as the Air-hammer -- > granite is tough stuff, y'know! Proven? As far as I know this is still an open problem. http://mathworld.wolfram.com/PerfectCuboid.html - Randy ==== [snip partial outline of computer verification of proof] > 9. Core error determination g's do not have a factor that is f in the ring of algebraic integers > goes. > 10. Conclusion Core error, of course. Wacky, isn't it? But, hey, it's just basic math. Yup, yup, yup!. -- A fool and his proof are soon refuted. -- Democracy: The triumph of popularity over principle. -- http://www.crbond.com ==== >>I did have two typos, critize for criticize, >Not criticise? Just wondering... I'll check my copy at home tonight. It's possible my fingers got ahead >of me there. The Open Court edition, which I own, was re-edited and published in >Chicago, with additional notes by David Eugene Smith. It's possible >that some of the spelling may have been altered to reflect american >standards along the way... I checked; except for the two typos, critize for criticize (so spelled in de Morgan's original) and extend for extent, the quotation was accurate in spelling. The only other difference in there must be the indefinite 'something' in the mysterious 'all this'. De Morgan uses italics rather than quotes. The paragraph in full is: Why do you take so much trouble to expose such a reasoner as Mr. Smith? I answer as a deceased friend of mine used to answer on like occasions - A man's capacity is no measure of his power to do mischief. Mr. Smith has untiring energy, which does something; self-evident honesty of conviction, which does more; and a long purse, which does most of all. He has made at least ten publications, full of figures few readers can criticize. A great many people are staggered to this extent, that they imagine there must be the indefinite something in the mysterious all this. They are brought to the point of suspicion that the mathematicians ought not to treat all this with such undisguised contempt, at least. Now, I have no fear for pi: but I do think it possible that general opinion might in time demand the crowd of circle-squarers, etc. should be admitted to the honors of opposition; and this would be a time-tax of five per cent., one man with another, upon those who are better employed. Mr. James Smith may be made useful, in hands which understand how to do it, towards preventing such opinion from growing. A speculator who expressly assumes what he wants to prove, and argues that all which contradicts it is absurde, ->because<- [italics in the original] it cannot stand side by side with his assumption, is a case which can be exposed to all. Arturo Magidin, sans .sig ==== >I checked; except for the two typos, critize for criticize (so >spelled in de Morgan's original) and extend for extent, the >quotation was accurate in spelling. [ ... ] >> ... growing. A speculator who expressly assumes what he wants to prove, >> and argues that all which contradicts it is absurde, ->because<- ^ Absurd, of coruse. Joseph Nebus ---------------------------------------------------------------------------- -- ==== > ... growing. A speculator who expressly assumes what he wants to prove, > and argues that all which contradicts it is absurde, ->because<- > ^ > Absurd, of coruse. ^^ Heh! Isn't that funny -- in the process of correcting a typo, you too made a tyop! ==== >> ... growing. A speculator who expressly assumes what he wants to prove, >> and argues that all which contradicts it is absurde, ->because<- >>^ >>Absurd, of coruse. > ^^ > Heh! Isn't that funny -- in the process of correcting a typo, you too > made a tyop! This is the principle of conversation of typos. -- Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html Needless to say, I had the last laugh. Alan Partridge, _Bouncing Back_ (14 times) ==== > ... growing. A speculator who expressly assumes what he wants to prove, > and argues that all which contradicts it is absurde, ->because<- >^ >Absurd, of coruse. >> ^^ >> Heh! Isn't that funny -- in the process of correcting a typo, you too >> made a tyop! This is the principle of conversation of typos. Heh-heh... (I hope I spelled that right.) ************************ David C. Ullrich ==== > 3. Let P(m) = g_1(m) g_2(m) g_3(m) > Variables: g_1, g_2, g_3 defined as follows > g_1(m) = (a_1(m) x + uf), > g_2(m) = (a_2(m) x + uf), > g_3(m) = (a_3(m) x + uf). ... > Then from previous definitions: > a. g_1 has value uf at m=0 indicating indepedent term uf > b. g_2 has value uf at m=0 indicating independent term uf > c. g_3 has value 3x + uf at m=0 indicating independent term 3x + uf ... > 6. List resultant independent term > a. g_1(0)/f is coprime to f > b. g_2(0)/f is coprime to f > c. g_3(0) is coprime to f (Depends on the value of x.) > Preliminary Finding: > Independent terms of resultants are coprime to f. > That sets up for the finale. > 7. Backwards Theorem: Reverse use of distributive property proves > g_1, g_2 have factor that is f. > I find it interesting that no comments from others have been made here > at the heart of the proof. Perhaps because most readers even do not come as far as this? > g_1(m) = a_1(m) x + uf > g_2(m) = a_1(m) x + uf > so to remove factor f from independent term uf, f must divide g_1(m) > and g_2(m), from reverse use of distributive property: Eh? You wish to prove that g_1(m) is divisible by f. To prove that you can not use that it is divisible by f (i.e. that you can remove a factor f). You have shown (trivially) that for m=0 g_1(m) is divisible by f (because a_1(0) is divisible by f). You have not yet shown that a_1(m) or g_1(m) is divisible by f when m != 0 and that you *can* remove the factor f in that case. Until this step you had *only* m=0. So why can you remove the factor f when m != 0? There is a gap. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ ==== Mucho thanx! Dries <3c65f87.0310131913.3b561b84@posting.google.com> <5isnov0qlvfu38a71np60eenbecdqabcae@4ax.com> <585ab5d8.0310141203.4589c1bb@posting.google.com> <87he2aihf0.fsf@phiwumbda.org> ==== >He also was apparently in gifted-talented programs as a >>youngster and had a lot of people telling him how smart >>he was. > Yes, I covered this in another post. It's Sesame Street > all over. >Tain't a damn thing wrong with Sesame Street. Well, yes there is, >>now. The past year or two, the show has begun to completely suck, but >>prior to that, tweren't a damn thing wrong with it. It destroyed childrens' natural long-term attention span abilities. I think that you and I will respectfully disagree on Sesame Street, one of the most entertaining shows (and educational as well) ever broadcast. (Before the current abomination with too much reliance on computer-generated animation and overly long and dull segments like Elmo's (Endlessly Annoying) World, Monster Time -- which features singularly dull monsters and Journey to Ernie, a dull game whose only redeeming feature is that they occasionally show classic Sesame Street segments during this game -- but I'm not bitter about these changes, oh no, because I still have a dozen videotapes of actual good Sesame Street, and also the Dutch play the older style Sesame Street, but my Dutch isn't good enough for it and besides the voices are all wrong...) -- Jesse Hughes How come there's still apes running around loose and there are humans? Why did some of them decide to evolve and some did not? Did they choose to stay as a monkey or what? -Kans. Board of Ed member ==== > That's because I figure it may take me a few months to get everything > through a computerized proof check myself, and saving those months is > worth $100,000 US to me. > You hate to work THAT much? > Well, given what I've discovered over the past two years and how long > I've waited $100,000 US is not a big deal. You'll achieve something faster by working instead of waiting. > Waiting usually worth nothing. > Readers, here's a funny post as it demonstrates to you how casually > posters on sci.math lie, as at the end this poster makes a claim, > which allows me to put forward the actual outline of the proof, yet > again. Please pay careful attention. Many posters repeatedly lie in their posts depending on readers > skimming through, with the assumption that I'm wrong. Like you assume the other people are wrong, without reading what they write. > Besides, I have to admit that it'd be neat to share *something* with > someone else, so we could party together, meet celebs, heads of state, > and wonder about why math society fought for so long and hard. You already dreaming about parties? Then yes, you hate to work. :) Work hard. Play hard. I'm talking about celebrating with someone who stepped up to the plate > to make history. Celebration is not an indication of laziness. Concentration on celebration too early *is*. It's called to sell the bear's skin before one has caught the bear. > I find it interesting when posters attack normal social rituals. > Then again, if no one is up to the challenge, I'll go ahead and do it > all myself, like usual. Start right now. Don't wait. > Or that math journal will finish its review of my paper Advanced > Polynomial Factorization in my favor. Notice no commentary here from the poster. Why should I care about your paper? But I noticed no commentary in the thread Harris's Big Fat Blunder from you. > In any event, readers can be sure that the poster here doesn't have > the skills needed to handle a computer check, or I'd think he wouldn't > be wasting time, when there's money to be made. Oh, I have skills, but your writings are still too informal for successful conversion. > These computers are unbelievable nitpickers - you just can't imagine! I asked you to rewrite your short explanation of the error in core without >that > non-math word should, but you refused. > And I can't convert should to a formal logic statement. So ball's in your >court right now. > Given the fact that I've repeatedly given the outline of the proof in > this thread, it should be *extraordinary* to the reader that this > poster make that claim, as, of course, I'll happily give it again. I said *short* explanation. Can you explain the error in core in two-three lines of text, without details? Just what is the end result? I know you can, you did so previously. You just used word *should*. > Notice there is no use of the word should. Is it extraordinary to anyone else that posters here lie so boldly, > especially given that its mathematics under discussion. I mean > sci.math is a *math* newsgroup, right? Or is it? Here's the current outline. PROOF OF CORE ERROR 1. Given P(m) = f^2((m^3 f^4 - 3m^2 f^2 + 3m) x^3 - 3(-1+mf^2 )x u^2 + u^3 f) Variables: m, f, x, u E Ring of Algebraic integers P(m) is a polynomial with m the key variable. > 2. Let P(m) = (a_1(m) x + uf)(a_2(m) x + uf)(a_3(m) x + uf) Variables: a_1, a_2, a_3, roots of cubic defined as follows. Cubic: a^3 + 3(-1+mf^2)a^2-f^2(m^3 f^4 - 3m^2 f^2 + 3m) Solving for roots of P(m) by setting x = -uf/a will give cubic. > 3. Let P(m) = g_1(m) g_2(m) g_3(m) Variables: g_1, g_2, g_3 defined as follows g_1(m) = (a_1(m) x + uf), g_2(m) = (a_2(m) x + uf), g_3(m) = (a_3(m) x + uf). > Tautological base: Change in terms independent of m happens independent of m. > My point is that concentrating on terms independent of m, will give me > results independent of m. So I get terms independent of m. 4. List of independent terms. Independent terms are found by setting m=0. Doing so with cubic > gives: a^3 - 3a^2 = 0, which gives a_1(0) = 0, a_2(0) = 0, a_3(0) = 3. (indices selected arbitrarily) Then from previous definitions: a. g_1 has value uf at m=0 indicating indepedent term uf b. g_2 has value uf at m=0 indicating independent term uf c. g_3 has value 3x + uf at m=0 indicating independent term 3x + uf So far so good, as now I have independent terms, which therefore will > not change with m. CONDITION: f is coprime to 3, x and u This condition sets up the coprimeness results. PRIMARY ARGUMENT 5. Divide off f^2 from P(m). P(m)/f^2 = (m^3 f^4 - 3m^2 f^2 + 3m) x^3 - 3(-1+mf^2 )x u^2 + u^3 f Now I'm forcing a change by dividing off f^2, but again, I'm doing > things independent of the value of m. 6. List resultant independent term P(0)/f^2 = u^2(3x + uf) Note that P(0)/f^2 is coprime to f given the condition above. which is P(0)/f^2 = u^2 g_3(0) which is P(0)/f^2 = g_1(0)/f g_2(0)/f g_3(0) Here the proof is basically complete as I've determined that f is a > factor of two of the g's which may seem obvious, but remember, I'm > setting up for a machine to check. Detail is necessary. a. g_1(0)/f is coprime to f b. g_2(0)/f is coprime to f c. g_3(0) is coprime to f > Preliminary Finding: Independent terms of resultants are coprime to f. That sets up for the finale. 7. Backwards Theorem: Reverse use of distributive property proves > g_1, g_2 have factor that is f. I find it interesting that no comments from others have been made here > at the heart of the proof. g_1(m) = a_1(m) x + uf g_2(m) = a_1(m) x + uf so to remove factor f from independent term uf, f must divide g_1(m) > and g_2(m), from reverse use of distributive property: g_1(m)/f = a_1(m)/f x + u. That is, I found that the independent term changes by a factor of f > when I divide P(m) by f^2, and I made that finding *independent* of m, > so now I use it without concern about the value of m, i.e. in general. Then by a reverse use of the distributive property, it follows that > a_1 and g_1 have f as a factor. (Note to readers: The point of using independent terms is that they > are *independent* of the value of m.) > 8. Verification: Determine independent term of g_1(m)/f, by setting m=0. g_1(0)/f = a_1(0)/f x + u = u. Confirmed factor f for g_1. Now maybe you see why posters have ignored the full outline in their > replies. Determine independent term of g_2(m)/f, by setting m=0. g_2(0)/f = a_2(0)/f x + u = u. Confirmed factor f for g_1. You see, there's no room for reasonable doubt. 9. Core error determination g's do not have a factor that is f in the ring of algebraic integers > goes. > 10. Conclusion Core error, of course. The gap at step 7. You still need to prove that g_1(m) is divisible by f when m<>0 ==== > According to the OED, criticize is the preferred spelling. > >>What does the OED say about, say, generalize/generalise? They only have generalize. But about a third of their quotations > use generalise. OED says this under -ize: > > [...] > > > Next time I co-author a paper, I will insist on -ize, then. I haven't > done it previously because I thought -ize was just an American > version, and here in Europe they prefer British misspellings. Don't blame the misspelling on us. Unlike may Brits, I am aware that many of the differences between our versions of English are not because you have changed but because we have changed. Many words that are often regarded as American, e.g. reckon and gotten (*), were common here once but fell out of use. Similarly many, but not all, pronunciation differences are due to us changing and not you. But in the case of spelling, I am fairly sure that most or all of the differences are because you have changed: colour / color, theatre / theater. I prefer the ize spelling because of the sources already quoted. Unfortunately, many PC spell checkers insist on ise once you select UK English. I cannot select US English since then I get color and theater which are regarded as wrong here. (*) Surprisingly, my spell checker accepted this even though it is in UK mode. It did not like color and theater. J <8765iqi5ee.fsf@phiwumbda.org> <87ad81zgqn.fsf@phiwumbda.org> <386aaf52.0310161037.4583f618@posting.google.com> ==== Next time I co-author a paper, I will insist on -ize, then. I haven't >> done it previously because I thought -ize was just an American >> version, and here in Europe they prefer British misspellings. Don't blame the misspelling on us. Well, misspellings was just tongue-in-cheek, of course. I assume that you're right that differences in spelling are mostly due to American variation rather than British. -- Jesse Hughes Wiles made somewhere around half a million dollars U.S. that I heard about, and I know he didn't take major endorsements. --JSH on the rewards of proving Fermat's last theorem. ==== > Next time I co-author a paper, I will insist on -ize, then. I haven't >> done it previously because I thought -ize was just an American >> version, and here in Europe they prefer British misspellings. Don't blame the misspelling on us. > > Well, misspellings was just tongue-in-cheek, of course. > > I assume that you're right that differences in spelling are mostly due > to American variation rather than British. Don't worry, I was just having a laugh. After a potentially unpleasant start, this sub-thread seemed to move in a more fun direction. I would be happy to get our variants of English to converge and am realistic enough to accept that most of the movement would have to be on our part. In fact some of this is happening but people don't always notice. Many words once considered American are now common here (e.g. truck instead or lorry). American pronunciations are creeping in as well (e.g. mall now rhymes with fall rather than pal). But spelling seems to be resisting this trend, I guess (*) it is more obvious. (*) This use of guess used to be considered an Americanism but is now common. J ==== >I am looking for some old HP calculators like HP 41CV, HP 41CX, HP >71B, HP 15C, HP 16C, HP 67 and any others in the 1980's era...If you I have a HP28S: I don't know if it's old enough for you, but... certainly it isn't for me, and no, I'm not selling it. When it will die I won't sell its corpse and I won't throw it away either. No way!! MIchele -- > Comments should say _why_ something is being done. Oh? My comments always say what _really_ should have happened. :) - Tore Aursand on comp.lang.perl.misc ==== OK, so I haven't carried through with the whole thing; once you see the essential geometry of it, it's not hard -- no errors in the core, either, at this time. it does, however, go to Bucky's essential dictum about geometry, which boils-down to the question, Why is the tetragon called, skware, and the hexahedron, qyoob? to state the solution without the proof: a rectangular box has these 7 measurements, and only 6 of them can be made integral at one time (any six); of course, they are only dependent on 3 of them, the 3 different edges e.g. > but, yeah: I've proven that there is no perfect box, > whose edges and diagonals, including the interior one, are integral, > with just the pyhtagorean theorem as the Air-hammer -- > granite is tough stuff, y'know! > > Proven? As far as I know this is still an open problem. --les ducs de Buffet; vote NONE OF THE BELOW on Trickier Dick Cheney's California Recall & e-Dereg! http://larouchepub.com http://www.rwgrayprojects.com/synergetics/plates/figs/plate01.html ==== it uses the symmetry of the hexahedron, of course; so, since I have to analyze some pyhtagorean trigona, let's call it, the Airguitar Pick! > http://mathworld.wolfram.com/PerfectCuboid.html --UN HYDROGEN (sic; Methanex (TM) reformanteurs) ECONOMIE?... La Troi Phases d'Exploitation de la Protocols des Grises de Kyoto: (FOSSILISATION [McCainanites?] (TM/sic))/ BORE/GUSH/NADIR @ http://www.tarpley.net/aobook.htm. Http://www.tarpley.net/bushb.htm (content partiale, below): 17 -- L'ATTEMPTER de COUP D'ETAT, 3/30/81 http://www.rwgrayprojects.com/synergetics/plates/figs/plate01.html ==== > >>Is it your intention that JSH should take what you say about him >>seriously? If so I find it a rather cruel kind of sport. >Gib > > > For those who wonder about posts like this one, where one of the > regular attention parasites who tend to reply in my threads makes a > comment having *deleted* out much of the pertinent information, my > assessment is that it has to do with Google Groups. Just a point of curiousity... what percentage of the people are actually using Google as their news-reader? For example, Gib is not posting through Google, so this conclusion seems unlikely. If he is using a threaded newsreader (which I suspect is true of almost anyone not going through Google), then this assessment seems unlikely at best. For example, I'm reading this as the *middle* of a very large thread and it appears in the middle, with what is being responded to directly above it. > > Google Groups brings a lot of readers to Usenet over the Internet, but > its setup puts the *last* post forward, so that some posters have > clearly adopted a strategy of trying to get in the last post, so that > they are seen first by readers. When I've used Google, I switched to the thread view. That gives me a way to easily get the context. When I read news out of Google, it's almost always in threads. > > Being seen first gets you guaranteed readership in popular threads. > > Assuming that readers skim along checking out posts quickly, it's not > necessarily the case that they'll bother to look back at previous > posts, so a poster can try to influence the discussion without having > to deal with other posts in the thread, knowing that a lot of readers > will just see their post. How can Gib's comment make sense unless someone goes back? It's not even clear who is being responded to. > > If nothing else, it puts the spotlight on a particular poster, who > might otherwise be drowned out, especially when they give very weak > posts of little interest to others. True, this does say something about a particular poster. I have to wonder what percentage of posters are going through Google, however. I suspect on this newsgroup it's lower than you think. -- Will Twentyman ==== > 3. Let P(m) = g_1(m) g_2(m) g_3(m) > Variables: g_1, g_2, g_3 defined as follows > g_1(m) = (a_1(m) x + uf), > g_2(m) = (a_2(m) x + uf), > g_3(m) = (a_3(m) x + uf). > ... > Then from previous definitions: > a. g_1 has value uf at m=0 indicating indepedent term uf > b. g_2 has value uf at m=0 indicating independent term uf > c. g_3 has value 3x + uf at m=0 indicating independent term 3x + uf > ... > 6. List resultant independent term > a. g_1(0)/f is coprime to f > b. g_2(0)/f is coprime to f > c. g_3(0) is coprime to f > (Depends on the value of x.) BiZARRE!!! Readers can look at my original post and see that coprimeness to x is listed as a condition yet this poster deleted it out!!! These people are clearly NOT SANE!!! What's wrong with mathematicians??!!! Don't ANY of you tell the truth? James Harris ==== > >Besides, I have to admit that it'd be neat to share *something* with >someone else, so we could party together, meet celebs, heads of state, >and wonder about why math society fought for so long and hard. > > You're doing *math* to party with people and meet celebs and heads of > state? I'm a discoverer. It turns out that certain math discoveries are worth a lot of money. So I made them. What's remarkable to me is that so many of you don't realize that *helping* me can make you rich. Your mathematician friends will be broken soon enough, and then you'll have nothing. *with* me. James Harris ==== > >Besides, I have to admit that it'd be neat to share *something* with >someone else, so we could party together, meet celebs, heads of state, >and wonder about why math society fought for so long and hard. > > You're doing *math* to party with people and meet celebs and heads of > state? > > I'm a discoverer. It turns out that certain math discoveries are > worth a lot of money. > > So I made them. > > What's remarkable to me is that so many of you don't realize that > *helping* me can make you rich. > > Your mathematician friends will be broken soon enough, and then you'll > have nothing. > > *with* me. Heads of lettuce, maybe. ==== >Once upon a time, the battery died and thought that I'd >just use this other calculator until I had time to get >a new one. I could not function. RPN is so imbedded >into my thinking that I could not use a regular calculator. >I ended up doing the stuff on paper and the task of getting >a new battery jumped to number 1 priority. I've got a similar problem - I've used an HP 48SX since 1991 (freshman calc/physics), and I've used it well. Now I'm a professor, and in all three of my classes, the TI-83 is required, so I have to use it (since I'm expected to be able to show my students things on them). Very frustrating. :-) Doug ==== Anyone? ==== >Besides, I have to admit that it'd be neat to share *something* with >someone else, so we could party together, meet celebs, heads of state, >and wonder about why math society fought for so long and hard. You're doing *math* to party with people and meet celebs and heads of > state? I'm a discoverer. It turns out that certain math discoveries are > worth a lot of money. So I made them. What's remarkable to me is that so many of you don't realize that > *helping* me can make you rich. Your mathematician friends will be broken soon enough, and then you'll > have nothing. *with* me. > James Harris Get help..........quick David Moran ==== >3. Let P(m) = g_1(m) g_2(m) g_3(m) >Variables: g_1, g_2, g_3 defined as follows >g_1(m) = (a_1(m) x + uf), >g_2(m) = (a_2(m) x + uf), >g_3(m) = (a_3(m) x + uf). > ... >Then from previous definitions: >a. g_1 has value uf at m=0 indicating indepedent term uf >b. g_2 has value uf at m=0 indicating independent term uf >c. g_3 has value 3x + uf at m=0 indicating independent term 3x + uf > ... >6. List resultant independent term >a. g_1(0)/f is coprime to f >b. g_2(0)/f is coprime to f >c. g_3(0) is coprime to f > (Depends on the value of x.) > > BiZARRE!!! Readers can look at my original post and see that > coprimeness to x is listed as a condition yet this poster deleted it > out!!! BIZARRE!!! a1(0)x is divisible by f, uf is divisible by f. x is coprime to f, a1(0)/f is coprime to f, u is coprime to f. But (a1(0).x/f + u) is not necessarily coprime to f. But this was only a side remark (hence the pareenthesis), you omitted my main objection. > > These people are clearly NOT SANE!!! > > What's wrong with mathematicians??!!! > > Don't ANY of you tell the truth? > > > James Harris -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ ==== > > >Besides, I have to admit that it'd be neat to share *something* with >someone else, so we could party together, meet celebs, heads of state, >and wonder about why math society fought for so long and hard. > > You're doing *math* to party with people and meet celebs and heads of > state? > > I'm a discoverer. It turns out that certain math discoveries are > worth a lot of money. > > So I made them. > > What's remarkable to me is that so many of you don't realize that > *helping* me can make you rich. > > Your mathematician friends will be broken soon enough, and then you'll > have nothing. > > *with* me. > > Heads of lettuce, maybe. Loser. I'm doing what I do. Is there not a single mathematician in the world worth anything? James Harris ==== > >> Is it your intention that JSH should take what you say about him > seriously? If so I find it a rather cruel kind of sport. > Gib For those who wonder about posts like this one, where one of the >> regular attention parasites who tend to reply in my threads makes a >> comment having *deleted* out much of the pertinent information, my >> assessment is that it has to do with Google Groups. > > > Just a point of curiousity... what percentage of the people are actually > using Google as their news-reader? For example, Gib is not posting > through Google, so this conclusion seems unlikely. If he is using a > threaded newsreader (which I suspect is true of almost anyone not going > through Google), then this assessment seems unlikely at best. For > example, I'm reading this as the *middle* of a very large thread and it > appears in the middle, with what is being responded to directly above it. My view of the thread, in Netscape, makes it perfectly obvious who is replying to whom. Since this is the only way I've ever seen the newsgroups, I don't know how they appear to others. Gib ==== >*with* me. Supermodels. Don't forget to mention the supermodels. - Randy ==== too much California Recall coverage on TV, I surmize.... partying with Warren Buffet and George Schulz?... -- *all* of the very best drugs, in deed! > *with* me. --Dec.2000 'WAND' Chairman Paul O'Neill, reelected to Board. Newsish? http://www.rand.org/publications/randreview/issues/rr.12.00/ http://members.tripod.com/~american_almanac ==== we're your only fans, man; get over it! > Assuming that readers skim along checking out posts quickly, it's not > necessarily the case that they'll bother to look back at previous > posts, so a poster can try to influence the discussion without having > to deal with other posts in the thread, knowing that a lot of readers > will just see their post. As I said, Fuller's writings on geometry are meaningful and probably usually correct. But let me assure you that you would have gained so much more by reading geometry from a more sensible source. --Conway --Dec.2000 'WAND' Chairman Paul O'Neill, reelected to Board. Newsish? http://www.rand.org/publications/randreview/issues/rr.12.00/ http://members.tripod.com/~american_almanac ==== oops; that should have been TIM Conway. > As I said, Fuller's writings on geometry are meaningful and probably > usually correct. But let me assure you that you would have gained so > much more by reading geometry from a more sensible source. --Conway --les ducs d'Enron! X-Received: (from approve@localhost) by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id h9H1kmx21662; ==== The is a physics problem, but I'm hoping someone here might be able to help. >I'm trying to find the tangential velocity of a body (mass: .127kg), flying >around in a circle from a string of unknown length. The radius is the circle >is .43m, and using an astrolabe, I found the angle to be 58 degrees. With v = wr, my problem right now is trying to find the angular velocity (w) >to mutliply by the radius. I converted the 58 degrees to radian to get 1.012 >rad, but I'm not sure what else to do. The time for the body to complete a >full circle is not given, and we're supposed to be able to get this using >the information listed above. Please help! > What angle is 58 degrees? If it is the angle turned in a specific time, then the angular velocity is that angle (in radians) divided by the time. X-Received: (from approve@localhost) by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id h9H1kmO21670; ==== How many atoms in 26.98 grams of aluminum X-Received: (from approve@localhost) by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id h9H1knG21689; ==== > > I've got a question, it's fairly newbe, so bare with me. > > I want to do math as a selfstudie , for fun and soothing a little > fascination/obsession.(well , everybody needs a hobby , eh?) > > What are actually good books or websites on calculus and algebra > one can recommend? (Difficulty level is not important, I have a > notion that most things can be learned given time, motivation > and persperation). > > I want to studie the proofs of calculus and algebra theorems and > I'm searching for a textbook/site where those proofs are as > exact and precise as can be, as close to the original proof as > the person who thougt of it. > > If some one knows such books, I'd be a happy lad. > why don't you take some math courses at a local university? > Bye. ==== > > >He also was apparently in gifted-talented programs as a >youngster and had a lot of people telling him how smart >he was. >Yes, I covered this in another post. It's Sesame Street >>all over. >Tain't a damn thing wrong with Sesame Street. Well, yes there is, >now. The past year or two, the show has begun to completely suck, but >prior to that, tweren't a damn thing wrong with it. >It destroyed childrens' natural long-term attention span abilities. > > > I think that you and I will respectfully disagree on Sesame Street, > one of the most entertaining shows (and educational as well) ever > broadcast. I share your enthusiasm for Sesame St. I watched a lot of it about 15 years ago when my daughter was small, and I enjoyed most of it. The musical segments with people like Smokey Robinson and Celia Cruz were wonderful. The only children's program that has come close in my opinion (and limited experience) is Pingu (sp?) which has the virtue of using a language all of its own. Gib ==== >Can't you just write P + cQ = (I + cQP^{-1})P ? Then (P+cQ)^{-1} = P^{-1} (I + cQP^{-1})^{-1}, which reduces you to the case you know how to do, namely I+cR for a >matrix R. (I'm not sure where the positive definiteness is coming in >here, it looks like you just need P invertible and for c to avoid >being the negative of any of the eigenvalues of QP^{-1}.) > To use the positive definiteness, find a square root sqrt(P) of P. Then P + cQ = sqrt(P)* (I + c*sqrt(P)^(-1)*Q*sqrt(P)^(-1))*sqrt(P). Actaully, you need only sqrt(P)^(-1), not sqrt(P). >BTW, you probably mean to say efficient, rather than effective. Given the matrix P + cQ, where P and Q are known positive definite >> matrices, and c is a positive scalar. I want to compute the inverse of >> P + cQ for various values of c as effectively as possible, by exploiting >> that I know P and Q beforehand. >> >> For instance, if P is the identity matrix, and VLV' is the eigenvalue >> decomposition of Q, then I can compute the inverse as V(I +c L)^{-1}V', >> and only have to do some scalar inversions (more effective methods might exist). >> >> Any hints? I have tried using the matrix inversion lemma, but it didn't >> seem to help me. >> >> Lars -- ARNOLD = Anagram of RONALD ENEGGER = Backwards mis-pronounced REAGAN This is a black -- I mean SCHWARZ -- period in California. Peter-Lawrence.Montgomery@cwi.nl Home: San Rafael, California Microsoft Research and CWI ==== >(p->q) xor (q<->r) >with only 12 letter and using operator and,or and not >..... Let P denote your formula. Let T and F denote true and false. The variable q appears twice in P. When q = T, P simplifies to (p -> T) xor (T <-> r) = T xor r = (not r) When q = F, P simplifies to (p -> F) xor (F <-> r) = (not p) xor (not r) = (p xor r) Comparing the outputs, we might try using (something xor r). We need (T xor r) when q = T (p xor r) when q = F This leads us to (p or q) xor r (8 letters, 2 parentheses, 4 blanks). We can check this by remembering that <-> is negated xor, plus laws relating not and xor P = (p -> q) xor (q <-> r) = not (p -> q) xor q xor r = ((p and not q) xor q) xor r and verifying that ((p and not q) xor q) has the same truth table as (p or q). -- ARNOLD = Anagram of RONALD ENEGGER = Backwards mis-pronounced REAGAN This is a black -- I mean SCHWARZ -- period in California. Peter-Lawrence.Montgomery@cwi.nl Home: San Rafael, California Microsoft Research and CWI ==== A form of this question came up in our group meeting today and I was hoping to get some opinions on it. Suppose that: Y(x)=(k_1 - k_2/x)^.5 Where the k's are positive constants. Is it proper to claim that Y is proportional to x^-.5? In the presentation, the symbol alpha was used in place of the words is proportional to and I was wondering if that was a rigorous use of that symbol. I have always thought that f(x) alpha g(x) implied that f(x)/g(x) = positive constant, but the speaker disagreed. Any thoughts? Adam ==== A form of this question came up in our group meeting today and I was >hoping to get some opinions on it. Suppose that: Y(x)=(k_1 - k_2/x)^.5 Where the k's are positive constants. Is it proper to claim that Y is proportional to x^-.5? In the >presentation, the symbol alpha was used in place of the words is >proportional to and I was wondering if that was a rigorous use of >that symbol. You've already been told the answer is no. However, coming from a physics background I'll add that under some circumstances, one might say something like Y varies as x^0.5 for small x, if that was the regime of interest. The physicist would write something like Y ~ x^-0.5 for small x I say under some circumstances. That probably isn't the case here, because as x goes to 0 and the 1/x term dominates, the expression in parentheses becomes negative. So probably the regime of interest is *NOT* small x, but large x. And as x increases, it is more proper to say Y ~ constant. Where the physicist might use the tilde (~), the mathematician would make a more precise statement involving Big-O, e.g. Y = O(x^-0.5) or Y = O(1). In neither case would either person be likely to use the symbol that looks like an alpha. In my opinion. - Randy ==== > > Partly right. The point of the thread is that although > >> probability of ll is 1/4 >> probability of rr is 1/4 >> probability of lr is 1/2 > > are the probabilities that physicists would have expected to find, > the probabilities that they have found are: > >> probability of ll is 1/3 >> probability of rr is 1/3 >> probability of lr is 1/3 > > I'm affraid that you are not right. They will find the above > probabilities (1/4, 1/4, 1/2). I agree, that you cannot distiguish between the > three configurations have the same probablity. They actually do not. > > The question then arises, what is it about quanta that is > responsible for the difference between classical statistics > and quantum statistics. Some physicists have attributed > this difference to what they refer to as a 'lack of individuality' > in quanta. > Within the quantum statistics, the states which differ only by exchange > counted only once into the statistical sums. > states are numbered and you work with the ocupation numbers of > particular state. > all. > Did I missed some point? > > > Palo lot of space to the 1/3,1/3,1/3-1/2/1/4/1/4 question. --John ==== > I need to find an algorithm that can produce a unique non-predictable 12 > digit (0-9) number for any given 12 digit number. This is to be used to > create a unique barcode on a ticket that cannot be predicted. It is not > required that the original seed number be computed from the resulting > barcode, so some form of one-way hashing function would be acceptable. > Any help in this problem would be appreciated. > > > Mark. > > A simple solution would be to make your own block cipher that uses 12-digit numbers as the input block.. then run the sucker in CTR mode. This will guarantee uniqueness and it shouldn't be that hard to produce a secure design for the roughly 40-bit block in question. It doesn't even have to be that efficient for this job - use a randomly selected 100 element s-boxes and iterate it algorithm for 30 rounds - you don't even have to worry about the inverse operation because it works in CTR. It'd be