mm-181 === Subject: Evil Western people stole our numbers. You are not allowed anymore to use the stolen Arabian numbers !You must use Roman numbers !Or you have to become muslims === Subject: Re: Evil Western people stole our numbers> You are not allowed anymore to use the stolen Arabian numbers !You must use Roman numbers !Or you have to become muslims !I see. What about Hindu numbers, such as zero? If you use zero, doyou have to become Hindu?David Ames === Subject: Re: Evil Western people stole our numbers> You are not allowed anymore to use the stolen Arabian numbers !>> You must use Roman numbers !>> Or you have to become muslims !>> I see. What about Hindu numbers, such as zero? If you use zero, do> you have to become Hindu?Carl B. Boyer, A History of Matematics: see. binary system (talk about theoldest number systems).Q: Does junior need the stolen binary system in his computer to sende-mail message to sci.math?If you use binary system, do you have to become stone aged?Tapio>> David Ames === Subject: Re: Evil You are not allowed anymore to use the stolen Arabian numbers !You must use Roman numbers !Or you have to become muslims !Are you a hindu?-- Aatu Koskensilta (aatu.koskensilta@xortec.')Wovon man nicht sprechen kann, daruber muss man schweigen - Ludwig Wittgenstein, Tractatus Logico-Philosophicus === Subject: Re: Evil Western people stole our numbers omar_lasolt@yahoo.com (Osama Bin Laden junior) numbers !You must use Roman numbers !Or you have to become === Subject: Re: Evil zero!Now THAT is very funny!Joke of the week. Well done.---------- Bill Taylor W.Taylor@math.canterbury.ac.nz---------- When I was a kid I used to pray every night for a new bike. Then I realised that The Lord doesn't work that way, so I stole one and asked him to forgive me.---------- === Subject: Re: Evil Western people stole our numbers> omar_lasolt@yahoo.com (Osama Bin Laden Arabian numbers !You must use Roman numbers !Or you have to === what you really think of this racist idiot?Subject: Re: Evil wtwentyman@copper.net not allowed anymore to use the stolen Arabian numbers !You must use Roman numbers !Or you have to become muslims !Funny, by stealing your numbers it seems we are obviously acknowledging your mathematical superiority at some point in the past. Just think of it as a compliment.-- Will Twentymanemail: wtwentyman at copper dot net === Subject: Re: Evil Western people stole our You are not allowed anymore to use the stolen Arabian numbers !You must use Roman numbers !Or you have to become muslims !Says someone using English instead of Arabic? === Subject: Re: Evil Western people stole our numbersVirgil stolen Arabian numbers !>> You must use Roman numbers !>> Or you have to become muslims !>Says someone using English instead of Arabic?Even worse, the Arabs stole the numbers from the Indians.Also, many believe the Indians got the idea from the base60 usage of the inhabitants of Mesopotamia, who got itfrom the Sumerians in particular.-- This address is for information only. I do not claim that these viewsare those of the Statistics Department or of Purdue University.Herman Rubin, Department of Statistics, Purdue Universityhrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 === Subject: Re: Evil Western people stole our are not allowed anymore to use the stolen Arabian numbers !>> You must use Roman numbers !>> Or you have to become muslims !> Even worse, the Arabs stole the numbers from the Indians.>> Also, many believe the Indians got the idea from the base> 60 usage of the inhabitants of Mesopotamia, who got it> from the Sumerians in particular.This is the account of their genesis that I was taught, too. But we allknow they were originally a Soviet inwention.LH === Subject: Re: A =4 x4 matrix.Eigenvalues=?> Alex.Lupas 0 f / > c e f 0 / >where a^2+b^2+c^2+d^2+e^2+f^2 = 6 .>Consider that r_1 =< r_2 =< r_3 =< r_4 are eigenvalues of A.>It is known that r_4= 10. >It's true that all eigenvalues are integer numbers ?>If A is non-singular, which is the inverse matrix A^{-1} ?