mm-88 === 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 thingon his site), but he made a dumb error on another problem, so,I didn't pursue it; I'm not very accomplished in mumbertheory (andthe 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 ?d 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. Thereviewed the problem are not as young and inexperienced (usually) as thetypical math olympiad contestant. People get better at that kind of problemwith practice. Moreover, developing model solutions for an olympiad problemcan sometimes take weeks, while the contestants have at most hours to ?d asuitable solution. The judges have solutions at hand, so they can be sparedthe effort of devising a solution from scratch, and can simply do (what Iacknowledge is still hard work) a comparison between the model answer andthe 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 dif?ult to see which ice skater, forexample, is better and the judging standards are suf?iently unclear evento the judges that most ice-skating competitions are judged by panels.Machines can tell who won a foot race, but fallible human beings have tomake debatable decisions to decide, for example, how many points should beawarded 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 MathematicsInstitutehttp://www.claymath.org/Education/ Olympiad_Scholar/for the student who displays the most original and mathematically correctsolution to a problem in the USA Mathematical Olympiad. As you canimagine, the students who win this award are those who DON'T follow themodel solution developed beforehand by the judges, but who come up withsomething unexpected. And I'm sure choosing the winner of that award eachyear is a dif?ult task in judging.P.S. I judge at a MUCH lower level of mathematical competitions, whichexhausts my personal mathematical abilities. I admire the people who canjudge at a higher level.-- Karl M. Bunday Christ has set us free. Galatians 5:1Learn 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 fromonlookers 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 bookCalculus (Publish or Perish Press, third edition). This textbook is notspeci?ally written to the AP Calculus syllabus and thus is unknown to manyAP calculus teachers, but it is unanimously recommended by mathematicians.> What comes after calculus?What comes after a ?st course in calculus is a second try at learningcalculus to really UNDERSTAND calculus. Hardly any universities use MichaelSpivak's book Calculus (third edition, Publish or Perish Press) as atextbook for a ?st calculus course, but it is positively SCARY howunanimous mathematicians are in recommending that book for people who reallywant to understand calculus. Spivak's book also has good humor, as most goodmathematical books do.A little while earlier, someone else on the same newsgroup asked a series ofdetailed 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 reviewsfrom professional mathematicians, with many calling it the best calculusbook, is Calculus by Michael Spivak (3rd edition, Publish or Perish Press).I own Spivak's book, and know several people locally who think it iswonderful. However, Spivak's Calculus is not an EASY introduction tocalculus--it's very useful to have for clear explanations and workingthrough it would probably give you a deep understanding of calculus thatwould be dif?ult 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 amalso trying to learn calculus by self-study. In the end, the only way tolearn calculus is to do A LOT of problems that build progressively onearlier understanding--on that, all teachers of calculus agree, whateverelse they disagree on. And calculus is, indeed, one of the math courses forwhich there is the most varied assortment of textbooks, sometimes takingwildly differing approaches.> Can I learn calculus in the internet?There is a distance learning course on calculus for which you can getcollege credit (if you PAY for the college credit and keep up with yourrequired homework) offered by the University of Illinois Urbana-Champaignhttp://www-cm.math.uiuc.edu/called Calculus and Mathematica which some math professors like a lot, andothers decry. I MAY just buy the book for that course through Amazon.com andwork through it myself with a student copy of Mathematica, forgoing thecollege credit, but I'm still trying to decide.There is another distance learning course about calculus offered by theEducation Program for Gifted Youth (EPGY) at Stanford Universityhttp://epgy.standford.edu/but that course, as its name implies, is for gifted young people who haven'tyet graduated from high school. That course uses a combination of the Antontextbook and innovative course software developed by Stanford. My oldest sonis taking EPGY courses that are prerequisites for the calculus course rightnow, 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 atleast one case. Those includehttp://www.math.gatech.edu/~morley/1507/ MeaninglessSymbolicManipulation.html(approaches to studying Calculus, including a recommendation of some of thebooks I just mentioned)http://www.math.washington.edu/~duchamp/124notes/ k124-main.pdfhttp://www.math.washington.edu/~duchamp/125notes /k125-main.pdf(Two lengthy Adobe Acrobat .PDF ?es with a college calculus course, freefor the downloading, by Professor Neal Koblitz of the University ofWashington)http://www.math.hawaii.edu/~lee/calculus/ University of Hawaii)There is a lot more where these links came from; you could ?d good stuffabout calculus on the Web for hours. Try Googlehttp://www.google.com/to run more searches of your own.homeschooled kids are looking for something like a high school calculusbook. The ?st place to look is in your friendly local public library,where you may ?d several different calculus books aimed at high schoolstudents. Stewart's book is used here in Minnesota by the University ofMinnesota Talented Youth Mathematics Program (UMTYMP) and the Anton book isused by EPGY; I can get both in my local library systems. How to LearnCalculus: A Streetwise Guide looks pretty good to me, although I would haveyour local library request it rather than buying it yourself. Calculus MadeEasy is NOT a complete calculus course, but it is good for motivation andCalculus is a good introductory text; there are lots of high school crambooks on calculus in good public libraries. There are many good calculuspreparation 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 betweenundergraduate calculus and math courses beyond calculus for math and sciencemajors. Those books often have titles like Introduction to Proof, orProblem Solving or Introduction to Advanced Mathematics or MathematicalThinking or phrases more or less like that. It is a good idea to startreading a book like that, and working through its exercises, BEFORE?ishing a calculus course. Probably your local university has several booklike this in the campus bookstore, and the math department could recommendwhatever 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 5:1Learn in Freedom (TM) http://learninfreedom.org/ === > That's because I ?ure 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 longI've waited $100,000 US is not a big deal.Besides, I have to admit that it'd be neat to share *something* withsomeone 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 itall myself, like usual.Or that math journal will ?ish its review of my paper AdvancedPolynomial Factorization in my favor.In any event, readers can be sure that the poster here doesn't havethe skills needed to handle a computer check, or I'd think he wouldn'tbe wasting time, when there's money to be made.James Harris === > It doesnt 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 AMathematician's Miscellany, deals with seemingly unlikely events, andocomputing how likely they really are. For example, he says it is notunreasonable that about once a year in England, someone receives aBridge 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 hasbeen> rolled 27 times in a row, it seems unlikely that it hasn't happened to> someone. Have a tolerable existence. EliA very rough approximation gives around E 22 dice rolls in the last 200years.this is the same order of magnitude as the inverse probability of 27consecutive rolls of seven.I don't see however that the sample space of all connected throws of twodice would be anywhere this large.Does anyone know of actual events or legends where anyone broke the bank bya run of 27 sevens, or if it ever happened.(not to mention that supernatural things start to happen in the Casino'sfavor if doom is lurking!)Bob Pease === Dik T. Winter pushed brie?the front of thedoor:^ >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 re?merican^ >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 ragwithout regarding it as a personal insult.Bill Taylor, sci.math === > That's because I ?ure 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 ?ish 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 thatnon-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 ?d 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 ?st in French; in mod.F. the suf? 