a fun cipher to make :P Simon. -- <3c65f87.0310131913.3b561b84@posting.google.com> <5isnov0qlvfu38a71np60eenbecdqabcae@4ax.com> <585ab5d8.0310141203.4589c1bb@posting.google.com> <87he2aihf0.fsf@phiwumbda.org> <87k7752m9b.fsf@phiwumbda.org> ==== >> I think that you and I will respectfully disagree on Sesame Street, >> one of the most entertaining shows (and educational as well) ever >> broadcast. I share your enthusiasm for Sesame St. I watched a lot of it about 15 > years ago when my daughter was small, and I enjoyed most of it. The > musical segments with people like Smokey Robinson and Celia Cruz were > wonderful. The parodies are beautiful. ZZ Blues done by a three piece band, the guitarist and base guitarist with long beards. A Dylan-type folksinger sings How many elephants will fit in a room before they fall through the floor and then counts until the four elephants fall through the floor -- no rhetorical questions here! A Billy Idol sound-alike sings about the Rebel L, and The Beetles sing Letter B to the tune of Let It Be. I didn't wait for my son to be born before I started watching Sesame Street again. I began as an undergrad. It is only in the past two years that the program has been horribly re-formatted and the really funny bits are few and far between now. (The most adult humor was in a prime time special during the Iran-Contra affair. There is a segment in which Robin MacNeil, formerly of the MacNeil-Lehrer Newshour, interviews Cookie Monster about Cookiegate. Before each question is answered, Kermit, acting as Cookie's lawyer, leans over and whispers to Cookie. The funniest bit is fairly juvenile, though -- Cookie Monster refers to the interviewer as Mr. MacLehrer. This bit and the whole special can be found on Put Down the Duckie.) -- Jesse F. Hughes C is for Cookie. That's good enough for me. Cookie Monster ==== > > >>I think that you and I will respectfully disagree on Sesame Street, >one of the most entertaining shows (and educational as well) ever >broadcast. >I share your enthusiasm for Sesame St. I watched a lot of it about 15 >>years ago when my daughter was small, and I enjoyed most of it. The >>musical segments with people like Smokey Robinson and Celia Cruz were >>wonderful. > > > The parodies are beautiful. ZZ Blues done by a three piece band, the > guitarist and base guitarist with long beards. A Dylan-type > folksinger sings How many elephants will fit in a room before they > fall through the floor and then counts until the four elephants fall > through the floor -- no rhetorical questions here! A Billy Idol > sound-alike sings about the Rebel L, and The Beetles sing Letter B > to the tune of Let It Be. ... It's all coming back. Great stuff. It was very clever of them to put in enough adult-recognizable humour to draw the parents in. Gib ==== A form of this question came up in our group meeting today and I was >hoping to get some opinions on it. Suppose that: Y(x)=(k_1 - k_2/x)^.5 Where the k's are positive constants. Is it proper to claim that Y is proportional to x^-.5? In the >presentation, the symbol alpha was used in place of the words is >proportional to and I was wondering if that was a rigorous use of >that symbol. I have always thought that f(x) alpha g(x) implied >that f(x)/g(x) = positive constant, but the speaker disagreed. Any >thoughts? Adam > > You are correct, and the speaker is wrong. It seems to me the best you could say (for what it's worth) is that x is inversely proportional to a constant less Y^2. -- Stephen J. Herschkorn herschko@rutcor.rutgers.edu ==== I have recently finished teaching myself basic group/ring/field >>theory using I.N. Herstein's Abstract Algebra. I am seeking the >>name/publisher/possibly ISBN of a good textbook of Galois theory. >> Ian Stewart, Galois Theory, published by Chapman and Hall. > Seconded. -- Stephen J. Herschkorn herschko@rutcor.rutgers.edu ==== > I have recently finished teaching myself basic group/ring/field >>theory using I.N. Herstein's Abstract Algebra. I am seeking the >>name/publisher/possibly ISBN of a good textbook of Galois theory. >Ian Stewart, Galois Theory, published by Chapman and Hall. Seconded. > Thirded. I got me through the Galois Theroy part of my Master's Comps ==== > > No, Jesse F. Hughes is being a presumptuous moron. > > I've noticed a consistent double standard from posters. > > Arturo has already said that his copy of de Morgan's work is by Dover > books, if I recall correctly. Hence, it is plausible that it is an > English translation of the text, so John's stupid criticisms ought to > be directed to the translator and not Arturo (aside from the typos in > the words criticize and extent, presumably). > > Here Jesse F. Hughes apparently *wishes* to defend Arturo Magidin, and > has decided to attack John Corry, apparently out of anger. > > In any case, John's criticism of the use of figures is bumfuzzling. > What word is preferable there? Also, what is wrong with [1]? Surely > one does not *do* publications, but makes them? I presume [4], [6] > and [7] are faithful translations of de Morgan's tone and intent, so > John's complaint is with the author, not Arturo. The same goes for > the majority of the remainder. > > Usenet criticisms of translations of historic texts are worth what > they cost, I suppose. > > The way I see it, Arturo Magidin was being a smartass with a > translation, and was unaware of problems with his usage of a text, and > the meaning as John Correy sees it from reading it in its original > language. > > Rather than just nod at what's not necessarily a big deal--another > screw-up from Arturo Magidin--the poster Jesse F. Hughes decides to > create another thread to attack John Correy, and THEN at the end > belabors Usenet criticism of translations!!! > > If anything is true in general about Usenet, it's that people can go > on and on about just about anything. > > > James Harris Your average sci.mathie/sci.logikoi is (as you put it) a troll critic, with no ideas of his or her own--and no talents other than for establishing whether something is same-old, same-old--if it is it's good, if it isn't it's not. For this there is a reason. As I.B. Cohen said: New and revolutionary systems of science tend to be resisted rather than welcomed with open arms, because every successful scientist has a vested intellectual, social, and even financial interest in maintaining the status quo. --Revolution in Science Apart from the fact that very few who post here are 'successful scientists', they are *like* successful scientists in the respects I.B. Cohen describes. Of course you've said many similar things. But because the Boyz see no advantage in kissing up to you, because you are not a high-ranking professor like I.B. Cohen was, whenever you say anything on this topic they attack you for it, because most of the things you say about mathematicians ARE true of the worst of them, and it is the worst of them whom the others emulate in these groups. John Sigh. Yes, the following, if the reasoning as (sic) actually correct, can be easily formalized in ZF. ... note that for example the in operator below is not going to correspond to the in in ZF, it's going to be just some predicate, with axioms involving it. > C3 EyAx[x in y <-> Et(x in t) & A] (with y not free in A) >Classification > > C4 AyAx[Az(z in y <-> z in x) -> {(set y & set x) <-> y=x}] > (Equi-membered classes are identical iff these are sets.) > --David Ullrich ==== > >Besides, I have to admit that it'd be neat to share *something* with >someone else, so we could party together, meet celebs, heads of state, >and wonder about why math society fought for so long and hard. > > You're doing *math* to party with people and meet celebs and heads of > state? I noticed that this thread was full of off-topic posts, as various posters, whom I assume couldn't find their way around a proof checking program, have continually made wacky posts distracting from the proof outline I've given. So, back on topic. PROOF OF CORE ERROR 1. Given P(m) = f^2((m^3 f^4 - 3m^2 f^2 + 3m) x^3 - 3(-1+mf^2 )x u^2 + u^3 f) Variables: m, f, x, u E Ring of Algebraic integers P(m) is a polynomial with m the key variable. 2. Let P(m) = (a_1(m) x + uf)(a_2(m) x + uf)(a_3(m) x + uf) Variables: a_1, a_2, a_3, roots of cubic defined as follows. Cubic: a^3 + 3(-1+mf^2)a^2-f^2(m^3 f^4 - 3m^2 f^2 + 3m) Solving for roots of P(m) by setting x = -uf/a will give cubic. 3. Let P(m) = g_1(m) g_2(m) g_3(m) Variables: g_1, g_2, g_3 defined as follows g_1(m) = (a_1(m) x + uf), g_2(m) = (a_2(m) x + uf), g_3(m) = (a_3(m) x + uf). Tautological base: Change in terms independent of m happens independent of m. My point is that concentrating on terms independent of m, will give me results independent of m. So I get terms independent of m. 4. List of independent terms. Independent terms are found by setting m=0. Doing so with cubic gives: a^3 - 3a^2 = 0, which gives a_1(0) = 0, a_2(0) = 0, a_3(0) = 3. (indices selected arbitrarily) Then from previous definitions: a. g_1 has value uf at m=0 indicating indepedent term uf b. g_2 has value uf at m=0 indicating independent term uf c. g_3 has value 3x + uf at m=0 indicating independent term 3x + uf So far so good, as now I have independent terms, which therefore will not change with m. CONDITION: f is coprime to 3, x and u This condition sets up the coprimeness results. PRIMARY ARGUMENT 5. Divide off f^2 from P(m). P(m)/f^2 = (m^3 f^4 - 3m^2 f^2 + 3m) x^3 - 3(-1+mf^2 )x u^2 + u^3 f Now I'm forcing a change by dividing off f^2, but again, I'm doing things independent of the value of m. 6. List resultant independent term P(0)/f^2 = u^2(3x + uf) Note that P(0)/f^2 is coprime to f given the condition above. which is P(0)/f^2 = u^2 g_3(0) which is P(0)/f^2 = g_1(0)/f g_2(0)/f g_3(0) Here the proof is basically complete as I've determined that f is a factor of two of the g's which may seem obvious, but remember, I'm setting up for a machine to check. Detail is necessary. a. g_1(0)/f is coprime to f b. g_2(0)/f is coprime to f c. g_3(0) is coprime to f Preliminary Finding: Independent terms of resultants are coprime to f. That sets up for the finale. 7. Backwards Theorem: Reverse use of distributive property proves g_1, g_2 have factor that is f. I find it interesting that no comments from others have been made here at the heart of the proof. g_1(m) = a_1(m) x + uf g_2(m) = a_1(m) x + uf so to remove factor f from independent term uf, f must divide g_1(m) and g_2(m), from reverse use of distributive property: g_1(m)/f = a_1(m)/f x + u. That is, I found that the independent term changes by a factor of f when I divide P(m) by f^2, and I made that finding *independent* of m, so now I use it without concern about the value of m, i.e. in general. Then by a reverse use of the distributive property, it follows that a_1 and g_1 have f as a factor. (Note to readers: The point of using independent terms is that they are *independent* of the value of m.) 8. Verification: Determine independent term of g_1(m)/f, by setting m=0. g_1(0)/f = a_1(0)/f x + u = u. Confirmed factor f for g_1. Now maybe you see why posters have ignored the full outline in their replies. Determine independent term of g_2(m)/f, by setting m=0. g_2(0)/f = a_2(0)/f x + u = u. Confirmed factor f for g_1. You see, there's no room for reasonable doubt. 9. Core error determination 10. Conclusion Core error, of course. James Harris X-Received: (from approve@localhost) by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id h9H6oaB07638; ==== >out there can help me with it. Its a word problem from my algebra/trig >class and I've been trying it but I cant solve it. So please try it. Its >really important and I'll really appreciate it if someone tries it. Well, >here it is. > During 100 km of city driving Sue averaged 8 km/L. She then >drove 300 km on an interstate highway and averaged 12 km/L for the entire >400 km. Find her average fuel consumption on the highway. james summerfield > X-Received: (from approve@localhost) by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id h9H6oa207642; ==== try this: (((100km)/(8km per L)) + ((300km)/(X km per L)))/2 = 12km/L so: (100/8) + (300/X) = 24 then: since 100/8 = 12.5 (300/X) = 11.5 then 300 = 11.5X and you have: X =(approx.)= 26.09 km/L Coming 7 years late, I doubt it has any use to you. But hopefully it does to some dumbass trying to solve their teacher's extra credit homework. ==== >A form of this question came up in our group meeting today and I was >hoping to get some opinions on it. Suppose that: Y(x)=(k_1 - k_2/x)^.5 Where the k's are positive constants. Is it proper to claim that Y is proportional to x^-.5? In the >presentation, the symbol alpha was used in place of the words is >proportional to and I was wondering if that was a rigorous use of >that symbol. I have always thought that f(x) alpha g(x) implied >that f(x)/g(x) = positive constant, but the speaker disagreed. Any >thoughts? Adam > Nope. It sure isn't proper to claim that y is proportional to x^-.5 Y is proportional to x^-.5 means (as you said) that y(x)*Sqrt[x] = constant (note that the constant is not necessarily postive) This is obviously not the case since: y Sqrt[x] = (x^.5) (k_1 - k_2/x)^.5 = ( (x) k_1 - k_2 )^.5 If the above quantity is constant than it shouldn't depend on x... but it does. E.g. if x = 0 then (y Sqrt[x]) = (-k_2)^.5 but if x = 1 then (y Sqrt[x]) = (k_1 - k_2)^.5 Not the same this...i.e. not constant. I we have the case that k_2/x >> k_1 then y is approximately proportional to x^-.5 ..But, long story short; you are right, and the speaker was wrong. adam ==== >A form of this question came up in our group meeting today and I was >hoping to get some opinions on it. Suppose that: Y(x)=(k_1 - k_2/x)^.5 Where the k's are positive constants. Is it proper to claim that Y is proportional to x^-.5? In the >presentation, the symbol alpha was used in place of the words is >proportional to and I was wondering if that was a rigorous use of >that symbol. I have always thought that f(x) alpha g(x) implied >that f(x)/g(x) = positive constant, but the speaker disagreed. Any >thoughts? Adam > Nope. It sure isn't proper to claim that y is proportional to x^-.5 Y is proportional to x^-.5 means (as you said) that y(x)*Sqrt[x] = constant (note that the constant is not necessarily postive) This is obviously not the case since: y Sqrt[x] = (x^.5) (k_1 - k_2/x)^.5 = ( (x) k_1 - k_2 )^.5 If the above quantity is constant than it shouldn't depend on x... but it does. E.g. if x = 0 then (y Sqrt[x]) = (-k_2)^.5 but if x = 1 then (y Sqrt[x]) = (k_1 - k_2)^.5 Not the same this...i.e. not constant. I we have the case that k_2/x >> k_1 then y is approximately proportional to x^-.5 ..But, long story short; you are right, and the speaker was wrong. adam ==== It's also little use giving the wrong answer! 26.09 obviously can't be right! Your left hand side is in liters, right hand in km/L; and why divide by 2? the correct answer: 100 / 8 + 300 / X = 400 / 12 300 / X = 800 / 24 - 300 / 24 = 500 / 24 X = 3 . 24 / 5 = 14.4 no one special schreef in bericht > try this: > (((100km)/(8km per L)) + ((300km)/(X km per L)))/2 = 12km/L > so: > (100/8) + (300/X) = 24 > then: since 100/8 = 12.5 > (300/X) = 11.5 > then > 300 = 11.5X > and you have: X =(approx.)= 26.09 km/L Coming 7 years late, I doubt it has any use to you. But hopefully it does to some dumbass trying to solve their teacher's extra credit homework. > ==== >Does anyone know of a statement of Bliss's Theorem on a website? If >so, will you please share the link with me? In case there is more than one Bliss's Theorem, it's the theorem >that it used to justify the arc length formula for parametric >equations being a Riemann integral, when the derivation doesn't lead >to a Riemann sum. I'm not at all clear on exactly what that last when the derivation doesn't lead to a Riemann sum means... (is that one of the hypotheses, or a comment on why the proof is not clear or what?) If you could give a precise statement of what you want to prove someone could show you how to prove it. _Is_ the question just how to prove that the arclength is given by that integral? (That's what it sounds like the question is, but I'd be surprised to hear that that fact was someone's theorem... _if_ that's the question then what are the hypotheses? In particular are we assuming that the curve is continuously differentiable?) John ************************ David C. Ullrich ==== I'm not asking about the arc length for parametric equations in particular. I had just heard that Bliss's Theorem was used to justify some applications of elementary calculus where the value at the ith subinterval of the partition is chosen conveniently rather than arbitrarily, as in a Riemann Sum. John > >Does anyone know of a statement of Bliss's Theorem on a website? If >so, will you please share the link with me? In case there is more than one Bliss's Theorem, it's the theorem >that it used to justify the arc length formula for parametric >equations being a Riemann integral, when the derivation doesn't lead >to a Riemann sum. > > I'm not at all clear on exactly what that last when the derivation > doesn't lead to a Riemann sum means... (is that one of the > hypotheses, or a comment on why the proof is not clear or what?) > > If you could give a precise statement of what you want to prove > someone could show you how to prove it. _Is_ the question just > how to prove that the arclength is given by that integral? > (That's what it sounds like the question is, but I'd be surprised > to hear that that fact was someone's theorem... _if_ that's > the question then what are the hypotheses? In particular > are we assuming that the curve is continuously differentiable?) > John > > ************************ > > David C. Ullrich ==== I'm not asking about the arc length for parametric equations in >particular. I had just heard that Bliss's Theorem was used to >justify some applications of elementary calculus where the value at >the ith subinterval of the partition is chosen conveniently rather >than arbitrarily, as in a Riemann Sum. Right. I can't figure out what there is to be justified there: If f is Riemann integrable then it follows from the definition of the Riemann integral that you _can_ choose those points conveneniently... John >>Does anyone know of a statement of Bliss's Theorem on a website? If >>so, will you please share the link with me? >In case there is more than one Bliss's Theorem, it's the theorem >>that it used to justify the arc length formula for parametric >>equations being a Riemann integral, when the derivation doesn't lead >>to a Riemann sum. >> >> I'm not at all clear on exactly what that last when the derivation >> doesn't lead to a Riemann sum means... (is that one of the >> hypotheses, or a comment on why the proof is not clear or what?) >> >> If you could give a precise statement of what you want to prove >> someone could show you how to prove it. _Is_ the question just >> how to prove that the arclength is given by that integral? >> (That's what it sounds like the question is, but I'd be surprised >> to hear that that fact was someone's theorem... _if_ that's >> the question then what are the hypotheses? In particular >> are we assuming that the curve is continuously