> ==> It can't happen that r_4 = 10. The characteristic polynomial of> A is t^4 - (a^2+b^2+...+f^2) t^2 + c1 t + c0 for some c1 and c0.> So you'd need r1 + r2 + r3 + r4 = 0 and > -6 = r1 r2 + r1 r3 + r1 r4 + r2 r3 + r2 r4 + r3 r4 > = 1/2 ((r1 + r2 + r3 + r4)^2 - r1^2 - r2^2 - r3^2 - r4^2)> i.e. r1^2 + r2^2 + r3^2 + r4^2 = 12. In particular > r4 <= 2 sqrt(3). > Suppose we remove the requirement r_4=10. The only ways to > get 12 as a sum of four squares are 1^2 + 1^2 + 1^2 + 3^2 and > 0^2 + 2^2 + 2^2 + 2^2, so the only integer solutions to> r1+r2+r3+r4=0 and r1^2+r2^2+r3^2+r4^2=12 with r1<=r2<=r3<=r4> are [-1,-1,-1,3] and [-3,1,1,1]. It is possible to get these> eigenvalues, e.g. with a=b=c=d=e=f=1 or a=b=c=d=e=f=-1 respectively.It looks to me (without being able to prove it) like the only casewhere 3 is an eigenvalue is a=b=c=d=e=f=1, i.e. a^2+...+f^2=6 anddet(A-3I) = 0 imply a=b=...=f=1. Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada V6T 1Z2 === Subject: Is this simplifed multidimensional packing problem still NP-hard?Hi folks, It's known that the traditional multidimensional packing problem is NP-hard. The Traditional multidimensional packing problem is as follows: Given: vector w (1 x n), matrix A (m x n), vector b (m x 1) w, A, b are integer valued. 'nd: vector y (n x 1) maximize: w * y subject to: Ay 1? Any hints or === Subject: Demostration: Binomial Distribution mean and var. Need help Please!!!!HiI need to demonstrate that the mean of a binomial distribution is npand the variance is np(1-p).Please, I need all your help. i'm a 'rst year university student andI need === Subject: Re: Demostration: Binomial Distribution mean and var. Need help Please!!!!Very simple solution.Let X = number of trials you had successes in N total trials.Now X = I1 + I2 + ...+ INwhere Ij = outcome of jth trial (it is distributed like Bernoulli(p)So the expectation of a sum is th sum of the expectationsE(X) = p + p + ...+p = Np (there are N of them)I won't work out the formula for the variance, but the principle is the same(although here you need to know that the trials are independent in orderto justify that the variance of a sum is the sum of the variances> Hi> I need to demonstrate that the mean of a binomial distribution is np> and the variance is np(1-p).> Please, I need all your help. i'm a 'rst year university student and> I need this ASAP.>> === Subject: Re: Demostration: Binomial Distribution mean and var. Need help Please!!!!> Hi> I need to demonstrate that the mean of a binomial distribution is np> and the variance is np(1-p).> Please, I need all your help. i'm a 'rst year university student and> I need this ASAP.The technique of indicator variables is easiest.Let k = the number of successes in n independent trials,where the probability of success on each trial is p. Sok is a binomial random variable with parameters n, p. Youwant the mean and variance of k.De'ne a variable I_j = 1 if the j-th trial is a success, and0 if it is a failure. Here are a few pertinent facts:1. All the I's have the same distribution.2. k = sum(I_j), j=1, n a. Therefore the mean of k is the mean of the sum of the I's, which is the same of the sum of the means.3. What's the mean (expectation value) of I? It has twopossible values, 0 and 1, so the expectation value isE[I] = 1*P(I=1) + 0*P(I=0).4. You can also work out E[I^2] from the de'nition ofexpectation value (what possible values does I^2 have)?5. Again noting that k is a sum of random variables,and that these variables are INDEPENDENT, thenvar(k) = sum[var(I_j)]. So you need to work outvar(I_j), which I just gave you strong hints on howto do.The suggestion has been made to look in your universitylibrary. I suggest you do so. This proof will be found inmany elementary probability texts, and likely many of themwill use the indicator variable technique. I 'nd thateasiest, but there are other approaches. - Randy === Subject: Re: Demostration: Binomial Distribution mean I need to demonstrate that the mean of a binomial distribution is np> and the variance is np(1-p).