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 suf? 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.caDepartment of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada V6T 1Z2 === Would someone post a de?ition of the semi-direct product?OK. Let G and H be groups. A semidirect product of G by H involves ahomomorphism phi: H -> Aut(G) - you can de?e a semidirect productfor 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 de?ed by (g1,h1) (g2,h2) = (g1 phi(h1)(g2), h1 h2).You can check that this de?es a group - associativity needs checking,for example. The direct product is the special case in which phi(h) isthe identity automorphism for all h in H.Any semidirect product has a normal subgroup { (g,1) | g in G } isomorphicto G and a subgroup H (which is normal only in the case of the directproduct) { (1,h) | h in H }, so G sd_phi H = GH and G intersect H istrivial. So H is a complement of G.Coversely, if E is any group having a normal subgroup G and a subgroupH such that GH = E and G intersect H is trivial, then you can prove thatE is isomorphic to a semidirect product G sd_phi H, where phi isde?ed by phi(h)(g) = h g h^-1.Semidirect products are extremely common, particularly among groups ofsmall 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'tdone it previously because I thought -ize was just an Americanversion, and here in Europe they prefer British misspellings.-- Jesse F. HughesIf anything is true in general about Usenet, it's that people can goon and on about just about anything. -- James Harris speaks thetruth. === >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 ofstate? === > 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 andFowler prefer -ize. I think the -ise alternative crept in (under Frenchin?) after English and US spelling had parted company, so the USspelling 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 inconsistentmyself. One lazy reason for using -ise is that it becomes unnecessary toworry about those words like `revise' and `advise' which can only bespelt -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) hewas proving Fermat's Last Theorem was because it impressedwomen.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 canconsult experts and books. They can re-write and revise untilpolished.The contestants have only 3 hours (or whatever) and no outsideresources. === >> 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 ?h>> in little pond to little ?h 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 ?ter, drop it]Once upon a time, the battery died and thought that I'djust use this other calculator until I had time to geta new one. I could not function. RPN is so imbeddedinto my thinking that I could not use a regular calculator.I ended up doing the stuff on paper and the task of gettinga 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 de?ed 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 withsome of the details. There are 4 cyclic normal subgroups of order 4,with the elements of order 2 identi?d, 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 whichdoesn't appear in in others. Perhaps it shows up in order p^n forany 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 ?ter, 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 =-calculatorand I'm lost.I had my battery pack die so many times I stoppedcounting. Each time it had to be ordered and it tookweeks. And it cost a fortune. So ?ally I decidedto go out for some naked NiCd batteries, cut openthe plastic packaging of the pack and replace thebatteries myself. I was a mess (with aluminum papercontacts and such) but it worked and it was MUCHcheaper ;-)Dirk Vdm === > Is it your intention that JSH should take what you say about him > seriously? If so I ?d it a rather cruel kind of sport.> GibFor those who wonder about posts like this one, where one of theregular attention parasites who tend to reply in my threads makes acomment having *deleted* out much of the pertinent information, myassessment is that it has to do with Google Groups.Google Groups brings a lot of readers to Usenet over the Internet, butits setup puts the *last* post forward, so that some posters haveclearly adopted a strategy of trying to get in the last post, so thatthey are seen ?st by readers.Being seen ?st gets you guaranteed readership in popular threads.Assuming that readers skim along checking out posts quickly, it's notnecessarily the case that they'll bother to look back at previousposts, so a poster can try to in? the discussion without havingto deal with other posts in the thread, knowing that a lot of readerswill just see their post.If nothing else, it puts the spotlight on a particular poster, whomight otherwise be drowned out, especially when they give very weakposts of little interest to others.James Harris === > That's because I ?ure 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 casuallyposters 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, yetagain.Please pay careful attention.Many posters repeatedly lie in their posts depending on readersskimming 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 plateto make history.Celebration is not an indication of laziness.I ?d 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 ?ish 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 inthis thread, it should be *extraordinary* to the reader that thisposter 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 meansci.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 de?ed 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 de?ed 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 meresults 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 cubicgives: 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 de?itions: 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 + ufSo far so good, as now I have independent terms, which therefore willnot change with m. CONDITION: f is coprime to 3, x and uThis 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 fNow I'm forcing a change by dividing off f^2, but again, I'm doingthings 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 afactor of two of the g's which may seem obvious, but remember, I'msetting 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 ?ale.7. Backwards Theorem: Reverse use of distributive property provesg_1, g_2 have factor that is f.I ?d it interesting that no comments from others have been made hereat the heart of the proof.g_1(m) = a_1(m) x + uf g_2(m) = a_1(m) x + ufso 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 fwhen I divide P(m) by f^2, and I made that ?ding *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 thata_1 and g_1 have f as a factor. (Note to readers: The point of using independent terms is that theyare *independent* of the value of m.) 8. Veri?ation: Determine independent term of g_1(m)/f, by setting m=0. g_1(0)/f = a_1(0)/f x + u = u. Con?med factor f for g_1.Now maybe you see why posters have ignored the full outline in theirreplies. Determine independent term of g_2(m)/f, by setting m=0. g_2(0)/f = a_2(0)/f x + u = u. Con?med 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 suf?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 ?d 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 ?st by readers. Being seen ?st 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 in? 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 Harrislook 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 -- andthe 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 veri?ation 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 ?gers 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 re?eri can>standards along the way...I checked; except for the two typos, critize for criticize (sospelled in de Morgan's original) and extend for extent, thequotation was accurate in spelling. The only other difference in there must be the inde?ite ?something' in the mysterious ?allthis'. 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 ?ures few readers can criticize. A great many people are staggered to this extent, that they imagine there must be the inde?ite 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 ?e 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 toomade 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.htmlNeedless 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 de?ed 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 de?itions: > 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 ?ale. > 7. Backwards Theorem: Reverse use of distributive property proves > g_1, g_2 have factor that is f. > I ?d 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 youcan 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 (becausea_1(0) is divisible by f). You have not yet shown that a_1(m) or g_1(m) isdivisible by f when m != 0 and that you *can* remove the factor f in thatcase. Until this step you had *only* m=0. So why can you remove the factorf when m != 0? There is a gap.-- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131home: 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) everbroadcast.(Before the current abomination with too much reliance oncomputer-generated animation and overly long and dull segments likeElmo's (Endlessly Annoying) World, Monster Time -- which featuressingularly dull monsters and Journey to Ernie, a dull game whose onlyredeeming feature is that they occasionally show classic Sesame Streetsegments during this game -- but I'm not bitter about these changes,oh no, because I still have a dozen videotapes of actual good SesameStreet, and also the Dutch play the older style Sesame Street, but myDutch isn't good enough for it and besides the voices are allwrong...)-- Jesse Hughes How come there's still apes running around loose and there arehumans? Why did some of them decide to evolve and some did not? Didthey choose to stay as a monkey or what? -Kans. Board of Ed member === > That's because I ?ure 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 ?d 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 ?ish 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 de?ed 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 de?ed 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 de?itions: 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 ?ale. 7. Backwards Theorem: Reverse use of distributive property proves> g_1, g_2 have factor that is f. I ?d 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 ?ding *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. Veri?ation: Determine independent term of g_1(m)/f, by setting m=0. g_1(0)/f = a_1(0)/f x + u = u. Con?med 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. Con?med 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 ourversions of English are not because you have changed but because wehave 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 uschanging and not you.But in the case of spelling, I am fairly sure that most or all of thedifferences 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 selectUK English. I cannot select US English since then I get color andtheater which are regarded as wrong here.(*) Surprisingly, my spell checker accepted this even though it is inUK 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 dueto American variation rather than British.-- Jesse HughesWiles made somewhere around half a million dollars U.S. that I heardabout, 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 potentiallyunpleasant start, this sub-thread seemed to move in a more fundirection.I would be happy to get our variants of English to converge and amrealistic enough to accept that most of the movement would have to beon our part. In fact some of this is happening but people don'talways notice. Many words once considered American are now commonhere (e.g. truck instead or lorry). American pronunciations arecreeping 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 moreobvious.(*) This use of guess used to be considered an Americanism but isnow 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 youI 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 willdie 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, andthe hexahedron, qyoob?to state the solution without the proof:a rectangular box has these 7 measurements, andonly 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 BELOWon Trickier Dick Cheney's California Recall & e-Dereg!http://larouchepub.comhttp://www.rwgrayprojects.com/ synergetics/plates/?s/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, 3/30/81http://www.rwgrayprojects.com/synergetics/plates/?s/ plate01.html === >>Is it your intention that JSH should take what you say about him >>seriously? If so I ?d 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 ?st 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 ?st 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 in? 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 de?ed 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 de?itions:> 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 thatcoprimeness to x is listed as a condition yet this poster deleted itout!!!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 areworth 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'llhave 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 (freshmancalc/physics), and I've used it well. Now I'm a professor, and in allthree of my classes, the TI-83 is required, so I have to use it (since I'mexpected 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 HarrisGet help..........quickDavid Moran === >3. Let P(m) = g_1(m) g_2(m) g_3(m)>Variables: g_1, g_2, g_3 de?ed 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 de?itions:>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 coprimeto f, a1(0)/f is coprime to f, u is coprime to f. But (a1(0).x/f + u) isnot necessarily coprime to f. But this was only a side remark (hence thepareenthesis), 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, +31205924131home: 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 ?d 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 in? 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 ?d the tangential velocity of a body (mass: .127kg), ?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 ?d 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 speci? 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 aluminumX-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? (Dif?ulty 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 de?iteness 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 de?iteness, ?d 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 ef?ient, rather than effective. Given the matrix P + cQ, where P and Q are known positive de?ite >> 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 REAGANThis 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 simpli?s to (p -> T) xor (T <-> r) = T xor r = (not r)When q = F, P simpli?s 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 rand 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 REAGANThis 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 washoping to get some opinions on it.Suppose that:Y(x)=(k_1 - k_2/x)^.5Where the k's are positive constants.Is it proper to claim that Y is proportional to x^-.5? In thepresentation, the symbol alpha was used in place of the words isproportional to and I was wondering if that was a rigorous use ofthat symbol. I have always thought that f(x) alpha g(x) impliedthat f(x)/g(x) = positive constant, but the speaker disagreed. Anythoughts?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)^.5Where 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 aphysics background I'll add that under some circumstances, one mightsay something like Y varies as x^0.5 for small x, if that was theregime of interest. The physicist would write something like Y ~ x^-0.5 for small xI 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 inparentheses becomes negative. So probably the regime of interest is*NOT* small x, but large x. And as x increases, it is more proper tosay Y ~ constant.Where the physicist might use the tilde (~), the mathematician wouldmake 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 usethe 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 ?d,> 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 ?d the above> probabilities (1/4, 1/4, 1/2). I agree, that you cannot distiguish between the > three con?urations 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?> Palolot of space to the 1/3,1/3,1/3-1/2/1/4/1/4 question.--John === > I need to ?d 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 ef?ient 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 :PSimon.-- <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, theguitarist and base guitarist with long beards. A Dylan-typefolksinger sings How many elephants will ? in a room before theyfall through the ?nd then counts until the four elephants fallthrough the ?- no rhetorical questions here! A Billy Idolsound-alike sings about the Rebel L, and The Beetles sing Letter Bto the tune of Let It Be.I didn't wait for my son to be born before I started watching SesameStreet again. I began as an undergrad. It is only in the past two years that the program has been horriblyre-formatted and the really funny bits are few and far between now.