differentiable?) >> >John >> >> ************************ >> >> David C. Ullrich ************************ David C. Ullrich ==== Ellipse is produced if a plane intersects only one nappe of a cone. Is there a way to get the parameters of the ellipse as a function of the angle of the plane with the axis of the cone? I know that they depend on the height of the cone and diameter of the circle at the bottom of the cone. (Plane that is perpendicular to the axis produces a circle.) <3c65f87.0310131913.3b561b84@posting.google.com> <5isnov0qlvfu38a71np60eenbecdqabcae@4ax.com> ==== Tain't a damn thing wrong with Sesame Street. Well, yes there is, >>now. The past year or two, the show has begun to completely suck, but >>prior to that, tweren't a damn thing wrong with it. > It destroyed childrens' natural long-term attention span abilities. Yeah, but Mr. Rogers got it back. Nope. Mr. Rogers concentrated on and they lived happily ever after but forgot to mention that it was a fairy tale. Once upon a time, I watched 10 minutes of a Mr. Rogers show before I had to go to the bathroom to throw up. /BAH <3c65f87.0310131913.3b561b84@posting.google.com> <5isnov0qlvfu38a71np60eenbecdqabcae@4ax.com> ==== [pardon the OT, but I am moved to respond...] > Nope. Mr. Rogers concentrated on and they lived happily ever > after but forgot to mention that it was a fairy tale. I strongly disagree. Mr. Rogers was one of only a very few children's shows that addressed feelings in a way that at all corresponds to reality. For what it aspired to do, it was a gem. > Once upon a time, I watched 10 minutes of a Mr. Rogers show > before I had to go to the bathroom to throw up. Surely you are exaggerating. (If your stomach is really that weak, you need to see a doctor!) I've no doubt you disliked the show -- indeed my own first impression was similar -- but I'm sorry, 10 min is not sufficient time to arrive at the conclusion you stated in your opening sentence. Even for the single show that you partially watched. (How do you know he didn't mention that it was a fairy tale after you headed off to the WC?) Look, some children's shows -- Sesame Street being the prime example -- are designed to entertain *both* children and adults. Others are not. That doesn't make the others necessarily bad. (Nor does it necessarily make Sesame Street good, as I gather you'd be the first to agree. Actually I do find S.S. okay on balance, even though I share some of your concerns about it.) In any case, getting back to reality, Mr. Rogers was quite possibly the realest person on TV. That counted for a lot. Whatever the faults of his show might have been, lack of reality wasn't one of them. ==== [pardon the OT, but I am moved to respond...] > >> Nope. Mr. Rogers concentrated on and they lived happily ever >> after but forgot to mention that it was a fairy tale. I strongly disagree. Mr. Rogers was one of only a very >few children's shows that addressed feelings in a way that >at all corresponds to reality. For what it aspired to do, >it was a gem. I'm not arguing that. I'm stating that the show is a demonstration of how not to get work done. When you spend more time and energy on feelings and how you fit in the social strata of any organization, you will not make anything because you don't have time. All of this stuff happens in any human endeavour; however, it should not be top priority 100% of the time. When you combine the short attention span reinforcement demonstrated in Sesame Street with touchy feelies getting high priority as presented by Mr. Rogers _and_ Sesame Street, you get a population (adults and kids who later grow up to be well-tamed adults who have kids) who cannot deal with survival problems and skills. More importantly, this programming is hour after hour, day after day. Once upon a time, I watched 10 minutes of a Mr. Rogers show >> before I had to go to the bathroom to throw up. Surely you are exaggerating. Yup. I didn't physically throw up but I sure learned why getting something at work was in such a mess. > ..(If your stomach is really that >weak, you need to see a doctor!) I've no doubt you disliked >the show -- indeed my own first impression was similar -- but >I'm sorry, 10 min is not sufficient time to arrive at the >conclusion you stated in your opening sentence. Even for the >single show that you partially watched. (How do you know he >didn't mention that it was a fairy tale after you headed off >to the WC?) Because I also heard _educators_ marvel at his teachings. I saw the results of such spoilage. Look, some children's shows -- Sesame Street being the prime >example -- are designed to entertain *both* children and adults. That's one of the fucking problems. Adults think it's good for their kids because the adults like the show. Kids aren't left alone to play. Kids naturally have a long attention span. The premise of S.S's teaching is that kids can't possibly have a long attention span. What nobody seems to notice is that long attention spans generally disappear when people grow up. The rare few adults who haven't lost that ability are usually considered our geniuses. >Others are not. That doesn't make the others necessarily bad. (Nor does it necessarily make Sesame Street good, as I gather >you'd be the first to agree. Actually I do find S.S. okay >on balance, even though I share some of your concerns about >it.) In any case, getting back to reality, Mr. Rogers was quite >possibly the realest person on TV. That counted for a lot. >Whatever the faults of his show might have been, lack of >reality wasn't one of them. There are lots of times when the opposite is necessary. Not correcting the kids' work in school because it might damage their confidence is an example. The teachers are trained to get along with their students. Kids are very adept at manipulating this flaw. As a result, these kids don't learn about learning from mistakes. JSH is an extreme example of someone who didn't have his feelings hurt when he made an error. Look at how he reacts. Now look at how certain so-called liberals react when they're told don't do that or we can't afford that. /BAH <3c65f87.0310131913.3b561b84@posting.google.com> <5isnov0qlvfu38a71np60eenbecdqabcae@4ax.com> <585ab5d8.0310141203.4589c1bb@posting.google.com> <87he2aihf0.fsf@phiwumbda.org> <3F8EA02E.4F84DBA@ix.netcom.com> <3F906786.AB80B7B@mdli.com> ==== > In any case, getting back to reality, Mr. Rogers was quite > possibly the realest person on TV. That counted for a lot. > Whatever the faults of his show might have been, lack of > reality wasn't one of them. No doubt. I never watched Mr. Rogers much, once I got to college. It was, as you said, not a program for adults. But Mr. Rogers devotion to educating young children and his earnestness was apparent to even a casual observer. This devotion isn't an embarrassment, but a great virtue for Fred Rogers. am not sure, but I think it's still available online. -- Jesse Hughes There's a thrill that's gone that I'll probably not have in quite the same way again. After all, FLT was a unique animal, and we had a great dance. -J.S. Harris on proving Fermat's last theorem <3c65f87.0310131913.3b561b84@posting.google.com> <5isnov0qlvfu38a71np60eenbecdqabcae@4ax.com> ==== >He also was apparently in gifted-talented programs as a >youngster and had a lot of people telling him how smart >he was. > Yes, I covered this in another post. It's Sesame Street >> all over. >Tain't a damn thing wrong with Sesame Street. Well, yes there is, >now. The past year or two, the show has begun to completely suck, but >prior to that, tweren't a damn thing wrong with it. > It destroyed childrens' natural long-term attention span abilities. I think that you and I will respectfully disagree on Sesame Street, >one of the most entertaining shows (and educational as well) ever >broadcast. Sure, we can disagree :-). Note that I didn't say anything about the content of the show. What it did was train kids _and_ adults that instant gratification was the only way to learn. If you can't think of the answer in a nanosecond or be given the answer from somebody in a picosecond, then complaining about the turn around time is OK...not only OK but a compulsory action. This program has trained generations that learning does not require working at it. Thus you have all those college kiddies who whine when they aren't getting straight As without work, merit or thinking. I saw no Sesame Street program (granted, I didn't see them all..just a few) that encouraged working at learning. All learning had to be a Pavlovian response without any process. (Before the current abomination with too much reliance on >computer-generated animation and overly long and dull segments like >Elmo's (Endlessly Annoying) World, Monster Time -- which features >singularly dull monsters and Journey to Ernie, a dull game whose only >redeeming feature is that they occasionally show classic Sesame Street >segments during this game -- but I'm not bitter about these changes, >oh no, because I still have a dozen videotapes of actual good Sesame >Street, and also the Dutch play the older style Sesame Street, but my >Dutch isn't good enough for it and besides the voices are all >wrong...) Look, Sesame Street was a fine cartoon but that's all it was (even though the presentation involved breathing critters). To tout it as educational is..excuse me[emoticon rushes to the can to deposit stomach contents]. /BAH <3c65f87.0310150828.8233a9e@posting.google.com> <3c65f87.0310151831.f102eb6@posting.google.com> <3c65f87.0310170020.7cf06e80@posting.google.com> ==== >> >>Besides, I have to admit that it'd be neat to share *something* with >>someone else, so we could party together, meet celebs, heads of state, >>and wonder about why math society fought for so long and hard. >> >> You're doing *math* to party with people and meet celebs and heads of >> state? I noticed that this thread was full of off-topic posts, as various > posters, whom I assume couldn't find their way around a proof checking > program, have continually made wacky posts distracting from the proof > outline I've given. There is an alternative. Perhaps, just perhaps, some of us know a thing or two about proof-checkers but choose not to take you up on your offer. Perhaps we don't believe a checker can ever validate your argument, so our efforts to do so wouldn't be worth a plug nickel to us. You only offer money for a successful effort. Moreover, an unsuccessful effort would do nothing to convince you that you're wrong, since you may always claim that the argument as formalized doesn't capture your argument. It's ever so slightly possible that your readers are aware of your generous offer to party with celebrities and heads of state (like all world class mathematicians are wont to do), and still regard the benefits from participation as negligible. Of course, once you learn how to validate your own proof, you can show us that our cost-benefit analysis was butt-wrong. (Once again, my random .sig generator chose a reasonably apt signature.) -- Sorry, wakeup to the real world. You're on your own dependent on me as your guide. Luckily for you, I'm self-correcting to a large extent, so if the proof were wrong, I'd tell you. It's not wrong. --- James Harris confirms that his proof is correct. ==== Once upon a time, the battery died and thought that I'd >>just use this other calculator until I had time to get >>a new one. I could not function. RPN is so imbedded >>into my thinking that I could not use a regular calculator. >>I ended up doing the stuff on paper and the task of getting >>a new battery jumped to number 1 priority. I've got a similar problem - I've used an HP 48SX since 1991 (freshman >calc/physics), and I've used it well. Now I'm a professor, and in all >three of my classes, the TI-83 is required, Barf! > .. so I have to use it (since I'm >expected to be able to show my students things on them). Very frustrating. :-) That [teaching about calculator choices] sounds like a worthwhile war to fight and win. I do not see how RPN logic can be ignored when teaching calculus and physics. All the apps that I've encountered has to store away intermediate results that are retrieved later. Not subtly training calc and physics thinking with RPN will produce messy analytical thinking. They can't even write computer code with RPN approaches. /BAH ==== >>Once upon a time, the battery died and thought that I'd >just use this other calculator until I had time to get >a new one. I could not function. RPN is so imbedded >into my thinking that I could not use a regular calculator. >I ended up doing the stuff on paper and the task of getting >a new battery jumped to number 1 priority. >I've got a similar problem - I've used an HP 48SX since 1991 (freshman >>calc/physics), and I've used it well. Now I'm a professor, and in all >>three of my classes, the TI-83 is required, Barf! .. so I have to use it (since I'm >>expected to be able to show my students things on them). >Very frustrating. :-) That [teaching about calculator choices] sounds like a worthwhile >war to fight and win. I do not see how RPN logic can be >ignored when teaching calculus and physics. All the apps that >I've encountered has to store away intermediate results that >are retrieved later. Not subtly training calc and physics >thinking with RPN will produce messy analytical thinking. >They can't even write computer code with RPN approaches. DAMMIT! I did it again. ^without RPN approaches. /BAH ==== in message <70ae81fd.0310141839.106ebdcc@posting.google.com>: [...] > What do you mean by a^b? I have seen some call this the conjugate > of a by b, though this is new to me. Yes, a^b is just a shortcut for b^{-1}ab. -- Jim Heckman <3c65f87.0310131806.1cd51d3f@posting.google.com> <8765iqu9lr.fsf@phiwumbda.org> <3c65f87.0310150749.3f5d21af@posting.google.com> ==== >> >> No, Jesse F. Hughes is being a presumptuous moron. >> >> I've noticed a consistent double standard from posters. >> >> Arturo has already said that his copy of de Morgan's work is by Dover >> books, if I recall correctly. Hence, it is plausible that it is an >> English translation of the text, so John's stupid criticisms ought to >> be directed to the translator and not Arturo (aside from the typos in >> the words criticize and extent, presumably). >> >> Here Jesse F. Hughes apparently *wishes* to defend Arturo Magidin, and >> has decided to attack John Corry, apparently out of anger. >> >> In any case, John's criticism of the use of figures is bumfuzzling. >> What word is preferable there? Also, what is wrong with [1]? Surely >> one does not *do* publications, but makes them? I presume [4], [6] >> and [7] are faithful translations of de Morgan's tone and intent, so >> John's complaint is with the author, not Arturo. The same goes for >> the majority of the remainder. >> >> Usenet criticisms of translations of historic texts are worth what >> they cost, I suppose. >> >> The way I see it, Arturo Magidin was being a smartass with a >> translation, and was unaware of problems with his usage of a text, and >> the meaning as John Correy sees it from reading it in its original >> language. >> >> Rather than just nod at what's not necessarily a big deal--another >> screw-up from Arturo Magidin--the poster Jesse F. Hughes decides to >> create another thread to attack John Correy, and THEN at the end >> belabors Usenet criticism of translations!!! >> >> If anything is true in general about Usenet, it's that people can go >> on and on about just about anything. >> >> >> James Harris Your average sci.mathie/sci.logikoi is (as you put it) a troll critic, > with no ideas of his or her own--and no talents other than for > establishing whether something is same-old, same-old--if it is > it's good, if it isn't it's not. For this there is a reason. > As I.B. Cohen said: New and revolutionary systems of science tend to be resisted > rather than welcomed with open arms, because every successful > scientist has a vested intellectual, social, and even financial > interest in maintaining the status quo. > --Revolution in Science Apart from the fact that very few who post here are 'successful > scientists', they are *like* successful scientists in the respects > I.B. Cohen describes. Of course you've said many similar things. But because the Boyz > see no advantage in kissing up to you, because you are not a > high-ranking professor like I.B. Cohen was, whenever you say > anything on this topic they attack you for it, because most > of the things you say about mathematicians ARE true of the > worst of them, and it is the worst of them whom the others > emulate in these groups. Perhaps mathematicians resist new and revolutionary ideas. I'm doubtful that's true[1], but let's suppose so. How does this pertain to James's writing? Surely, mathematicians also resist incoherent ravings, or simply incorrect reasoning, or even somewhat interesting distractions of no particular depth. Surely not everyone that complains their new idea is revolutionary is correct. So, are you merely asserting that mathematicians reject revolutions out of hand, but that this is irrelevant to James Harris's grand journey? Or, are you asserting that JSH is being wronged by mathematicians that reject his largely correct and revolutionary writings? Is the Cohen quote at all relevant to the rejection of JSH's research, in your ever-so-humble opinion, or is it an irrelevant distraction that you bring up merely to denigrate mathematicians? Footnotes: [1] Your pet project hardly counts as revolutionary, since it doesn't seem particularly interesting in general practice and its already the subject of study in limited areas, namely PER-models in computer science. Note that the students of PER-models don't claim that existence is really the same as self-identity, but that it is sometimes useful as a metaphor. Take what I say about PER-models with a large grain of salt in any case, as they aren't part of my studies. Heck, I'm not even a computer scientist any more. I'm a philosopher, apparently. (Well, that's what I scribbled on my door in red crayola, anyway.) -- Just because you're ... in a Ph.d program it does not mean that you're up to the challenge of being a real mathematician. Only those who have a purity of mind and dedication to the truth as the highest ideal have a chance. --James Harris, as Sir Galahad the Pure. ==== > >> >> No, Jesse F. Hughes is being a presumptuous moron. >> >> I've noticed a consistent double standard from posters. >> >> Arturo has already said that his copy of de Morgan's work is by Dover >> books, if I recall correctly. Hence, it is plausible that it is an >> English translation of the text, so John's stupid criticisms ought to >> be directed to the translator and not Arturo (aside from the typos in >> the words criticize and extent, presumably). >> >> Here Jesse F. Hughes apparently *wishes* to defend Arturo Magidin, and >> has decided to attack John Corry, apparently out of anger. >> >> In any case, John's criticism of the use of figures is bumfuzzling. >> What word is preferable there? Also, what is wrong with [1]? Surely >> one does not *do* publications, but makes them? I presume [4], [6] >> and [7] are faithful translations of de Morgan's tone and intent, so >> John's complaint is with the