> Please, I need all your help. i'm a 'rst year university student and> I need this university libraryshould be at a walking distance. And it must have a few booksthat present the proofs.Also, for 'rst year university students the school usuallyprovides teaching assistants (TA's) to help.(2) The proofs I saw start with the binomial expansion (u+v)^n = sum[k=0 to n] (n choose k) * u^k * v^(n-k)then onedifferentiates by u,multiplies by u,differentiates again by u,multiplies again by u,sets u = p, v = 1-p,does some extra algebra.You have seen V(X) = E(X^2) - === Subject: Re: Star Gate Topology of the Universedoes anybody just look up a see the clouds blow by any more?holog === Subject: a this:B =[ b11, b12, b13, b14][ b12, b22, b23, b24][ b13, b23, b33, b34][ b14, b24, b34, b44]BB =[ b11*b33-b13^2, b12*b33-b13*b23, b14*b33-b13*b34][ b12*b33-b13*b23, b22*b33-b23^2, b24*b33-b23*b34][ b14*b33-b13*b34, b24*b33-b23*b34, b44*b33-b34^2]It is known that B is positive de'nite, to determine whether BB is of fullrank, that is === Subject: Re: a problem of VCME2sZ-YeMEvn3QAe8QWnreO9l88n78BWWZJl5FxJ9Yr3zx1ICmUaLiu Tong determine whether BB is of full> rank, that is det(BB)!=0.If B is positive de'nite, then det(B)>0. det(AB)=det(A)*det(B).M. K. Shen---------------http:://home.t-online.de/home/mok-kong.shen= === ==Subject: Re: a problem of the determinate of a matrixNntp-Posting-Host: apps.cwi.nlLiu Tong b14]>[ b12, b22, b23, b24]>[ b13, b23, b33, b34]>[ b14, b24, b34, b44]>>BB =>[ b11*b33-b13^2, b12*b33-b13*b23, b14*b33-b13*b34]>[ b12*b33-b13*b23, b22*b33-b23^2, b24*b33-b23*b34]>[ b14*b33-b13*b34, b24*b33-b23*b34, b44*b33-b34^2]>>It is known that B is positive de'nite, to determine whether BB is of full>rank, that is det(BB)!=0.> According to Maple, det(BB) = det(B)*b33^2. To con'rm this,do some row and column manipulations on B until you get BB.-- 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 === Subject: Re: Constant is not too far off topic? I am interested in> constructing constant weight codes using elements from a Galois group> GF(2^m)? How can I construct such codes? In the literature that I> have found up to now, the authors only consider binary constant weight> codes.>> Any comments, suggestions and/or pointers to literature will be> greatly appreciated> Jaco Versfeld>Well, this old paper of mine gives a description of the cyclic, equidistantcodes over GF(q). If you throw out 0 you have a constant weight code:Clark, W. EdwinEquidistant cyclic codes over ${rm GF}(q)$.Discrete Math. 17 (1977), no. 2, 139--141. It is proved that a cyclic $(n,k)$ code over $text{GF}(q)$ is equidistantif and only if its parity check polynomial is irreducible and has exponent$e=(q^k-1)/a$ where $a$ divides $q-1$ and $(a,k)=1$. The length $n$ may beany multiple of $e$. The proof of this theorem also shows that if a cyclic$(n,k)$ code over $text{GF}(q)$ is not a repetition of a shorter code andthe average weight of its nonzero code words is integral, then its paritycheck polynomial is irreducible over $text{GF}(q)$ with exponent$n=(q^k-1)/a$ where $a$ divides $q-1$. === Subject: Re: JSH: Fun time> newsreader that executes javascript? If so,> why on earth would you want to?> Sorry for the javascript. I thought the Heh-heh. >> Nothing makes a donkey happier than a rut in the barnyard, as this> hee-hawing hoofer knows!>> Nothing makes a donkey happier than a rut in the barnyard, as this> hee-hawing hoofer knows!>> http://www.rubylane.com/ni/shops/viperswife/iteml/GW-684http:/ /www.cogsci.indiana.edu/farg/harry/bio/zoo/donkey.wav--John === Subject: Re: JSH: Fun timeJohnboy, go **** yourself, or any other consenting parties, butleave the donkey alone. I'm a Democrat, after all! > /~~~> / | /~~| `=` |/~~> /_/ | `` | | `` |/~~> / | | | | `` |> { <| | | | | > | ==. . == . == |> | |> | / . . ` /> | . . /> . /> . /> /> /> | |> | |--les ducs 031022webcast.htm === Subject: Free the masses: Free the math!A science journal, instead of charging readers a subscription rate, index.htmlI am all for this, except that the authors seem, to me, to be chargedahuge amount.theirpublic(non-student/faculty)-access to on-line journals subscribed tobythese libraries.Here in my area, as an example, the university library has now cut offthe public's access to its internet terminals, and consequently tomember-only journal-searches.