(The most adult humor was in a prime time special during theIran-Contra affair. There is a segment in which Robin MacNeil,formerly of the MacNeil-Lehrer Newshour, interviews Cookie Monsterabout Cookiegate. Before each question is answered, Kermit, acting asCookie's lawyer, leans over and whispers to Cookie. The funniest bitis fairly juvenile, though -- Cookie Monster refers to the intervieweras Mr. MacLehrer. This bit and the whole special can be found onPut Down the Duckie.)-- Jesse F. HughesC 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 ? in a room before they> fall through the ?nd then counts until the four elephants fall> through the ?- 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)^.5Where 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 ?ished teaching myself basic group/ring/?ld>>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 ?ished teaching myself basic group/ring/?ld>>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 ?ures 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 HarrisYour 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 forestablishing whether something is same-old, same-old--if it isit'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 resistedrather than welcomed with open arms, because every successfulscientist has a vested intellectual, social, and even ?ancialinterest in maintaining the status quo.--Revolution in ScienceApart from the fact that very few who post here are ?successfulscientists', they are *like* successful scientists in the respectsI.B. Cohen describes.Of course you've said many similar things. But because the Boyzsee no advantage in kissing up to you, because you are not ahigh-ranking professor like I.B. Cohen was, whenever you sayanything on this topic they attack you for it, because mostof the things you say about mathematicians ARE true of theworst of them, and it is the worst of them whom the othersemulate in these groups.JohnSigh. Yes, the following, if the reasoning as (sic) actuallycorrect, can be easily formalized in ZF.... note that for example the in operator belowis not going to correspond to the in in ZF, it'sgoing to be just some predicate, with axiomsinvolving it. > C3 EyAx[x in y <-> Et(x in t) & A] (with y not free in A)>Classi?ation> 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 variousposters, whom I assume couldn't ?d their way around a proof checkingprogram, have continually made wacky posts distracting from the proofoutline 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 de?ed 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 de?ed 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 meresults 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 cubicgives: 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 de?itions: 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 + ufSo far so good, as now I have independent terms, which therefore willnot change with m. CONDITION: f is coprime to 3, x and uThis 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 fNow I'm forcing a change by dividing off f^2, but again, I'm doingthings 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 afactor of two of the g's which may seem obvious, but remember, I'msetting 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 ?ale.7. Backwards Theorem: Reverse use of distributive property provesg_1, g_2 have factor that is f.I ?d it interesting that no comments from others have been made hereat the heart of the proof.g_1(m) = a_1(m) x + uf g_2(m) = a_1(m) x + ufso 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 fwhen I divide P(m) by f^2, and I made that ?ding *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 thata_1 and g_1 have f as a factor. (Note to readers: The point of using independent terms is that theyare *independent* of the value of m.) 8. Veri?ation: Determine independent term of g_1(m)/f, by setting m=0. g_1(0)/f = a_1(0)/f x + u = u. Con?med factor f for g_1.Now maybe you see why posters have ignored the full outline in theirreplies. Determine independent term of g_2(m)/f, by setting m=0. g_2(0)/f = a_2(0)/f x + u = u. Con?med 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 HarrisX-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 summer?ld>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/Lso:(100/8) + (300/X) = 24then: since 100/8 = 12.5(300/X) = 11.5then300 = 11.5Xand you have: X =(approx.)= 26.09 km/LComing 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)^.5Where 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 proportionalto x^-.5Y 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 )^.5If 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)^.5but if x = 1 then (y Sqrt[x]) = (k_1 - k_2)^.5Not the same this...i.e. not constant. I we have the case that k_2/x >> k_1then y is approximately proportional to x^-.5..But, long story short; you are right, and the speakerwas 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)^.5Where 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 proportionalto x^-.5Y 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 )^.5If 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)^.5but if x = 1 then (y Sqrt[x]) = (k_1 - k_2)^.5Not the same this...i.e. not constant. I we have the case that k_2/x >> k_1then y is approximately proportional to x^-.5..But, long story short; you are right, and the speakerwas wrong.adam === It's also little use giving the wrong answer! 26.09 obviously can't beright!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 / 12300 / X = 800 / 24 - 300 / 24 = 500 / 24X = 3 . 24 / 5 = 14.4no 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 doesto 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 derivationdoesn't lead to a Riemann sum means... (is that one of thehypotheses, or a comment on why the proof is not clear or what?)If you could give a precise statement of what you want to provesomeone could show you how to prove it. _Is_ the question justhow to prove that the arclength is given by that integral?(That's what it sounds like the question is, but I'd be surprisedto hear that that fact was someone's theorem... _if_ that'sthe question then what are the hypotheses? In particularare we assuming that the curve is continuously differentiable?)John************************David C. Ullrich === I'm not asking about the arc length for parametric equations inparticular. I had just heard that Bliss's Theorem was used tojustify some applications of elementary calculus where the value atthe ith subinterval of the partition is chosen conveniently ratherthan 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 ?ure out what there is to be justi?d there:If f is Riemann integrable then it follows from the de?itionof the Riemann integral that you _can_ choose those pointsconveneniently...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 ofthe angle of the plane with the axis of the cone?I know that they depend on the height of the cone and diameter of thecircle 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 everafter but forgot to mention that it was a fairy tale.Once upon a time, I watched 10 minutes of a Mr. Rogers showbefore 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 veryfew children's shows that addressed feelings in a way thatat 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 thatweak, you need to see a doctor!) I've no doubt you dislikedthe show -- indeed my own ?st impression was similar -- butI'm sorry, 10 min is not suf?ient time to arrive at theconclusion you stated in your opening sentence. Even for thesingle show that you partially watched. (How do you know hedidn't mention that it was a fairy tale after you headed offto the WC?)Look, some children's shows -- Sesame Street being the primeexample -- 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 gatheryou'd be the ?st to agree. Actually I do ?d S.S. okayon balance, even though I share some of your concerns aboutit.)In any case, getting back to reality, Mr. Rogers was quitepossibly the realest person on TV. That counted for a lot.Whatever the faults of his show might have been, lack ofreality 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 ademonstration of how not to get work done. When you spendmore time and energy on feelings and how you ? in thesocial strata of any organization, you will not make anythingbecause you don't have time. All of this stuff happens in any human endeavour; however, it should not be top priority100% of the time.When you combine the short attention span reinforcement demonstratedin Sesame Street with touchy feelies getting high priority aspresented by Mr. Rogers _and_ Sesame Street, you get a population(adults and kids who later grow up to be well-tamed adults whohave kids) who cannot