author, not Arturo. The same goes for >> the majority of the remainder. >> >> Usenet criticisms of translations of historic texts are worth what >> they cost, I suppose. >> >> The way I see it, Arturo Magidin was being a smartass with a >> translation, and was unaware of problems with his usage of a text, and >> the meaning as John Correy sees it from reading it in its original >> language. >> >> Rather than just nod at what's not necessarily a big deal--another >> screw-up from Arturo Magidin--the poster Jesse F. Hughes decides to >> create another thread to attack John Correy, and THEN at the end >> belabors Usenet criticism of translations!!! >> >> If anything is true in general about Usenet, it's that people can go >> on and on about just about anything. >> >> >> James Harris Your average sci.mathie/sci.logikoi is (as you put it) a troll critic, > with no ideas of his or her own--and no talents other than for > establishing whether something is same-old, same-old--if it is > it's good, if it isn't it's not. For this there is a reason. > As I.B. Cohen said: New and revolutionary systems of science tend to be resisted > rather than welcomed with open arms, because every successful > scientist has a vested intellectual, social, and even financial > interest in maintaining the status quo. > --Revolution in Science Apart from the fact that very few who post here are 'successful > scientists', they are *like* successful scientists in the respects > I.B. Cohen describes. Of course you've said many similar things. But because the Boyz > see no advantage in kissing up to you, because you are not a > high-ranking professor like I.B. Cohen was, whenever you say > anything on this topic they attack you for it, because most > of the things you say about mathematicians ARE true of the > worst of them, and it is the worst of them whom the others > emulate in these groups. > > Perhaps mathematicians resist new and revolutionary ideas. I'm > doubtful that's true[1], but let's suppose so. How does this pertain > to James's writing? > > Surely, mathematicians also resist incoherent ravings, or simply > incorrect reasoning, or even somewhat interesting distractions of no > particular depth. Surely not everyone that complains their new idea > is revolutionary is correct. So, are you merely asserting that > mathematicians reject revolutions out of hand, but that this is > irrelevant to James Harris's grand journey? Or, are you asserting > that JSH is being wronged by mathematicians that reject his largely > correct and revolutionary writings? > > Is the Cohen quote at all relevant to the rejection of JSH's research, > in your ever-so-humble opinion, or is it an irrelevant distraction > that you bring up merely to denigrate mathematicians? > > Footnotes: > [1] Your pet project hardly counts as revolutionary, since it doesn't > seem particularly interesting in general practice and its already the > subject of study in limited areas, namely PER-models in computer > science. Note that the students of PER-models don't claim that > existence is really the same as self-identity, but that it is > sometimes useful as a metaphor. > > Take what I say about PER-models with a large grain of salt in any > case, as they aren't part of my studies. Heck, I'm not even a > computer scientist any more. I'm a philosopher, apparently. (Well, > that's what I scribbled on my door in red crayola, anyway.) The motive for your non-expert and uncalled for intervention here is to make it easier for the likes of Ullrich and Magidin to pump themselves up at JSH's expense--and at the expense of all who call into question the fundamental tenets of well-heeled scientific and mathematical interest groups. But from you, this is not unexpected. For a bumfuzzler is a bumfuzzler is a bumfuzzler! --John If some quantum theorist somewhere wants to mess about with a thoroughly non-standard idea of identity, what the heck should Ullrich care? --Jesse Hughes <3c65f87.0310131806.1cd51d3f@posting.google.com> <8765iqu9lr.fsf@phiwumbda.org> <3c65f87.0310150749.3f5d21af@posting.google.com> <87n0c0m9av.fsf@phiwumbda.org> ==== >> So, are you merely asserting that mathematicians reject revolutions >> out of hand, but that this is irrelevant to James Harris's grand >> journey? Or, are you asserting that JSH is being wronged by >> mathematicians that reject his largely correct and revolutionary >> writings? >> >> Is the Cohen quote at all relevant to the rejection of JSH's research, >> in your ever-so-humble opinion, or is it an irrelevant distraction >> that you bring up merely to denigrate mathematicians? The motive for your non-expert and uncalled for intervention here is > to make it easier for the likes of Ullrich and Magidin to pump > themselves up at JSH's expense--and at the expense of all who call > into question the fundamental tenets of well-heeled scientific and > mathematical interest groups. No, the motive is that I am interested in an answer to my question. You keep quoting sources that discuss experts' intransigence when face with revolutionary new ideas. You keep doing this in James Harris threads. Is James Harris in possession of revolutionary (and correct) mathematics which is being wrongly ignored, in your opinion? Or is James Harris presenting bad mathematical arguments that ought to be ignored and/or refuted? If you feel unqualified to comment on the correctness of James's mathematics, then what relevance have these quotes? Unless James is correct in his arguments, there is no example of unreasonable rejection of his ideas here[1]. Footnotes: [1] You may, I suppose, take issue with the degree of charity accompanying those rejections. But, that has nothing to do with your quotations, I think. I am not expressing any opinion about the appropriateness of the tone that James's correspondents take. -- Jesse Hughes There's a thrill that's gone that I'll probably not have in quite the same way again. After all, FLT was a unique animal, and we had a great dance. -J.S. Harris on proving Fermat's last theorem ==== > >> So, are you merely asserting that mathematicians reject revolutions >> out of hand, but that this is irrelevant to James Harris's grand >> journey? Or, are you asserting that JSH is being wronged by >> mathematicians that reject his largely correct and revolutionary >> writings? >> >> Is the Cohen quote at all relevant to the rejection of JSH's research, >> in your ever-so-humble opinion, or is it an irrelevant distraction >> that you bring up merely to denigrate mathematicians? The motive for your non-expert and uncalled for intervention here is > to make it easier for the likes of Ullrich and Magidin to pump > themselves up at JSH's expense--and at the expense of all who call > into question the fundamental tenets of well-heeled scientific and > mathematical interest groups. > > No, the motive is that I am interested in an answer to my question. The motive for your nonexpert and uncalled for intervention here is to make it easier for the likes of Ullrich and Magidin to pump themselves up at JSH's expense, and at the expense of all who call into question the fundamental tenets of well-heeled scientific and mathematical interest groups. > > You keep quoting sources that discuss experts' intransigence when face > with revolutionary new ideas. You keep doing this in James Harris > threads. Is James Harris in possession of revolutionary (and correct) > mathematics which is being wrongly ignored, in your opinion? Or is > James Harris presenting bad mathematical arguments that ought to be > ignored and/or refuted? JSH knows far more mathematics than I; and I daresay far more mathematics than you. Who are you to pass judgment on his work? > > If you feel unqualified to comment on the correctness of James's > mathematics, then what relevance have these quotes? Unless James is > correct in his arguments, there is no example of unreasonable > rejection of his ideas here[1]. Sickos like you ALWAYS attack those who march to the beat of a different drummer. You are not intelligent enough to carry JSH's dirty water, let alone evaluate his work. > > Footnotes: > [1] You may, I suppose, take issue with the degree of charity > accompanying those rejections. But, that has nothing to do with your > quotations, I think. You don't say? Well, I never! > > I am not expressing any opinion about the appropriateness of the tone > that James's correspondents take. Really? Is that so? --John <3c65f87.0310131806.1cd51d3f@posting.google.com> <8765iqu9lr.fsf@phiwumbda.org> <3c65f87.0310150749.3f5d21af@posting.google.com> <87n0c0m9av.fsf@phiwumbda.org> <87brsfejyi.fsf@phiwumbda.org> ==== >> You keep quoting sources that discuss experts' intransigence when face >> with revolutionary new ideas. You keep doing this in James Harris >> threads. Is James Harris in possession of revolutionary (and correct) >> mathematics which is being wrongly ignored, in your opinion? Or is >> James Harris presenting bad mathematical arguments that ought to be >> ignored and/or refuted? JSH knows far more mathematics than I; and I daresay far more mathematics > than you. Who are you to pass judgment on his work? A working mathematician, when the term is interpreted reasonably loosely? One who has, in the distant past, learned a bit of mathematics? In any case, I thought that you were dismissing the idea that there are some authorities capable of judging work and others not. >> If you feel unqualified to comment on the correctness of James's >> mathematics, then what relevance have these quotes? Unless James is >> correct in his arguments, there is no example of unreasonable >> rejection of his ideas here[1]. Sickos like you ALWAYS attack those who march to the beat of a different > drummer. You are not intelligent enough to carry JSH's dirty water, let > alone evaluate his work. Look, you keep calling JSH intelligent. I guess that means that you feel JSH has some insight into the mathematical issues here. Else, why would you keep mentioning his brilliance? What evidence, aside from his mathematical contributions have you? And, if you really feel incompetent to judge his math, then how can you aver he's brilliant at all? >> Footnotes: >> [1] You may, I suppose, take issue with the degree of charity >> accompanying those rejections. But, that has nothing to do with your >> quotations, I think. You don't say? Well, I never! >> I am not expressing any opinion about the appropriateness of the tone >> that James's correspondents take. Really? Is that so? Yes. If you want to ask about particular responses, I'll give my opinion on those, but not on responses as a whole. Of course, who cares what I think anyway? -- Jesse Hughes We will run this with the same kind of openness that we've run Windows. Steve Ballmer, speaking about MS's new .Net project. <3c65f87.0310131806.1cd51d3f@posting.google.com> <8765iqu9lr.fsf@phiwumbda.org> <3c65f87.0310150749.3f5d21af@posting.google.com> <87n0c0m9av.fsf@phiwumbda.org> <87brsfejyi.fsf@phiwumbda.org> <87ad7y8r9n.fsf@phiwumbda.org> ==== > You keep quoting sources that discuss experts' intransigence when face > with revolutionary new ideas. You keep doing this in James Harris > threads. Is James Harris in possession of revolutionary (and correct) > mathematics which is being wrongly ignored, in your opinion? Or is > James Harris presenting bad mathematical arguments that ought to be > ignored and/or refuted? > JSH knows far more mathematics than I; and I daresay far more mathematics >> than you. Who are you to pass judgment on his work? A working mathematician, when the term is interpreted reasonably > loosely? One who has, in the distant past, learned a bit of > mathematics? In any case, I thought that you were dismissing the idea that there > are some authorities capable of judging work and others not. This was a bad response. I retract the first paragraph, though I still the second is apt. I have not publicly judged JSH's work. In fact, I have previously had a policy (well, tendency) of refraining from directly replying to JSH, with some exceptions. I have relaxed this tendency recently, but you will note that I still don't comment on his algebra as far as I can recall. But, whether or not I pass judgment on his work really has nothing at all to do with my questions. Do *you* think that his work is correct? If you refrain from proclaiming it correct, then on what grounds do you claim he is an expert mathematician (or at least knows far more than I)? I'm not *really* asserting my opinion here. I'm just curious about the strength of your conviction that his work has been wrongly rejected by mathematicians, given that you claim to be incapable of judging the work yourself. -- Jesse F. Hughes I have written many words to sci.math, some of them are not even meaningless. --Ross Finlayson ==== >> > So, are you merely asserting that mathematicians reject revolutions > out of hand, but that this is irrelevant to James Harris's grand > journey? Or, are you asserting that JSH is being wronged by > mathematicians that reject his largely correct and revolutionary > writings? > > Is the Cohen quote at all relevant to the rejection of JSH's research, > in your ever-so-humble opinion, or is it an irrelevant distraction > that you bring up merely to denigrate mathematicians? > The motive for your non-expert and uncalled for intervention here is >> to make it easier for the likes of Ullrich and Magidin to pump >> themselves up at JSH's expense--and at the expense of all who call >> into question the fundamental tenets of well-heeled scientific and >> mathematical interest groups. >> >> No, the motive is that I am interested in an answer to my question. The motive for your nonexpert and uncalled for intervention here >is to make it easier for the likes of Ullrich and Magidin to pump >themselves up at JSH's expense, and at the expense of all who call >into question the fundamental tenets of well-heeled scientific and >mathematical interest groups. Really? Hard for us to know what his motive is. Why don't you simply answer the question? >> You keep quoting sources that discuss experts' intransigence when face >> with revolutionary new ideas. You keep doing this in James Harris >> threads. Is James Harris in possession of revolutionary (and correct) >> mathematics which is being wrongly ignored, in your opinion? Or is >> James Harris presenting bad mathematical arguments that ought to be >> ignored and/or refuted? JSH knows far more mathematics than I; Perhaps. If so you know _very_ little mathematics. >and I daresay far more mathematics >than you. No, JSH most assuredly does not know more math than Jesse. >Who are you to pass judgment on his work? A person does not need to know any math at all to pass judgement on his work. Knowing no math at all one can still see that his answers to people's objections simply do not address the question that was asked. (For example, one can see this when he repeatedly illustrates something with m = 0, someone points out that knowing something for m = 0 doesn't prove it's true in general, and he comes back with more illustration of how the case m = 0 works.) >> If you feel unqualified to comment on the correctness of James's >> mathematics, then what relevance have these quotes? Unless James is >> correct in his arguments, there is no example of unreasonable >> rejection of his ideas here[1]. Sickos like you ALWAYS attack those who march to the beat of a different >drummer. You are not intelligent enough to carry JSH's dirty water, let >alone evaluate his work. Calling Jesse a sicko really doesn't answer the question he's asked. Regarding the question of who _is_ qualified to evaluate his work: It's been soundly rejected by everyone here who's looked closely. It's been rejected by editors of _many_ math journals, by proud of getting rejections from big names like Barry Mazur, for some reason), and by a math professor at his alma mater. Who _is_ qualified to judge his work? calling me a sicko, or explaining that hogs like me love to wallow in various troughs, it will look to anyone reading like you can't answer the question. Surely you don't want that. So tell us, who _is_ in your opinion competent to evaluate his work?) >> Footnotes: >> [1] You may, I suppose, take issue with the degree of charity >> accompanying those rejections. But, that has nothing to do with your >> quotations, I think. You don't say? Well, I never! >> I am not expressing any opinion about the appropriateness of the tone >> that James's correspondents take. Really? Is that so? --John ************************ David C. Ullrich X-Cise: tanbanso@iinet.net.au X-CompuServe-Customer: Yes X-Coriate: admin@interspeed.co.nz X-Ecrate: tanandtanlawyers.com X-Punge: Micro$oft ==== at 04:25 PM, dries@splinter.demon.nl (Drizer4Real) said: >I want to studie the proofs of calculus and algebra theorems and I'm >searching for a textbook/site where those proofs are as exact and >precise as can be, as close to the original proof as the person who >thougt of it. A few general observations. First, you will need to choose between history and rigor. The original proofs often had holes or outright errors in them. Second, a lot of Calculus books are oriented more to engineers and physicists, and teach calculations rather than actual Mathematics. If you want to understand the underlying Mathematics you may also need to read some Real Analysis. Third, there are many different learning styles, so you will be best served looking at several alternatives and seeing what works best for you. Fourth, work the exercises as you go along. In addition to the Spivac text mentioned by other posters, I'd recommend that you look at the text by Apostol. I haven't seen his Calculus text, but his Mathematical Analysis was excellent. If you haven't had any classes with real proofs, Linear Algebra is an easy way to get started. I'd recommend Halmos's Finite Dimensional Vector Spaces. Look for books with titles along the lines of Introduction to Abstract Algebra. -- Shmuel (Seymour J.) Metz, SysProg and JOAT not reply to spamtrap@library.lspace.org X-Cise: tanbanso@iinet.net.au X-CompuServe-Customer: Yes X-Coriate: admin@interspeed.co.nz X-Ecrate: tanandtanlawyers.com X-Punge: Micro$oft ==== >The following is an artical from this link: creationworldview.org What do those ignorant babblings have to do with Mathematics? *PLONK* -- Shmuel (Seymour J.) Metz, SysProg and JOAT not reply to spamtrap@library.lspace.org <845b431.0310141824.5fdae713@posting.google.com> X-Cise: tanbanso@iinet.net.au X-CompuServe-Customer: Yes X-Coriate: admin@interspeed.co.nz X-Ecrate: tanandtanlawyers.com X-Punge: Micro$oft ==== at 07:24 PM, snizpilbor@yahoo.com (Sniz Pilbor) said: >Shmuel (Seymour J.) Metz accuses me of introducing new nomenclature >by saying a field of integers. By this reasoning, the phrase a >set of integers must also be new nomenclature. No. The word set refers to collections of things, with no additional structure. The term filed refers to a structure. Would you refer to a filed of brick and expect to be understood? >Definition: A Field of Integers is any field F with the following >properties: > 1. If x is an element of F then x is also an element of Z, the set >of integers > 2. If x is not an element of Z, the set of integers, then x is not >an element > of F. So an example would be the field with the elements {0,1,2} and the operations 2+2=2 0+2=0 1+2=1 2+0=0 0+0=1 1+0=2 2+1=1 0+1=2 1+1=0 2*2=2 0*2=2 1*2=2 2*0=2 0*0=0 1*0=1 2*1=2 0*1=1 1*1=0 2 0 0 1 1 2 I'm not sure why you would want to do that, but it's legitimate. It certainly means that you must be more careful with your nomenclature than is usually necessary. > Please explain the counterexample which I posted, then. You didn't post a counterexample. You posted an example where more care is needed than normally to explicitly distinguish distinct elements and distinct operations. > By well defined I didn't ask what you meant by well defined; I asked what you meant by well behaved. >I meant that the multiplication and addition in >question were the normal multiplication and addition taught in 1st >grade. Why would you expect anybody to either know or care what you were taught in 1st grade? A field is an ordered set (E,+,*) where + and * are functions with specific properties. There is no reason for those operations to be similar to the corresponding operations in a different ring, whether or not it is a field, even if it has the same E. > Then you are claiming I made an arithmetical error. No. I'm claiming that you are applying the wrong constants and operators, because you have chosen ambiguous notation that makes it harder to keep track of context. -- Shmuel (Seymour J.) Metz, SysProg and JOAT not reply to spamtrap@library.lspace.org ==== in message <3f8f41cb$0$11274$afc38c87@>: > I am reading Hungerford's Algebra, and on page 42 (for those with the > book), he shows that If K and N are subgroups of a group G with N normal > in G, then NK = N V K = KN, where N V K is the join of N and K. In the > proof he says that if x is an element of N V K, then x is a product of > the form n_1k_1n_2k_2...n_rk_r where n_i in N and k_i in K. He justfies > this by invoking Theorem 2.8 (If G is a group and X is a nonempty subset > of G, then the subgroup generated by X consists of all finite > products {a_1}^{n_1}{a_2}^{n_2}...