(Why?? ..You guessed it!... Budget cuts...)That is why I love the internet, for the most part. Math information(orinformation), whether peer-reviewed or not even close, is availableinmany cases for FREE (technically, but not always in practice).Hopefully, through PUBLIC libraries' books and internet terminals,eventhose of modest income will be forever able to learn some, at least,ofthe mysterious art of mathematics.(Gettin' socialistic === Subject: Re: Free the internet, for the most part. Math information> (or information), whether peer-reviewed or not even close, is> available in many cases for FREE (technically, but not always in> practice). Hopefully, through PUBLIC libraries' books and internet> terminals, even those of modest income will be forever able to learn> some, at least, of the mysterious art of mathematics.>> (Gettin' socialistic about math...) ;)Where's the central planning?-- http://hertzlinger.blogspot.com === Subject: Re: Free the masses: Free the math!> A science journal, instead of charging readers a subscription rate, this makes as much sense as having the inventors of the chicken poxvaccine pay for publishing their results. well, almost. math does notsave lives, but rather ruins them in some cases.> index.htmlI am all for this, except that the authors seem, to me, to be> charged a huge amount.their public(non-student/faculty)-access to on-line journals subscribed> to by these libraries.Here in my area, as an example, the university library has now cut off> the public's access to its internet terminals, and consequently to> member-only journal-searches.what is wrong with paying membership?> (Why?? ..You guessed it!... Budget cuts...)budget cuts? public univs and colleges seem to be sucking more andmore money from the public now more than ever...> That is why I love the internet, for the most part. Math information> (or information), whether peer-reviewed or not even close, is> available in many cases for FREE (technically, but not always in> practice). Hopefully, through PUBLIC libraries' books and internet> terminals, even those of modest income will be forever able to learn> some, at least, of the mysterious art of mathematics.why should math be free?> (Gettin' socialistic === Subject: Re: Free the free?Mathematicians are frequently absent-minded. If you have a forgetfulfunctor, shouldn't you have a free functor to go with it?-- http://hertzlinger.blogspot.com === Subject: Re: Free instead of charging readers a subscription science.journal.ap/index.htmlI am all for this, except that the authors seem, to me, to be charged> a> huge amount.That is called vanity publishing. Few regard it as a Good Thing.-- Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.htmlNeedless to say, I had the last laugh. Alan Partridge, _Bouncing Back_ (14 times) === Subject: Re: Free the masses: Free the math! Robin subscription science.journal.ap/index.htmlI am all for this, except that the authors seem, to me, to be charged> a> huge amount.That is called vanity publishing. Few regard it as a Good Thing.But the very thing for JSH papers! === Subject: Re: Free the masses: Free journal, instead of charging readers a subscription science.journal.ap/index.html>>I am all for this, except that the authors seem, to me, to be charged>>a>>huge amount.>> >>That is called vanity publishing. Few regard it as a Good Thing.>economics/'nance has told me of 'rst-tier journals that charge a fee when one submits a paper to be refereed. The journal keeps the fee, regardless of whether the paper is accepted or not. I don't know if the journal charges for the resubmission of a revision.-- Stephen J. Herschkorn herschko@rutcor.rutgers.edu === Subject: Re: Free the masses: >A science journal, instead of charging readers a subscription rate,> science.journal.ap/index.html>>I am all for this, except that the authors seem, to me, to be charged>>a>>huge amount.