deal with survival problems and skills.More importantly, this programming is hour after hour, dayafter 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 whygetting 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 ?st impression was similar -- but>I'm sorry, 10 min is not suf?ient 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 sawthe 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 fortheir kids because the adults like the show. Kids aren't leftalone to play. Kids naturally have a long attention span.The premise of S.S's teaching is that kids can't possibly havea long attention span. What nobody seems to notice is thatlong attention spans generally disappear when people grow up.The rare few adults who haven't lost that ability are usuallyconsidered 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 ?st to agree. Actually I do ?d 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 damagetheir con?ence is an example. The teachers are trained toget along with their students. Kids are very adept atmanipulating this ?s a result, these kids don't learnabout learning from mistakes. JSH is an extreme example ofsomeone who didn't have his feelings hurt when he madean error. Look at how he reacts. Now look at how certainso-called liberals react when they're told don't do thator 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, asyou said, not a program for adults. But Mr. Rogers devotion toeducating young children and his earnestness was apparent to even acasual observer. This devotion isn't an embarrassment, but a greatvirtue for Fred Rogers.am not sure, but I think it's still available online.-- Jesse HughesThere's a thrill that's gone that I'll probably not have in quite thesame way again. After all, FLT was a unique animal, and we had agreat 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 aboutthe content of the show. What it did was train kids _and_ adultsthat instant grati?ation was the only way to learn. If you can'tthink of the answer in a nanosecond or be given the answer fromsomebody in a picosecond, then complaining about the turnaround time is OK...not only OK but a compulsory action.This program has trained generations that learning doesnot require working at it. Thus you have all those collegekiddies who whine when they aren't getting straight As withoutwork, merit or thinking. I saw no Sesame Street program (granted,I didn't see them all..just a few) that encouraged working atlearning. All learning had to be a Pavlovian response withoutany 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 ?e cartoon but that's all it was(even though the presentation involved breathing critters).To tout it as educational is..excuse me[emoticon rushes tothe 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 ?d 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 aboutproof-checkers but choose not to take you up on your offer. Perhapswe don't believe a checker can ever validate your argument, so ourefforts to do so wouldn't be worth a plug nickel to us.You only offer money for a successful effort. Moreover, anunsuccessful effort would do nothing to convince you that you'rewrong, since you may always claim that the argument as formalizeddoesn't capture your argument.It's ever so slightly possible that your readers are aware of yourgenerous offer to party with celebrities and heads of state (like allworld class mathematicians are wont to do), and still regard thebene?s from participation as negligible.Of course, once you learn how to validate your own proof, you can showus that our cost-bene? analysis was butt-wrong.(Once again, my random .sig generator chose a reasonably aptsignature.)-- Sorry, wakeup to the real world. You're on your own dependent on meas 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 con?ms 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 worthwhilewar to ?ht and win. I do not see how RPN logic can beignored when teaching calculus and physics. All the apps thatI've encountered has to store away intermediate results thatare 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 ?ht 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 ?ures 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 ?ancial> 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'mdoubtful that's true[1], but let's suppose so. How does this pertainto James's writing?Surely, mathematicians also resist incoherent ravings, or simplyincorrect reasoning, or even somewhat interesting distractions of noparticular depth. Surely not everyone that complains their new ideais revolutionary is correct. So, are you merely asserting thatmathematicians reject revolutions out of hand, but that this isirrelevant to James Harris's grand journey? Or, are you assertingthat JSH is being wronged by mathematicians that reject his largelycorrect 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 distractionthat you bring up merely to denigrate mathematicians?Footnotes: [1] Your pet project hardly counts as revolutionary, since it doesn'tseem particularly interesting in general practice and its already thesubject of study in limited areas, namely PER-models in computerscience. Note that the students of PER-models don't claim thatexistence is really the same as self-identity, but that it issometimes useful as a metaphor. Take what I say about PER-models with a large grain of salt in anycase, as they aren't part of my studies. Heck, I'm not even acomputer 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 thatyou're up to the challenge of being a real mathematician. Only thosewho have a purity of mind and dedication to the truth as the highestideal 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 ?ures 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 ?ancial> 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 isto make it easier for the likes of Ullrich and Magidin to pumpthemselves up at JSH's expense--and at the expense of all who callinto question the fundamental tenets of well-heeled scienti? andmathematical interest groups.But from you, this is not unexpected. For a bumfuzzler is abumfuzzler is a bumfuzzler!--JohnIf some quantum theorist somewhere wants to mess about with athoroughly 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 scienti? 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 facewith revolutionary new ideas. You keep doing this in James Harristhreads. Is James Harris in possession of revolutionary (and correct)mathematics which is being wrongly ignored, in your opinion? Or isJames Harris presenting bad mathematical arguments that ought to beignored and/or refuted?If you feel unquali?d to comment on the correctness of James'smathematics, then what relevance have these quotes? Unless James iscorrect in his arguments, there is no example of unreasonablerejection of his ideas here[1].Footnotes: [1] You may, I suppose, take issue with the degree of charityaccompanying those rejections. But, that has nothing to do with yourquotations, I think. I am not expressing any opinion about the appropriateness of the tonethat James's correspondents take. -- Jesse HughesThere's a thrill that's gone that I'll probably not have in quite thesame way again. After all, FLT was a unique animal, and we had agreat 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 scienti? 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 hereis to make it easier for the likes of Ullrich and Magidin to pumpthemselves up at JSH's expense, and at the expense of all who callinto question the fundamental tenets of well-heeled scienti? andmathematical 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 mathematicsthan you. Who are you to pass judgment on his work?> If you feel unquali?d 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 differentdrummer. You are not intelligent enough to carry JSH's dirty water, letalone 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 reasonablyloosely? One who has, in the distant past, learned a bit ofmathematics? In any case, I thought that you were dismissing the idea that thereare some authorities capable of judging work and others not. >> If you feel unquali?d 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 youfeel JSH has some insight into the mathematical issues here. Else,why would you keep mentioning his brilliance? What evidence, asidefrom his mathematical contributions have you? And, if you really feel incompetent to judge his math, then how canyou 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 myopinion on those, but not on responses as a whole. Of course, whocares what I think anyway?-- Jesse HughesWe will run this with the same kind of openness that we've runWindows. 