{a_t}^{n_t}. I am wondering if someone > can explain how it follows from this theorem. I realize that H V K = K>. That is, H join K is the subgroup generated by H union K. So we can > invoke this theorem letting X = H union K. But how does that give that > the product is of the form n_1k_1n_2k_2...n_rk_r? Err, in typing this message I think I thought of the answer, but since > the typing work has already been done, I may as well send it off. Is it > because some of the n's and some of the k's can be the identity? Not really. Rather, it's because since both K and N are subgroups, any product of elements of K is also in K, and likewise for N. Just collect terms in the general expression for an element of K V N = . -- Jim Heckman ==== a sphere : x^2 + (y-2)^2 + (z-3)^2 =1 let point p : when tangent line of sphere pass on (0,0,c) is meet x-y plane, the point of contact is named p let c1,c2 : value c that trace of p satify parabola. solve that c1+c2 ?? ------------------------------------- i will regard it as difficult...... help me....my genius teacher.... i wait your ultra power advice. thank sir. ==== > Can someone please explain in lay terms what al-Kharki's method is? TIA You mean al-Karkhi, aka al-Karagi, aka al-Karaji. I don't know what 'al-Karkhi method' refers to, but you can start your investigation here: http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Al-Karaji.html ==== >What's remarkable to me is that so many of you don't realize that >*helping* me can make you rich. I can't help you. Only a psychiatrist can do that. Seek professional counseling. Seriously. You're displaying signs of paranoia, psychosis and delusions of grandeur. I have a relative who suffers from schizophrenia and the medication removes all of the symptoms. <3c65f87.0310131913.3b561b84@posting.google.com> <5isnov0qlvfu38a71np60eenbecdqabcae@4ax.com> <585ab5d8.0310141203.4589c1bb@posting.google.com> <87he2aihf0.fsf@phiwumbda.org> <87k7752m9b.fsf@phiwumbda.org> ==== > Sure, we can disagree :-). Note that I didn't say anything about > the content of the show. What it did was train kids _and_ adults > that instant gratification was the only way to learn. If you can't > think of the answer in a nanosecond or be given the answer from > somebody in a picosecond, then complaining about the turn > around time is OK...not only OK but a compulsory action. > This program has trained generations that learning does > not require working at it. Thus you have all those college > kiddies who whine when they aren't getting straight As without > work, merit or thinking. I saw no Sesame Street program (granted, > I didn't see them all..just a few) that encouraged working at > learning. All learning had to be a Pavlovian response without > any process. You've raised children, have you? These ideas that shortening attention spans are due to Sesame Street and that a three year old needs to learn to endure extended periods of concentration in order to master counting are, to my mind, simply laughable. The related notion that Sesame Street encourages grade inflation is similarly stupid. You've managed to put together dubious interpretations of the messages of Sesame Street with silly exaggerations of the effect of the program on American life. However, I freely admit that my faith that Sesame Street is actually a useful educational tool is merely anecdotal. I don't study pedagogy, especially not for young children. I believe that Sesame Street had benefits for me when I was a child, and that my son now benefits, but I have no hard evidence that this is so. Nonetheless, I will not defer to your strongly voiced but unsubstantiated opinions about the worth of this program. Final comment: I've no idea why you believe that Sesame Street discourages effort. You write, If you can't think of the answer in a nanosecond or be given the answer from somebody in a picosecond, then complaining about the turn around time is OK...not only OK but a compulsory action. This comment appears to come from thin air. I really have no idea what makes you think that this comment relates to any features of Sesame Street. -- No feeling sympathy for mathematicians who start marching with signs like 'Will work for food' in the future... I will not show mercy going forward. I was trained as a soldier in the United States Army after all... We play to win. --James Harris, feel his wrath! <585ab5d8.0310141203.4589c1bb@posting.google.com> ==== Sure, we can disagree :-). Note that I didn't say anything about >> the content of the show. What it did was train kids _and_ adults >> that instant gratification was the only way to learn. If you can't >> think of the answer in a nanosecond or be given the answer from >> somebody in a picosecond, then complaining about the turn >> around time is OK...not only OK but a compulsory action. >> This program has trained generations that learning does >> not require working at it. Thus you have all those college >> kiddies who whine when they aren't getting straight As without >> work, merit or thinking. I saw no Sesame Street program (granted, >> I didn't see them all..just a few) that encouraged working at >> learning. All learning had to be a Pavlovian response without >> any process. You've raised children, have you? Nope. But I've been one and I've watched others. These ideas that shortening attention spans are due to Sesame Street Not due to but reinforced. Go learn Pavlov. >and that a three year old needs to learn to endure extended periods of >concentration in order to master counting are, to my mind, simply >laughable. See, you're already doing the same thing that S.S. does. You're trying insist that kids spend their play time (which is when the employ their long-term attention spans) on learning how to count, say the ABCs, etc. > ..The related notion that Sesame Street encourages grade >inflation is similarly stupid. You've managed to put together dubious >interpretations of the messages of Sesame Street with silly >exaggerations of the effect of the program on American life. However, I freely admit that my faith that Sesame Street is actually a >useful educational tool is merely anecdotal. I don't study pedagogy, >especially not for young children. I believe that Sesame Street had >benefits for me when I was a child, Yep. That's obvious. You've swallowed the programming hook line and sinker. > . and that my son now benefits, but >I have no hard evidence that this is so. Nonetheless, I will not defer to your strongly voiced but >unsubstantiated opinions about the worth of this program. Viewing the program as _entertainment_ makes the program worthwhile. Viewing the program as _educational_ makes it worthless. Just because you managed to learn how to count from that program does not make it educational. Final comment: I've no idea why you believe that Sesame Street >discourages effort. You write, If you can't think of the answer in a >nanosecond or be given the answer from somebody in a picosecond, then >complaining about the turn around time is OK...not only OK but a >compulsory action. This comment appears to come from thin air. You can't see the effect of basing teaching on short term attention spans? > .. I >really have no idea what makes you think that this comment relates to >any features of Sesame Street. Pavlov. /BAH <585ab5d8.0310141203.4589c1bb@posting.google.com> <87he2aihf0.fsf@phiwumbda.org> <87k7752m9b.fsf@phiwumbda.org> <87ekxcm55g.fsf@phiwumbda.org> ==== >>and that a three year old needs to learn to endure extended periods of >>concentration in order to master counting are, to my mind, simply >>laughable. See, you're already doing the same thing that S.S. does. You're > trying insist that kids spend their play time (which is when the > employ their long-term attention spans) on learning how > to count, say the ABCs, etc. God, but you're dense. Sometimes, my boy plays. Sometimes, he and I practice counting or the alphabet or do homework from books. Sometimes he watches Sesame Street. You have no reason at all to infer from my comments that I insist that kid spend their play time on learning how to count, say the ABCs, etc. However, I do appreciate the novel idea that you can criticize my parenting based on two or three Usenet posts which barely touch on parenting at all. See, if only you were less timid in sharing your deep thoughts, I'm sure the world would prosper. You do that. -- We want a single platform. We're trying to get there using the -- Madison, WI, superintendent Rainwater grasps subtlety in the operating system wars. ==== Before you start again James. Here a correction and an explanation: ... > 3. Let P(m) = g_1(m) g_2(m) g_3(m) > Variables: g_1, g_2, g_3 defined as follows > g_1(m) = (a_1(m) x + uf), > g_2(m) = (a_2(m) x + uf), > g_3(m) = (a_3(m) x + uf). > ... > Then from previous definitions: > a. g_1 has value uf at m=0 indicating indepedent term uf > b. g_2 has value uf at m=0 indicating independent term uf > c. g_3 has value 3x + uf at m=0 indicating independent term 3x + uf > ... > 6. List resultant independent term > a. g_1(0)/f is coprime to f > b. g_2(0)/f is coprime to f > c. g_3(0) is coprime to f >(Depends on the value of x.) BiZARRE!!! Readers can look at my original post and see that >coprimeness to x is listed as a condition yet this poster deleted it >out!!! > > BIZARRE!!! a1(0)x is divisible by f, uf is divisible by f. x is coprime > to f, a1(0)/f is coprime to f, u is coprime to f. But (a1(0).x/f + u) is > not necessarily coprime to f. But this was only a side remark (hence the > pareenthesis), you omitted my main objection. Note I made an error here. a1(0)/f is not coprime to f. When it were so my remark is true. But because a1(0)/f is *not* coprime to f the value of x is irrelevant. That x is coprime to f is totally irrelevant here. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ ==== 1)i need some reference on differentials forms with $L^p$ coefficients. can anybody tell which paper or book i should look at? <5isnov0qlvfu38a71np60eenbecdqabcae@4ax.com> <585ab5d8.0310141203.4589c1bb@posting.google.com> <87he2aihf0.fsf@phiwumbda.org> <3F8EA02E.4F84DBA@ix.netcom.com> ==== Tain't a damn thing wrong with Sesame Street. Well, yes there is, >>now. The past year or two, the show has begun to completely suck, but >>prior to that, tweren't a damn thing wrong with it. > It destroyed childrens' natural long-term attention span abilities. Yeah, but Mr. Rogers got it back. Nope. Mr. Rogers concentrated on and they lived happily ever > after but forgot to mention that it was a fairy tale. > Once upon a time, I watched 10 minutes of a Mr. Rogers show > before I had to go to the bathroom to throw up. /BAH It only took me 5 minutes, slowpoke. -- There are two things you must never attempt to prove: the unproveable -- and the obvious. -- Democracy: The triumph of popularity over principle. -- http://www.crbond.com ==== >Tain't a damn thing wrong with Sesame Street. Well, yes there is, >now. The past year or two, the show has begun to completely suck, but >prior to that, tweren't a damn thing wrong with it. > It destroyed childrens' natural long-term attention span abilities. >Yeah, but Mr. Rogers got it back. > Nope. Mr. Rogers concentrated on and they lived happily ever >> after but forgot to mention that it was a fairy tale. >> Once upon a time, I watched 10 minutes of a Mr. Rogers show >> before I had to go to the bathroom to throw up. > /BAH It only took me 5 minutes, slowpoke. I took longer because I know that first impressions are faulty. /BAH ==== > Is there not a single mathematician in the world worth anything? James Harris Worth anything? To whom? To you? Hopefully not! But I bet there are many mathematicians who are worth a great deal to their employers. You might still be able to get a job as a crash dummy. -- A fool and his proof are soon refuted. -- Democracy: The triumph of popularity over principle. -- http://www.crbond.com ==== I have a TI-36X Solar calculator that I bought for a beginning physics class that I'm taking this semester. I'm not very strong in math but seem to be making my way OK. Yesterday I discovered something about my calculator that is a real puzzlement to me. Perhaps you can shed some light on it. The calculator has a built in constant for the value of Universal Gravation (G). When you display the value of the constant you get 6.67259 ^-11 which is correct. However, if you enter this value manually into the calculator, 6.67259 x 10^-11 and press the equal key, you get 6.67259 ^-10. What happened to the exponent? Why is it one greater than what I entered. Note that I entered a negative 11 as the exponent. Can you tell me what's going on here? I would prefer to use the constant built into the calculator built into the calculator because of the savings of keystrokes, but others in the class don't have this feature and are entering the full equation. The problem is, our answer are different by a power of 10. Please help if you can. ==== > >> I need to find an algorithm that can produce a unique non-predictable 12 >> digit (0-9) number for any given 12 digit number. This is to be used to >> create a unique barcode on a ticket that cannot be predicted. It is not >> required that the original seed number be computed from the resulting >> barcode, so some form of one-way hashing function would be acceptable. >> Any help in this problem would be appreciated. >> >> >> Mark. >> >> > > A simple solution would be to make your own block cipher that uses > 12-digit numbers as the input block.. then run the sucker in CTR mode. > > This will guarantee uniqueness and it shouldn't be that hard to produce > a secure design for the roughly 40-bit block in question. It is not a roughly 40-bit block, the input and output set should contain exactly 10^12 elements. How do you handle the situation where the outputs are greater than 10^12? I posted a solution that should solve the whole problem. You can find it at http://groups.google.com/groups?hl=en&lr=&ie=UTF-8&selm=3f82eead%240%2414345 %2448b97d01%40reader20.wxs.nl greetings, Ernst Lippe ==== > I was thinking about the interesting (and apparently difficult) > problem of finding sets A and B that form a partition of R and are > such that every interval of R contains uncountably many points of A > and B. In other words, every element of R should be a condensation > point of A and B. You can do far better than that. > R is a maximally resolvable space, > i.e., R can be partitioned into c=2^w many disjoint dense subsets. Here is one way to do it. > P = {Q + x | x in R} partitions R into 2^w counatble sets. Ok, each Q+x is countable and there are c of them. > > Partition P into PP consisting of 2^w subsets each of size 2^w. Not just countable but of size c. How do I do that? You answer your own question two lines below > > Then { US | S in PP } satisfies the bill. US is the union of S. S in PP, means that S is collection of Q+x's. Yes, but S is not just any collection of Q+x's. It is a collection of 2^w disjoint Q+x's Because each Q+x is dense, every open set intersects every Q+x. Hence, every open intersects US in 2^w many different points. Virgil uses the same idea construct two in a separate post, but why stop at two? However, 2^w is the bset one could hope for. > > The jist is partitioning 2^w into 2^w sets of size 2^w. Getting dense is > easy. > ==== integrity to provide. >I have a TI-36X Solar calculator that I bought for a beginning physics class >that I'm taking this semester. I'm not very strong in math but seem to be >making my way OK. Yesterday I discovered something about my calculator that >is a real puzzlement to me. Perhaps you can shed some light on it. The calculator has a built in constant for the value of Universal Gravation >(G). When you display the value of the constant you get 6.67259 ^-11 which >is correct. However, if you enter this value manually into the calculator, >6.67259 x 10^-11 and press the equal key, you get 6.67259 ^-10. What >happened to the exponent? Why is it one greater than what I entered. Note >that I entered a negative 11 as the exponent. Can you tell me what's going >on here? I would prefer to use the constant built into the calculator built into the >calculator because of the savings of keystrokes, but others in the class >don't have this feature and are entering the full equation. The problem is, >our answer are different by a power of 10. Please help if you can. ==== The following is an artical from this link: creationworldview.org What do those ignorant babblings have to do with Mathematics? *PLONK* Sadly, the Protestant fundamentalist movement has an organized agenda to take over Science and Mathematics education in the USA. Although I think they deserve limited exposure in Sci.Math, it is important to know how the enemy thinks and who is on their side. Talk.origins is the usual forum for this. Bob Pease ==== > Just a point of curiousity... what percentage of the people are actually > using Google as their news-reader? For example, Gib is not posting > through Google, so this conclusion seems unlikely. If he is using a > threaded newsreader (which I suspect is true of almost anyone not going > through Google), then this assessment seems unlikely