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 ?st paragraph, though Istill the second is apt.I have not publicly judged JSH's work. In fact, I have previously hada policy (well, tendency) of refraining from directly replying to JSH,with some exceptions. I have relaxed this tendency recently, but youwill note that I still don't comment on his algebra as far as I canrecall.But, whether or not I pass judgment on his work really has nothing atall to do with my questions. Do *you* think that his work is correct?If you refrain from proclaiming it correct, then on what grounds doyou claim he is an expert mathematician (or at least knows far morethan I)? I'm not *really* asserting my opinion here. I'm just curious aboutthe strength of your conviction that his work has been wronglyrejected by mathematicians, given that you claim to be incapable ofjudging the work yourself.-- Jesse F. HughesI have written many words to sci.math, some of them are not evenmeaningless. --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 scienti? 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 scienti? and>mathematical interest groups.Really? Hard for us to know what his motive is. Why don't you simplyanswer 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 thanJesse.>Who are you to pass judgment on his work?A person does not need to know any math at all to passjudgement on his work. Knowing no math at all one canstill see that his answers to people's objections simplydo not address the question that was asked. (For example,one can see this when he repeatedly illustratessomething with m = 0, someone points out that knowingsomething for m = 0 doesn't prove it's true in general,and he comes back with more illustration of how thecase m = 0 works.) >> If you feel unquali?d 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'sasked.Regarding the question of who _is_ quali?d 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, byproud of getting rejections from big names like Barry Mazur,for some reason), and by a math professor at his alma mater.Who _is_ quali?d to judge his work?calling me a sicko, or explaining that hogs like me loveto wallow in various troughs, it will look to anyone readinglike you can't answer the question. Surely you don'twant that. So tell us, who _is_ in your opinion competentto 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. UllrichX-Cise: tanbanso@iinet.net.auX-CompuServe-Customer: YesX-Coriate: admin@interspeed.co.nzX-Ecrate: tanandtanlawyers.comX-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 originalproofs often had holes or outright errors in them.Second, a lot of Calculus books are oriented more to engineers andphysicists, and teach calculations rather than actual Mathematics. Ifyou want to understand the underlying Mathematics you may also need toread some Real Analysis.Third, there are many different learning styles, so you will be bestserved looking at several alternatives and seeing what works best foryou.Fourth, work the exercises as you go along.In addition to the Spivac text mentioned by other posters, I'drecommend that you look at the text by Apostol. I haven't seen hisCalculus text, but his Mathematical Analysis was excellent.If you haven't had any classes with real proofs, Linear Algebra is aneasy way to get started. I'd recommend Halmos's Finite DimensionalVector Spaces.Look for books with titles along the lines of Introduction to AbstractAlgebra.-- Shmuel (Seymour J.) Metz, SysProg and JOATnot reply to spamtrap@library.lspace.orgX-Cise: tanbanso@iinet.net.auX-CompuServe-Customer: YesX-Coriate: admin@interspeed.co.nzX-Ecrate: tanandtanlawyers.comX-Punge: Micro$oft === >The following is an artical from this link: creationworldview.orgWhat do those ignorant babblings have to do with Mathematics?*PLONK*-- Shmuel (Seymour J.) Metz, SysProg and JOATnot reply to spamtrap@library.lspace.org <845b431.0310141824.5fdae713@posting.google.com>X-Cise: tanbanso@iinet.net.auX-CompuServe-Customer: YesX-Coriate: admin@interspeed.co.nzX-Ecrate: tanandtanlawyers.comX-Punge: Micro$oft === at 07:24 PM, snizpilbor@yahoo.com (Sniz Pilbor) said:>Shmuel (Seymour J.) Metz accuses me of introducing new nomenclature>by saying a ?ld 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 additionalstructure. The term ?ed refers to a structure. Would you refer toa ?ed of brick and expect to be understood?>De?ition: A Field of Integers is any ?ld 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 ?ld with the elements {0,1,2} and theoperations2+2=2 0+2=0 1+2=12+0=0 0+0=1 1+0=22+1=1 0+1=2 1+1=02*2=2 0*2=2 1*2=22*0=2 0*0=0 1*0=12*1=2 0*1=1 1*1=02 00 11 2I'm not sure why you would want to do that, but it's legitimate. Itcertainly means that you must be more careful with your nomenclaturethan is usually necessary.> Please explain the counterexample which I posted, then. You didn't post a counterexample. You posted an example where morecare is needed than normally to explicitly distinguish distinctelements and distinct operations.> By well de?edI didn't ask what you meant by well de?ed; I asked what you meant bywell 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 weretaught in 1st grade? A ?ld is an ordered set (E,+,*) where + and *are functions with speci? properties. There is no reason for thoseoperations to be similar to the corresponding operations in adifferent ring, whether or not it is a ?ld, even if it has the sameE.> Then you are claiming I made an arithmetical error. No. I'm claiming that you are applying the wrong constants andoperators, because you have chosen ambiguous notation that makes itharder to keep track of context.-- Shmuel (Seymour J.) Metz, SysProg and JOATnot 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 just?s> 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 ?ite> 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 aresubgroups, any product of elements of K is also in K, andlikewise for N. Just collect terms in the general expression foran element of K V N = .-- Jim Heckman === a sphere : x^2 + (y-2)^2 + (z-3)^2 =1let point p : when tangent line of sphere pass on (0,0,c) is meet x-yplane,the point of contact is named plet c1,c2 : value c that trace of p satify parabola.solve that c1+c2 ??-------------------------------------i will regard it as dif?ult......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? TIAYou 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 professionalcounseling. Seriously. You're displaying signs of paranoia, psychosisand delusions of grandeur. I have a relative who suffers fromschizophrenia 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 grati?ation 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 Streetand that a three year old needs to learn to endure extended periods ofconcentration in order to master counting are, to my mind, simplylaughable. The related notion that Sesame Street encourages gradein? is similarly stupid. You've managed to put together dubiousinterpretations of the messages of Sesame Street with sillyexaggerations of the effect of the program on American life.However, I freely admit that my faith that Sesame Street is actually auseful educational tool is merely anecdotal. I don't study pedagogy,especially not for young children. I believe that Sesame Street hadbene?s for me when I was a child, and that my son now bene?s, butI have no hard evidence that this is so.Nonetheless, I will not defer to your strongly voiced butunsubstantiated opinions about the worth of this program.Final comment: I've no idea why you believe that Sesame Streetdiscourages effort. You write, If you can't think of the answer in ananosecond or be given the answer from somebody in a picosecond, thencomplaining about the turn around time is OK...not only OK but acompulsory action. This comment appears to come from thin air. Ireally have no idea what makes you think that this comment relates toany features of Sesame Street.-- No feeling sympathy for mathematicians who start marching with signslike ?Will work for food' in the future... I will not show mercygoing forward. I was trained as a soldier in the United States Armyafter 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 grati?ation 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 StreetNot 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'retrying insist that kids spend their play time (which is when theemploy their long-term attention spans) on learning howto count, say the ABCs, etc. > ..The related notion that Sesame Street encourages grade>in? 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>bene?s for me when I was a child,Yep. That's obvious. You've swallowed the programming hookline and sinker.> . and that my son now bene?s, 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_ makesit worthless. Just because you managed to learn how to countfrom 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 attentionspans?> .. 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 thealphabet or do homework from books. Sometimes he watches SesameStreet. You have no reason at all to infer from my comments that I insistthat kid spend their play time on learning how to count, say the ABCs,etc. However, I do appreciate the novel idea that you can criticizemy parenting based on two or three Usenet posts which barely touch onparenting at all. See, if only you were less timid in sharing yourdeep 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 de?ed 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 de?itions:> 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 myremark is true. But because a1(0)/f is *not* coprime to f the value of x isirrelevant. That x is coprime to f is totally irrelevant here.-- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === 1)i need some reference on differentials forms with $L^p$coef?ients. 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. /BAHIt only took me 5 minutes, slowpoke.--There are two things you must never attempt to prove: the unproveable -- andthe 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.> /BAHIt only took me 5 minutes, slowpoke. I took longer because I know that ?st impressionsare faulty./BAH === > Is there not a single mathematician in the world worth anything? James HarrisWorth anything? To whom? To you? Hopefully not! But I bet there are many mathematicians who are worth a great deal to theiremployers. 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 classthat I'm taking this semester. I'm not very strong in math but seem to bemaking my way OK. Yesterday I discovered something about my calculator thatis 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 whichis 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. Whathappened to the exponent? Why is it one greater than what I entered. Notethat I entered a negative 11 as the exponent. Can you tell me what's goingon here?I would prefer to use the constant built into the calculator built into thecalculator because of the savings of keystrokes, but others in the classdon'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 ?d 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 setshould contain exactly 10^12 elements.How do you handle the situation where the outputs aregreater than 10^12?I posted a solution that should solve thewhole problem. You can ?d it at http://groups.google.com/groups?hl=en&lr=&ie=UTF-8&selm= 3f82eead%240%2414345%2448b97d01%40reader20.wxs.nlgreetings, Ernst Lippe === > I was thinking about the interesting (and apparently dif?ult)> problem of ?ding 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 } satis?s 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'sBecause 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 totake over Science and Mathematics education in the USA.Although I think they deserve limited exposure in Sci.Math, it is importantto 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, Jamesassumes that because he can't understand how newsreaders work, neithercan anyone else...-- Wayne Brown (HPCC #1104) | When your tail's in a crack, you improvisefwbrown@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 aboutshooting your superior of?er with an M-16? Is that how you deal withpeople who treat you well? Oh, yes, I've seen how you've responded topeople like Arturo and Nora when they've tried to help you, so I supposethat *is* how you respond to good treatment...(Seehttp://groups.google.com/groups?selm= 01bc4498%2421ac77c0%24cc2b0c26%40minefor 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 anddozens and dozens of other people who get letters published each year.)You know, I got a letter published in Computerworld once, so I guessthat makes me the next Charles Babbage or something...-- Wayne Brown (HPCC #1104) | When your tail's in a crack, you improvisefwbrown@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 of?er 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? Jamesexplained long ago that what they published wasn't exactlywas, 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.> --Johndomin@javier.dnp.fmph.uniba.skPalo === Oh Please! Why must you be this way? Integrity has nothing to do with whyconstructive to add, why did you not just post in this newsgroup instead ofsaying something which adds nothing to my question. I continue to bedisappointed in posts like this one. :(> integrity to provide.I have a TI-36X Solar calculator that I bought for a beginning physicsclass>that I'm taking this semester. I'm not very strong in math but seem tobe>making my way OK. Yesterday I discovered something about my calculatorthat>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 UniversalGravation>(G). When you display the value of the constant you get 6.67259 ^-11which>is correct. However, if you enter this value manually into thecalculator,>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'sgoing>on here?I would prefer to use the constant built into the calculator built intothe>calculator because of the savings of keystrokes, but others in the class>don't have this feature and are entering the full equation. The problemis,>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 correctvalue of 6.67259 x 10^-11. Entering manually 6.67259, pressing EE andentering -11 followed with equals produces 6.67259 x 10^-11, just likeit 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 ofcourse, but you could try resetting with the AC/ON button and tryingagain. Sometimes after being in standby the calculator gets itsinternal state confused and will produce wrong results until reset. Ifnothing 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 wronganswer 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 ifan RPN calc isn't available. (Though my 48GX, 41CX and 16C are usuallywithin arm's reach.)-- Wayne Brown (HPCC #1104) | When your tail's in a crack, you improvisefwbrown@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 withwhySPAMfor> constructive to add, why did you not just post in this newsgroup insteadof> 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 themcriticising 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 in66.7259 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 knownmuch about him. The thing that struck me was that Mr. Rogers was notsome act he put on. One segment showed him testifying before Congress,talking to the chairman of the committee (the committee deciding on fundingfor 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 toact, and then he acted that way, though the world kept snickering. I imaginethat 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 pointhe'd (eventually) make here is that It's okay to have feelings. It's just ?e 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 (rhymingfails 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 treatingJames Harris. Your behavior would make Mr. Rogers very sad. Even littlechildren 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 ?e 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 theobvious.--Democracy: The triumph of popularity over principle.--http://www.crbond.com === I am very confused about the relationship between zeta(s) and thealternating zeta function (called eta(s), I believe), where the signof all the even terms is negative.Numerical summations in the complex plane suggest that eta(s) has azero at the origin, while zeta(s) does not.But it would seem that one could generate eta(s) from zeta(s) by thefollowing;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 eventerms, 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 simulationsof 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, numericalsummations of just the odd terms indicate that there is no zero at theorigin.I'm quite sure I am doing something very stupid; can someone point outthe 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 ?d 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 inlots 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 youall out of the loop.So you just get to sit and wait, and I guess hope that I fail becausewhen I succeed then I'll have you, and you know that I'm alreadypissed.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 ?ding someresidual ?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 followingexpressions:1) 2m+12) 3^m + 3m + 13) cos(m) + exp(m+2) + a/mDoes setting m=0 reveal ?those terms which are independent of m'?How about expressions with variables:1) a*m + b2) a^m + b*m + c/mDoes 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 = 02) cos(a*m) + b = 03) m + 2 = 04) a/m + b*m = 0Think 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' hasnothing to do with ?ding some> residual ?independent of m'. You have merely found the resultingexpression when m = 0.And thus the CORE ERROR of James' proof. Run James. Be afraid. You arenow 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 anexpression. 