at best. For > example, I'm reading this as the *middle* of a very large thread and it > appears in the middle, with what is being responded to directly above it. Not me. I'm using a Unix command-line newsreader. As usual, James assumes that because he can't understand how newsreaders work, neither can anyone else... -- Wayne Brown (HPCC #1104) | When your tail's in a crack, you improvise fwbrown@bellsouth.net | if you're good enough. Otherwise you give | your pelt to the trapper. e^(i*pi) = -1 -- Euler | -- John Myers Myers, Silverlock ==== > Vanderbilt University, to this country in a broad general sense, I've > been treated rather well throughout my life, which may explain my > discontent with mathematicians as well. Oh, you were so well-treated in the Army that you fantasized about shooting your superior officer with an M-16? Is that how you deal with people who treat you well? Oh, yes, I've seen how you've responded to people like Arturo and Nora when they've tried to help you, so I suppose that *is* how you respond to good treatment... (See http://groups.google.com/groups?selm=01bc4498%2421ac77c0%24cc2b0c26%40mine for the M-16 reference.) > established position about weapons of mass destruction in Iraq and > last year, but TIME is rather big in the news world. You got a letter to the editor published in TIME Magazine? Wow, that's something that happens to *nobody* (except all the dozens and dozens and dozens of other people who get letters published each year.) You know, I got a letter published in Computerworld once, so I guess that makes me the next Charles Babbage or something... -- Wayne Brown (HPCC #1104) | When your tail's in a crack, you improvise fwbrown@bellsouth.net | if you're good enough. Otherwise you give | your pelt to the trapper. e^(i*pi) = -1 -- Euler | -- John Myers Myers, Silverlock ==== Vanderbilt University, to this country in a broad general sense, I've >> been treated rather well throughout my life, which may explain my >> discontent with mathematicians as well. Oh, you were so well-treated in the Army that you fantasized about >shooting your superior officer with an M-16? Is that how you deal with >people who treat you well? Oh, yes, I've seen how you've responded to >people like Arturo and Nora when they've tried to help you, so I suppose >that *is* how you respond to good treatment... (See >http://groups.google.com/groups?selm=01bc4498%2421ac77c0%24cc2b0c26%40mine >for the M-16 reference.) established position about weapons of mass destruction in Iraq and >> last year, but TIME is rather big in the news world. You got a letter to the editor published in TIME Magazine? Wow, >that's something that happens to *nobody* (except all the dozens and >dozens and dozens of other people who get letters published each year.) >You know, I got a letter published in Computerworld once, so I guess >that makes me the next Charles Babbage or something... Wow. I never knew anyone who had a letter in Computerworld. Did they publish that actual letter or just the gist of it? James explained long ago that what they published wasn't exactly was, but he's declined to publish that here. ************************ David C. Ullrich ==== >> Within the quantum statistics, the states which differ only by exchange >> counted only once into the statistical sums. >> states are numbered and you work with the ocupation numbers of >> particular state. >> all. >> Did I missed some point? >> >> >> Palo > > lot of space to the 1/3,1/3,1/3-1/2/1/4/1/4 question. > --John domin@javier.dnp.fmph.uniba.sk Palo ==== Oh Please! Why must you be this way? Integrity has nothing to do with why constructive to add, why did you not just post in this newsgroup instead of saying something which adds nothing to my question. I continue to be disappointed in posts like this one. :( > integrity to provide. I have a TI-36X Solar calculator that I bought for a beginning physics class >that I'm taking this semester. I'm not very strong in math but seem to be >making my way OK. Yesterday I discovered something about my calculator that >is a real puzzlement to me. Perhaps you can shed some light on it. The calculator has a built in constant for the value of Universal Gravation >(G). When you display the value of the constant you get 6.67259 ^-11 which >is correct. However, if you enter this value manually into the calculator, >6.67259 x 10^-11 and press the equal key, you get 6.67259 ^-10. What >happened to the exponent? Why is it one greater than what I entered. Note >that I entered a negative 11 as the exponent. Can you tell me what's going >on here? I would prefer to use the constant built into the calculator built into the >calculator because of the savings of keystrokes, but others in the class >don't have this feature and are entering the full equation. The problem is, >our answer are different by a power of 10. Please help if you can. > ==== >I have a TI-36X Solar calculator that I bought for a beginning physics class >that I'm taking this semester. I'm not very strong in math but seem to be >making my way OK. Yesterday I discovered something about my calculator that >is a real puzzlement to me. Perhaps you can shed some light on it. The calculator has a built in constant for the value of Universal Gravation >(G). When you display the value of the constant you get 6.67259 ^-11 which >is correct. However, if you enter this value manually into the calculator, >6.67259 x 10^-11 and press the equal key, you get 6.67259 ^-10. I've had one for years. Pressing 3rd-Const-G produces the correct value of 6.67259 x 10^-11. Entering manually 6.67259, pressing EE and entering -11 followed with equals produces 6.67259 x 10^-11, just like it should. >What >happened to the exponent? Why is it one greater than what I entered. Note >that I entered a negative 11 as the exponent. Can you tell me what's going >on here? The only reason this should happen is if you enter 66 x 10^-11 of course, but you could try resetting with the AC/ON button and trying again. Sometimes after being in standby the calculator gets its internal state confused and will produce wrong results until reset. If nothing else helps, return it as faulty and ask for a replacement. >I would prefer to use the constant built into the calculator built into the >calculator because of the savings of keystrokes, but others in the class >don't have this feature and are entering the full equation. The problem is, >our answer are different by a power of 10. That said I'm having a hard time believing you would get a wrong answer on only this one constant. ==== > Once upon a time, the battery died and thought that I'd > just use this other calculator until I had time to get > a new one. I could not function. RPN is so imbedded > into my thinking that I could not use a regular calculator. > I ended up doing the stuff on paper and the task of getting > a new battery jumped to number 1 priority. It's the same with me. I use a slide rule and/or paper and pencil if an RPN calc isn't available. (Though my 48GX, 41CX and 16C are usually within arm's reach.) -- Wayne Brown (HPCC #1104) | When your tail's in a crack, you improvise fwbrown@bellsouth.net | if you're good enough. Otherwise you give | your pelt to the trapper. e^(i*pi) = -1 -- Euler | -- John Myers Myers, Silverlock ==== > Oh Please! Why must you be this way? Integrity has nothing to do with why SPAM for > constructive to add, why did you not just post in this newsgroup instead of > saying something which adds nothing to my question. I continue to be > disappointed in posts like this one. :( Some people, eh? Conforming to their etiquette is esential, but them criticising you for not doing so isn't rude? Live and let live ;o) Who knows what your stupid calculator is doing, maybe you are typing in 66.7259 x 10^-11. Why not try a few different numbers and see what happens ==== > > >Tain't a damn thing wrong with Sesame Street. Well, yes there is, >now. The past year or two, the show has begun to completely suck, but >prior to that, tweren't a damn thing wrong with it. >It destroyed childrens' natural long-term attention span abilities. >Yeah, but Mr. Rogers got it back. >Nope. Mr. Rogers concentrated on and they lived happily ever >>after but forgot to mention that it was a fairy tale. >>Once upon a time, I watched 10 minutes of a Mr. Rogers show >>before I had to go to the bathroom to throw up. >/BAH > > > It only took me 5 minutes, slowpoke. I watched a show about the life and work of Fred Rogers, having not known much about him. The thing that struck me was that Mr. Rogers was not some act he put on. One segment showed him testifying before Congress, talking to the chairman of the committee (the committee deciding on funding for public broadcasting, that is) in the same way that he might talk to, say, Miss Meow Meow, but with bigger words. The beautiful thing about Fred Rogers is that he decided on how he ought to act, and then he acted that way, though the world kept snickering. I imagine that if Fred encountered you two, his response would be something like this (assuming that you were young children when you vomited): Oh dear. Well look at me. I'm covered in vomit. I don't like being covered in vomit. It's messy. Yeah. Well, I'm going to go change my clothes, and take a hot shower, but then I'll come back. nice, clean clothes. Do you like my sweater? It's beige. Now I'd like to talk to you about why you vomited. In fact, I've written a little song: What do you do when people vomit on you? Do you hold your nose and say P-U!? Or open your mouth and start vomiting too? What do you do? Wait! Stop tape! I don't like that song very much. Let's take it from why you vomited Okay. How does your mouth feel? I bet it feels yucky. Cut! It does take the guy awhile to get to his point, doesn't it? The point he'd (eventually) make here is that It's okay to have feelings. It's just fine to be loved. There's no need for you to vomit, Just because you're loved. Oh, that's just terrible to use the same word twice instead of rhyming (rhyming fails to be an equivalence relation because it doesn't obey a=a). Sorry Fred. Anyway, Mr. Rogers would have a few words with you about how you're treating James Harris. Your behavior would make Mr. Rogers very sad. Even little children know not to act like you do. Where did it all go wrong? ==== > >>Tain't a damn thing wrong with Sesame Street. Well, yes there is, >now. The past year or two, the show has begun to completely suck, but >prior to that, tweren't a damn thing wrong with it. >It destroyed childrens' natural long-term attention span abilities. >Yeah, but Mr. Rogers got it back. >Nope. Mr. Rogers concentrated on and they lived happily ever >>after but forgot to mention that it was a fairy tale. >>Once upon a time, I watched 10 minutes of a Mr. Rogers show >>before I had to go to the bathroom to throw up. >/BAH > It only took me 5 minutes, slowpoke. I watched a show about the life and work of Fred Rogers, having not known > much about him. The thing that struck me was that Mr. Rogers was not > some act he put on. One segment showed him testifying before Congress, > talking to the chairman of the committee (the committee deciding on funding > for public broadcasting, that is) in the same way that he might talk to, > say, Miss Meow Meow, but with bigger words. The beautiful thing about Fred Rogers is that he decided on how he ought to > act, and then he acted that way, though the world kept snickering. I imagine > that if Fred encountered you two, his response would be something like this > (assuming that you were young children when you vomited): Oh dear. Well look at me. I'm covered in vomit. I don't like being > covered in vomit. It's messy. Yeah. Well, I'm going to go change my > clothes, and take a hot shower, but then I'll come back. nice, clean clothes. Do you like my sweater? It's beige. Now I'd like > to talk to you about why you vomited. In fact, I've written a little song: What do you do when people vomit on you? > Do you hold your nose and say P-U!? > Or open your mouth and start vomiting too? > What do you do? Wait! Stop tape! I don't like that song very much. Let's take it from > why you vomited Okay. How does your mouth feel? I bet it feels yucky. Cut! It does take the guy awhile to get to his point, doesn't it? The point > he'd (eventually) make here is that It's okay to have feelings. > It's just fine to be loved. > There's no need for you to vomit, > Just because you're loved. Oh, that's just terrible to use the same word twice instead of rhyming (rhyming > fails to be an equivalence relation because it doesn't obey a=a). Sorry Fred. Anyway, Mr. Rogers would have a few words with you about how you're treating > James Harris. Your behavior would make Mr. Rogers very sad. Even little > children know not to act like you do. Where did it all go wrong? -- There are two things you must never attempt to prove: the unprovable -- and the obvious. -- Democracy: The triumph of popularity over principle. -- http://www.crbond.com ==== I am very confused about the relationship between zeta(s) and the alternating zeta function (called eta(s), I believe), where the sign of all the even terms is negative. Numerical summations in the complex plane suggest that eta(s) has a zero at the origin, while zeta(s) does not. But it would seem that one could generate eta(s) from zeta(s) by the following; eta(s) = (1 - 2*(2^-s))*zeta(s). The term (2*(2^-s))*zeta(s) generates twice all the even terms (since (2^-s)*(K^-s) = (2K)^-s ), and therefore by subtracting twice the even terms, you invert the sign of the even terms. The problem is that the function (1 - 2*2^-s) has a zero at 1 + i*0, not the origin. So this does not agree with the numerical simulations of the eta function. Likewise, I could also generate just the odd terms by; eta(s) = (1 - 2^-s)*zeta(s), The term (1 - 2^-s) has a zero at the origin; however, numerical summations of just the odd terms indicate that there is no zero at the origin. I'm quite sure I am doing something very stupid; can someone point out the error of my ways? Bob Adams ==== > >> >>Besides, I have to admit that it'd be neat to share *something* with >>someone else, so we could party together, meet celebs, heads of state, >>and wonder about why math society fought for so long and hard. >> >> You're doing *math* to party with people and meet celebs and heads of >> state? I noticed that this thread was full of off-topic posts, as various > posters, whom I assume couldn't find their way around a proof checking > program, have continually made wacky posts distracting from the proof > outline I've given. > > There is an alternative. > > Perhaps, just perhaps, some of us know a thing or two about > proof-checkers but choose not to take you up on your offer. Perhaps > we don't believe a checker can ever validate your argument, so our > efforts to do so wouldn't be worth a plug nickel to us. Well I've given the outline I have so far, which is bound to change in lots of little ways once I start actually playing with proof checkers. It looks like mathematicians wish to go the hard way. The nice thing about switching to a proof checker is that I take you all out of the loop. So you just get to sit and wait, and I guess hope that I fail because when I succeed then I'll have you, and you know that I'm already pissed. James Harris ==== [snip] > Independent [of m] terms are found by setting m=0. Nonsense. Evaluating an expression by substituting '0' for 'm' has nothing to do with finding some residual 'independent of m'. You have merely found the resulting expression when m = 0. Did you think this was some grand algebraic principle you were invoking? If so, apply it to the following expressions: 1) 2m+1 2) 3^m + 3m + 1 3) cos(m) + exp(m+2) + a/m Does setting m=0 reveal 'those terms which are independent of m'? How about expressions with variables: 1) a*m + b 2) a^m + b*m + c/m Does setting m=0 reveal the terms 'independent of m'? Maybe you meant to invoke this principle in an equation, not an expression. Then: 1) a*m + b = 0 2) cos(a*m) + b = 0 3) m + 2 = 0 4) a/m + b*m = 0 Think about it... -- A fool and his proof are soon refuted. -- Democracy: The triumph of popularity over principle. -- http://www.crbond.com ==== [snip] Independent [of m] terms are found by setting m=0. Nonsense. Evaluating an expression by substituting '0' for 'm' has nothing to do with finding some > residual 'independent of m'. You have merely found the resulting expression when m = 0. And thus the CORE ERROR of James' proof. Run James. Be afraid. You are now recoiling in fear. It is natural. Did you think this was some grand algebraic principle you were invoking? If so, apply it to the following > expressions: 1) 2m+1 2) 3^m + 3m + 1 3) cos(m) + exp(m+2) + a/m Does setting m=0 reveal 'those terms which are independent of m'? How about expressions with variables: 1) a*m + b 2) a^m + b*m + c/m Does setting m=0 reveal the terms 'independent of m'? Maybe you meant to invoke this principle in an equation, not an expression. Then: 1) a*m + b = 0 2) cos(a*m) + b = 0 3) m + 2 = 0 4) a/m + b*m = 0 Think about it... -- > A fool and his proof are soon refuted. > -- > Democracy: The triumph of popularity over principle. > -- > http://www.crbond.com ==== An ideal, then, is a subset I of elements of a ring R which (1) form an additive group and (2) are such that whenever x belongs to R and y belongs to I, then xy belong to I. The set of even integers, for example, is an ideal in the ring of integers. --p665, Boyer and Merzbach, '89 > One thing I've been fascinated by as I've considered replies to my > posts is a loose group coordination between posters, as some try to > post with math, and others just post various jibes, but all keep > focused on pushing the false notion that my rather basic argument > showing a problem with the definition of algebraic integers is wrong. --les ducs d'Enron! ==== wow; I *knew* there was some thing funny about that usage of his, but I just don't do enough algebra to peel it out of the mess. maybe, it's a good time to take a breather, monsieur H.; it's not up to 800,000 Federal Reserve Notes work, yet. > Independent [of m] terms are found by setting m=0. > 1) 2m+1 > > 2) 3^m + 3m + 1 > > 3) cos(m) + exp(m+2) + a/m > > Does setting m=0 reveal 'those terms which are independent of m'? > > How about expressions with variables: > > 1) a*m + b > > 2) a^m + b*m + c/m > > Does setting m=0 reveal the terms 'independent of m'? > > Maybe you meant to invoke this principle in an equation, not an expression. Then: > > 1) a*m + b = 0 > > 2) cos(a*m) + b = 0 > > 3) m + 2 = 0 > > 4) a/m + b*m = 0 --les ducs d'Enron! X-Received: (from approve@localhost) by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id h9HCjcx28474; ==== >Given the matrix P + cQ, where P and Q are known positive definite >matrices, and c is a positive scalar. I want to compute the inverse of >P + cQ for various values of c as effectively as possible, by exploiting >that I know P and Q beforehand. For instance, if P is the identity matrix, and VLV' is the eigenvalue >decomposition of Q, then I can compute the inverse as V(I +c L)^{-1}V', >and only have to do some scalar inversions (more effective methods might exist). Any hints? I have tried using the matrix inversion lemma, but it didn't >seem to help me. Lars If you have an approximate inverse, you can use Newton's approximation formula to improve its accuracy: Xnew = 2*X - X*A*X Xnew = 3*X - 3*X*A*X + X*A*X*A*X Xnew = 4*X - 6*X*A*X + 4*X*A*X*A*X - X*A*X*A*X*A*X where X is the approximate inverse of A. (A couple of higher order formulas are also listed.) In the limit, Newton's formula doubles the number of digits accuracy with each iteration. The higher order formulas triple or quadruple the number of digits accuracy. X-Received: (from approve@localhost) by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id h9HCjmt28509; ==== 3 men went to a motel. There's only 1 room left and it costs 30 bucks. So, each man forked out 10 bucks. Later, the owner discovered he over-charged the 3 men. It should be 25 bucks instead. So, he sent his runner to give 5 bucks back to the 3 men. The 3 men think the owner is very honest, and thus each took 1 buck back, leaving 2 bucks to the runner as tips. Now, since they took 1 buck back, each of them paid 9 bucks. 