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 Rwhich (1) form an additive group and (2) are such thatwhenever x belongs to R and y belongs to I, thenxy belong to I. The set of even integers, for example, is an idealin 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 de?ition of algebraic integers is wrong.--les ducs d'Enron! === wow; I *knew* there was some thing funny about that usage of his, butI 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 de?ite >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.LarsIf you have an approximate inverse, you can use Newton's approximationformula to improve its accuracy:Xnew = 2*X - X*A*XXnew = 3*X - 3*X*A*X + X*A*X*A*XXnew = 4*X - 6*X*A*X + 4*X*A*X*A*X - X*A*X*A*X*A*Xwhere 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 accuracywith each iteration. The higher order formulas triple or quadruplethe 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 o?*z_2 = ln z_1 + ln z_2on a complex plane? Is it true thatfor any ln z_1 and any ln z_2 exists ln z_1*z_2 such thatln 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 writeln (z_1 z_2) = ln(z_1) + ln(z_2) + 2 pi i n for some integer nShouldn'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 inIs 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 de?ition of Z_1 and Z_2 .Panagiotis Stefanideswhich 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/~ israelUniversity of British Columbia >Vancouver, BC, Canada V6T 1Z2X-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 1This 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 ?e.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 speci? 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 ?e.> 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> speci? 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 ?st 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'tmake it so.If I tell you that Integral(e^(-x^2),-Infty,Infty) = Sqrt(2*Pi), that mayvery well be true, but that doesn't make it a proof.Doug === it doesn't equal one; it is one by de?ition of the decimalsby 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 resultmore 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 de?ition, 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 thereanything wrong in this proof? If so, what is it?>0.9999... = 0.9 + 0.09999...0.9999... = 0.9 + 0.9999.../100.9999... * 9/10 = 0.90.9999... = 0.9 * 10/90.9999... = 1QEDSteven === >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>QEDThis proof assumes a lot of what you're trying to prove.What's truly amazing is that this thread waited until October to startthis year, instead of the typical September.Doug === Doug Norris schreef in bericht0.9999... = 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 restlooks 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 theusual series for zeta is not valid at the origin, or anywhere left ofRe(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 25bucks instead. So, he sent his runner to give 5 bucks back to the 3 men. The3 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 tothe 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 de?e a sum: n 1s(n)= S ------------- k=0 k!Now, we want to get this sum: ooS(x)= S s(n) x^n ; x<1 n=0Is there a closed form and if so how to evaluate it === I have a TI-36X Solar calculator that I bought for a beginning physicsclass>that I'm taking this semester. I'm not very strong in math but seem tobe>making my way OK. Yesterday I discovered something about my calculatorthat>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 UniversalGravation>(G). When you display the value of the constant you get 6.67259 ^-11which>is correct. However, if you enter this value manually into thecalculator,>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 andpress = (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 youI have an HP55 and no, I'm not selling.>Bought it in 1975 and it still works :-)> http://www.dotpoint.com/xnumber/hp55.htmI 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 calculatoras a regular part of their job except for situations #1 and #2. But here I now read that people are indeed very attached to theircalculators, and so I am very curious: What do you use them for? I would be especially interested to discover any professional uses forthe graphing and symbolic calculators (my impression so far has beenthat no one uses them except high school teachers and their students).In particular, if anyone has ever denied employment to an applicantbecause he or she was found not to have the necessary competence withcalculators, that would be information I ought to have.dave === 1. simple arithmetic which involves too many digits to be fun orinteresting> 2. repetitive specialized calculations (e.g. a banker will use acalculator> which can compute effective interest rates on a loan or investment).For some reason, people seem to ask me lots of ?ancial questions.Frequently, this means that I have to calculate the effective interest rateor the payment. I can do this with a 4-function calculator because I knowthe formula. I even now (after many years) have enough con?ence in mymemory that (unless the application is extraordinary in some way) I don'teven have to derive the formula before I use it. Anything simpler people do by hand and anything more complex uses acomputer.> 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, ?ld engineers or geologists (usually water or oilrelated) used to do some esoteric water- or oil- (or even surveying-)related calculations. In the ?ld, so they didn't even have access to acomputer. The ?st laptops were considered too fragile for rugged ?lduse, so HP calculators were still the norm (the sales reps used todemonstrate 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 aretruly portable, I suspect that all those uses have gone away.Simple ?ancial calculations (bond pricing, amortization, the like) arestill done on hand calculators, because it's possible, but more complexthings (CMOs, Black-Scholes option pricing, etc.) require a computer.Hand-helds don't seem to have caught on enough for that yet, but I suspectit'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 pictureis worth a thousand words, and I think it's good for the students to getideas without getting bogged down in the details. (Top-down learning -- getthe Big Ideas, then ?l in the details. As opposed to Bottom-uplearning -- use the details to build up the Big Ideas. Some personalitiesadapt more readily to one model over the other. Real life demands both.)Of course, graphing calculators make it possible to get the Big Ideas andthen ignore the details. Which means that you don't really understand. Butit's not like that never happened Before Calculators.Oh, and my daughter uses one. (RA in chemistry.) Mostly to download datafrom some chemical apparatus and carry it over to the computer. But there'sat 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'trequire a computer. So they require a certain amount of computer power onthe 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'dneed very, very strong evidence.Unless the lack of necessary competence were explained by I couldn't do thecalculator problems on the test. But IMO, someone who can't ?ure out howto use a calculator will soon run into bigger problems anyway.One result of the reliance on calculators is that tests can now be moreaccurately constructed to measure knowledge. I know that I used to knowthat I had made an error because the calculations got hard. (The moredif?ult the question, the more likely the answer is to be 2 or pi. --Indrahand Sinha.) Now, you just punch the numbers and just keep continuingthe calculations. (Write down your intermediate steps, or no partialcredit.) Unfortunately, from what I see, tests are not always constructedmore reliably than in the old days, even though the easy numbers crutchcan 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 youI 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. daveI'd like to add this...My HP-55 had 49 programming steps, but the f- and g-shiftkeys counted as a step. Shortly after I had my 55, my atthat time future brother in law bought himself the smaller butcheaper HP-25 which had 49 steps as well, but the shifts did*not* count as separate steps, so his little machine was a bitmore powerful on the programming side. No need to say thatmade me a bit jealous...The manual listed a 49 steps ?moonlander' program sort ofgame, and of course it did not ? into my 55 at all :-(So I took the challenge to modify the program... and withsome clever (-ahem-) tricks I ?ally 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 ===