2 bucks to the runner. So: (9*3)+2 = 29. Where's the 1 dollar? ==== 3 men went to a motel. There's only 1 room left and it costs 30 bucks. So, each man forked out 10 bucks. Later, the owner discovered he over-charged the 3 men. It should be 25 bucks instead. So, he sent his runner to give 5 bucks back to the 3 men. The 3 men think the owner is very honest, and thus each took 1 buck back, leaving 2 bucks to the runner as tips. Now, since they took 1 buck back, each of them paid 9 bucks. 2 bucks to the runner. So: (9*3)+2 = 29. Where's the 1 dollar? > This is older than the hills and we've all seen it dozens of times. You're comparing things that are NOT supposed to be equal. Where is the money?? DUH! The hotel clerk has 25 Each man got 1 The runner has 2 That's the original 30. X-Received: (from approve@localhost) by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id h9HCjOk28430; ==== >>What is the interpretation of ln z_1*z_2 = ln z_1 + ln z_2 on a complex plane? Is it true that for any ln z_1 and any ln z_2 exists ln z_1*z_2 such that ln z_1*z_2 = ln z_1 + ln z_2 ? In this case that does happen to be true, because different branches >of ln(z) differ by a multiple of 2 pi i. Or you could choose, say, >values of ln z_1 and ln(z_1 z_2) and get a value of ln z_2. >On the other hand, a statement such as ln z^2 = 2 ln z is trickier: >every value of the right side is a value of the left side, but not every >value of the left side is a value of the right side. IMHO it would >be better to write ln (z_1 z_2) = ln(z_1) + ln(z_2) + 2 pi i n for some integer n Shouldn't this be 4pi i n instead of 2pi i n if Z_1 =e^[i(thita1+2pi n)] and Z_2=e[i(thita2+2pi n)] and product=e^[i(thita1+thita2+4pi n) = (Z_1 Z_2) ln(Z_1 Z_2)=ithita1 + ithita2 + 4pi in Is this not the requirement? However combining the RHS we get: ln(Z_1 Z_2) = ln(Z_1)+ln(Z_2) Unless I, have missinterpreted the definition of Z_1 and Z_2 . Panagiotis Stefanides which is true no matter what branches you choose for all the logarithms. Robert Israel israel@math.ubc.ca >Department of Mathematics http://www.math.ubc.ca/~israel >University of British Columbia >Vancouver, BC, Canada V6T 1Z2 X-Received: (from approve@localhost) by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id h9HCjfC28484; ==== 1/9 = 0.1111... 2/9 = 0.2222... ... 8/9 = 0.8888... 9/9 = 0.9999... But, 9/9 = 1, so 0.9999... equals 1 This is just some funny stuff that crept into my head. Now, is there anything wrong in this proof? If so, what is it? ==== > > 1/9 = 0.1111... > 2/9 = 0.2222... > ... > 8/9 = 0.8888... > 9/9 = 0.9999... > > But, 9/9 = 1, so 0.9999... equals 1 > > This is just some funny stuff that crept into my head. > Now, is there anything wrong in this proof? If so, > what is it? Informally, it's fine. Formally, though, you are assuming without proof a) 1/9 = 0.1111... b) 9=0.1111... = 0.9999... and c) both 0.1111... and 0.9999... somehow represent specific numbers. ==== > > >1/9 = 0.1111... >>2/9 = 0.2222... >>... >>8/9 = 0.8888... >>9/9 = 0.9999... >But, 9/9 = 1, so 0.9999... equals 1 >This is just some funny stuff that crept into my head. >>Now, is there anything wrong in this proof? If so, >>what is it? > > > Informally, it's fine. > > Formally, though, you are assuming without proof > > > a) 1/9 = 0.1111... > > b) 9=0.1111... = 0.9999... > > and c) both 0.1111... and 0.9999... somehow represent > specific numbers. There are all geometric series with ratio < 1 (1/10 to be exact) so the series of partial terms converges. Bob Kolker > > ==== > This is just some funny stuff that crept into my head. Now, is there anything wrong in this proof? If so, what is it? > You first have to show that 1/9 =0.1111.... . The rest follows. Bob Kolker ==== >This is just some funny stuff that crept into my head. Now, is there anything >wrong in this proof? If so, what is it? Well, it's not a proof, for one. Just saying something is true doesn't make it so. If I tell you that Integral(e^(-x^2),-Infty,Infty) = Sqrt(2*Pi), that may very well be true, but that doesn't make it a proof. Doug ==== it doesn't equal one; it is one by definition of the decimals by Simon Stevin in the 16th cce: it's the only ambiguity in the decimals, where [x].99999... can also be notated as [x+1].00000... -- you omitted the endless string of zeroes! of course, this applies, no matter where the endless nines begin, other than that crappy Beatles album. > 1/9 = 0.1111... > 2/9 = 0.2222... > ... > 8/9 = 0.8888... > 9/9 = 0.9999... > > But, 9/9 = 1, so 0.9999... equals 1 --les ducs d'Enron! ==== > > 1/9 = 0.1111... > 2/9 = 0.2222... > ... > 8/9 = 0.8888... > 9/9 = 0.9999... > > But, 9/9 = 1, so 0.9999... equals 1 > > This is just some funny stuff that crept into my head. Now, is > there anything wrong in this proof? There's nothing wrong with the result you obtained. proof as well as giving hints about how to show the result more formally. http://www.faqs.org/faqs/sci-math-faq/specialnumbers/0.999eq1/ http://mathforum.org/dr.math/faq/faq.0.9999.html - Randy ==== > > 1/9 = 0.1111... > 2/9 = 0.2222... > ... > 8/9 = 0.8888... > 9/9 = 0.9999... > > But, 9/9 = 1, so 0.9999... equals 1 > > This is just some funny stuff that crept into my head. Now, is there anything > wrong in this proof? If so, what is it? > By any reasonable definition, 0.999..., if it is to be any sort of real number, is the limit value of a Cauchy sequence of rational numbers, and that sequence converges in the set of reals to some real value. Thus if 0.999... is to have any real value, that value must be that limit, which is 1. ==== Yee Seng Chan schreef in bericht 1/9 = 0.1111... > 2/9 = 0.2222... > ... > 8/9 = 0.8888... > 9/9 = 0.9999... But, 9/9 = 1, so 0.9999... equals 1 This is just some funny stuff that crept into my head. Now, is there anything wrong in this proof? If so, what is it? > 0.9999... = 0.9 + 0.09999... 0.9999... = 0.9 + 0.9999.../10 0.9999... * 9/10 = 0.9 0.9999... = 0.9 * 10/9 0.9999... = 1 QED Steven ==== >0.9999... = 0.9 + 0.09999... >0.9999... = 0.9 + 0.9999.../10 >0.9999... * 9/10 = 0.9 >0.9999... = 0.9 * 10/9 >0.9999... = 1 >QED This proof assumes a lot of what you're trying to prove. What's truly amazing is that this thread waited until October to start this year, instead of the typical September. Doug ==== Doug Norris schreef in bericht 0.9999... = 0.9 + 0.09999... >0.9999... = 0.9 + 0.9999.../10 >0.9999... * 9/10 = 0.9 >0.9999... = 0.9 * 10/9 >0.9999... = 1 >QED This proof assumes a lot of what you're trying to prove. > The problem is the 0.9999... = 10 * 0.09999..., right? At least the rest looks basic arithmetic to me. LHS = 9*10^-1 + 9*10^-2 + 9*10^-3 + ... RHS = 10 * (9*10^-2 + 9*10^-3 + 9*10^-4 + ...) Sorry, I can't see the assumption you're referring at. Steven ==== Liz > I am very confused about the relationship between zeta(s) and the > alternating zeta function (called eta(s), I believe), where the sign > of all the even terms is negative. ... > eta(s) = (1 - 2*(2^-s))*zeta(s). True. ... > Likewise, I could also generate just the odd terms by; eta(s) = (1 - 2^-s)*zeta(s), True again. > The term (1 - 2^-s) has a zero at the origin; however, numerical > summations of just the odd terms indicate that there is no zero at the > origin. The other case (snipped) is similar to this one. The trouble is that the usual series for zeta is not valid at the origin, or anywhere left of Re(s)=1. LH ==== 3 men went to a motel. There's only 1 room left and it costs 30 bucks. So, each man forked out 10 bucks. Later, the owner discovered he over-charged the 3 men. It should be 25 bucks instead. So, he sent his runner to give 5 bucks back to the 3 men. The 3 men think the owner is very honest, and thus each took 1 buck back, leaving 2 bucks to the runner as tips. Now, since they took 1 buck back, each of them paid 9 bucks. 2 bucks to the runner. So: (9*3)+2 = 29. Where's the 1 dollar? That's a really old one. The 9*3+2 is wrong. The total paid is 25+2 = 27 = 3*9. ==== Let's define a sum: n 1 s(n)= S ------------- k=0 k! Now, we want to get this sum: oo S(x)= S s(n) x^n ; x<1 n=0 Is there a closed form and if so how to evaluate it ==== I have a TI-36X Solar calculator that I bought for a beginning physics class >that I'm taking this semester. I'm not very strong in math but seem to be >making my way OK. Yesterday I discovered something about my calculator that >is a real puzzlement to me. Perhaps you can shed some light on it. The calculator has a built in constant for the value of Universal Gravation >(G). When you display the value of the constant you get 6.67259 ^-11 which >is correct. However, if you enter this value manually into the calculator, >6.67259 x 10^-11 and press the equal key, you get 6.67259 ^-10. I've had one for years. Pressing 3rd-Const-G produces the correct > value of 6.67259 x 10^-11. Entering manually 6.67259, pressing EE and > entering -11 followed with equals produces 6.67259 x 10^-11, just like > it should. Ah, but there's a difference for me. When I enter 6.67259 x 10 EE -11 and press = (equal key), I get 6.67259 ^-10. ==== >I have a TI-36X Solar calculator that I bought for a beginning physics > class >that I'm taking this semester. I'm not very strong in math but seem to > be >making my way OK. Yesterday I discovered something about my calculator > that >is a real puzzlement to me. Perhaps you can shed some light on it. >The calculator has a built in constant for the value of Universal > Gravation >(G). When you display the value of the constant you get 6.67259 ^-11 > which >is correct. However, if you enter this value manually into the > calculator, >6.67259 x 10^-11 and press the equal key, you get 6.67259 ^-10. I've had one for years. Pressing 3rd-Const-G produces the correct > value of 6.67259 x 10^-11. Entering manually 6.67259, pressing EE and > entering -11 followed with equals produces 6.67259 x 10^-11, just like > it should. > > Ah, but there's a difference for me. When I enter 6.67259 x 10 EE -11 and > press = (equal key), I get 6.67259 ^-10. > > > You are multiplying by 10 EE -11 = 1 EE -10, not by 1 EE -11. Try multiplying by 1 EE -11 insted of 10 EE -11, and everything will work out right. A zero in the wrong place is not necessarily nothing! ==== I am looking for some old HP calculators like HP 41CV, HP 41CX, HP >> 71B, HP 15C, HP 16C, HP 67 and any others in the 1980's era...If you I have an HP55 and no, I'm not selling. >Bought it in 1975 and it still works :-) > http://www.dotpoint.com/xnumber/hp55.htm I would like to point out that this is a rarity in sci.math: a thread in which people wax eloquent about calculators. In my personal experience, I have seen calculators be useful at work for 1. simple arithmetic which involves too many digits to be fun or interesting 2. repetitive specialized calculations (e.g. a banker will use a calculator which can compute effective interest rates on a loan or investment). Anything simpler people do by hand and anything more complex uses a computer. In short: it always seemed to me that almost no one would use a calculator as a regular part of their job except for situations #1 and #2. But here I now read that people are indeed very attached to their calculators, and so I am very curious: What do you use them for? I would be especially interested to discover any professional uses for the graphing and symbolic calculators (my impression so far has been that no one uses them except high school teachers and their students). In particular, if anyone has ever denied employment to an applicant because he or she was found not to have the necessary competence with calculators, that would be information I ought to have. dave ==== 1. simple arithmetic which involves too many digits to be fun or interesting > 2. repetitive specialized calculations (e.g. a banker will use a calculator > which can compute effective interest rates on a loan or investment). For some reason, people seem to ask me lots of financial questions. Frequently, this means that I have to calculate the effective interest rate or the payment. I can do this with a 4-function calculator because I know the formula. I even now (after many years) have enough confidence in my memory that (unless the application is extraordinary in some way) I don't even have to derive the formula before I use it. Anything simpler people do by hand and anything more complex uses a computer. > In short: it always seemed to me that almost no one would use a calculator > as a regular part of their job except for situations #1 and #2. 1a. Too many summands. But here I now read that people are indeed very attached to their > calculators, and so I am very curious: What do you use them for? Back in the Old Days, field engineers or geologists (usually water or oil related) used to do some esoteric water- or oil- (or even surveying-) related calculations. In the field, so they didn't even have access to a computer. The first laptops were considered too fragile for rugged field use, so HP calculators were still the norm (the sales reps used to demonstrate them by throwing them at a wall, hard enough to crack the case, and then picking them up and calculating on them). Now that computers are truly portable, I suspect that all those uses have gone away. Simple financial calculations (bond pricing, amortization, the like) are still done on hand calculators, because it's possible, but more complex things (CMOs, Black-Scholes option pricing, etc.) require a computer. Hand-helds don't seem to have caught on enough for that yet, but I suspect it's coming. > I would be especially interested to discover any professional uses for > the graphing and symbolic calculators (my impression so far has been > that no one uses them except high school teachers and their students). But not that this is a bad thing. And certainly not a Bad Thing. A picture is worth a thousand words, and I think it's good for the students to get ideas without getting bogged down in the details. (Top-down learning -- get the Big Ideas, then fill in the details. As opposed to Bottom-up learning -- use the details to build up the Big Ideas. Some personalities adapt more readily to one model over the other. Real life demands both.) Of course, graphing calculators make it possible to get the Big Ideas and then ignore the details. Which means that you don't really understand. But it's not like that never happened Before Calculators. Oh, and my daughter uses one. (RA in chemistry.) Mostly to download data from some chemical apparatus and carry it over to the computer. But there's at least some analysis that can be done on the calculator. I think the reason for the high school use is that they feel they can't require a computer. So they require a certain amount of computer power on the cheap. > In particular, if anyone has ever denied employment to an applicant > because he or she was found not to have the necessary competence with > calculators, that would be information I ought to have. If such an allegation were made, I would immediately disbelieve it. I'd need very, very strong evidence. Unless the lack of necessary competence were explained by I couldn't do the calculator problems on the test. But IMO, someone who can't figure out how to use a calculator will soon run into bigger problems anyway. One result of the reliance on calculators is that tests can now be more accurately constructed to measure knowledge. I know that I used to know that I had made an error because the calculations got hard. (The more difficult the question, the more likely the answer is to be 2 or pi. -- Indrahand Sinha.) Now, you just punch the numbers and just keep continuing the calculations. (Write down your intermediate steps, or no partial credit.) Unfortunately, from what I see, tests are not always constructed more reliably than in the old days, even though the easy numbers crutch can now be removed. I can't believe I've written this much about this. Jon Miller ==== I am looking for some old HP calculators like HP 41CV, HP 41CX, HP >> 71B, HP 15C, HP 16C, HP 67 and any others in the 1980's era...If you I have an HP55 and no, I'm not selling. >Bought it in 1975 and it still works :-) > http://www.dotpoint.com/xnumber/hp55.htm I would like to point out that this is a rarity in sci.math: > a thread in which people wax eloquent about calculators. In my personal experience, I have seen calculators be useful at work for 1. simple arithmetic which involves too many digits to be fun or interesting > 2. repetitive specialized calculations (e.g. a banker will use a calculator > which can compute effective interest rates on a loan or investment). Anything simpler people do by hand and anything more complex uses a computer. > In short: it always seemed to me that almost no one would use a calculator > as a regular part of their job except for situations #1 and #2. But here I now read that people are indeed very attached to their > calculators, and so I am very curious: What do you use them for? > I would be especially interested to discover any professional uses for > the graphing and symbolic calculators (my impression so far has been > that no one uses them except high school teachers and their students). In particular, if anyone has ever denied employment to an applicant > because he or she was found not to have the necessary competence with > calculators, that would be information I ought to have. dave I'd like to add this... My HP-55 had 49 programming steps, but the f- and g-shift keys counted as a step. Shortly after I had my 55, my at that time future brother in law bought himself the smaller but cheaper HP-25 which had 49 steps as well, but the shifts did *not* count as separate steps, so his little machine was a bit more powerful on the programming side. No need to say that made me a bit jealous... The manual listed a 49 steps 'moonlander' program sort of game, and of course it did not fit into my 55 at all :-( So I took the challenge to modify the program... and with some clever (-ahem-) tricks I finally managed to do just that. That made me very proud :-)) Dirk Vdm > Comments should say _why_ something is being done. Oh? My comments always say what _really_ should have happened. :) - Tore Aursand on comp.lang.perl.misc ====