>> >>That is called vanity publishing. Few regard it as a Good Thing.>economics/'nance has told me of 'rst-tier journals that charge a fee > when one submits a paper to be refereed. The journal keeps the fee, > regardless of whether the paper is accepted or not. I don't know if the > journal charges for the resubmission of a revision.Sounds like a good scam.Yeah. Just submit your paper to our journal, and we will ,surely,certainly consider it for publication,..certainly, we REALLY will. YouONLY have to pay a *small* consideration-fee.... On those few occasions, when I have had a math-problem of minepublished in either the Mathematics Magazine or the AmericanMathematical Monthly, my friends sometimes ask, So, are they payingyou?...(of course not)I guess, or so it seems from this thread, I should actually be Quet === Subject: Re: Free the masses: Free the math!> A science journal, instead of charging readers a subscription rate,>> index.html>> I am all for this, except that the authors seem, to me, to be charged> a> huge amount.>> their> public(non-student/faculty)-access to on-line journals subscribed to> by> these libraries.>> Here in my area, as an example, the university library has now cut off> the public's access to its internet terminals, and consequently to> member-only journal-searches.>> (Why?? ..You guessed it!... Budget cuts...)> That is why I love the internet, for the most part. Math information> (or> information), whether peer-reviewed or not even close, is available> in> many cases for FREE (technically, but not always in practice).> Hopefully, through PUBLIC libraries' books and internet terminals,> even> those of modest income will be forever able to learn some, at least,> of> the mysterious art of mathematics.>> (Gettin' socialistic about math...) ;)>pay 1 the idea.ecommerce hasn't centralised yet, cent per image view or page view areabout a decade away. I'll give you all premium accounts, they're 2c.don't fret about the library, avoiding $1 a day for an internet connection ismismanagement and a plea for funds not lack of them.Herc === Subject: Re: Free the masses: Free the math!> A science journal, instead of charging readers a subscription rate, index.htmlI am all for this, except that the authors seem, to me, to be charged> a> huge amount.I share your sentiment in many ways, but one thing that should benoted about the PLOS journals (right now at least) is that they arestrictly biology and soon medicine.Big budget science. This kind of stuff just ends up taking up a wholelot of elbow grease and 鮢tuff'. The publication fee is relativelygiven the costs involved in these types of scienti'c endavour. Notto mention the fact, that their policy implies that if the work is ofsuf'cient merit and the costs cannot be borne by the author, theywill waive the fee.their> public(non-student/faculty)-access to on-line journals subscribed to> by> these libraries.Here in my area, as an example, the university library has now cut off> the public's access to its internet terminals, and consequently to> member-only journal-searches.(Why?? ..You guessed it!... Budget cuts...)> That is why I love the internet, for the most part. Math information> (or> information), whether peer-reviewed or not even close, is available> in> many cases for FREE (technically, but not always in practice).> Hopefully, through PUBLIC libraries' books and internet terminals,> even> those of modest income will be forever able to learn some, at least,> of> the mysterious art of Leroy> Quet === Subject: Re: Free the masses: Free the math!Leroy Quet> A science journal, instead of charging readers a subscription rate,>> index.htmlSix Hours a-day the young Students were employed in thisLabour, and the Professor shewed me several Volumes inlarge Folio already collected, of broken Sentences, whichhe intended to piece together, and out of those richMaterials to give the World a compleat Body of all Artsand Sciences; which however might be still improved, andmuch expedited, if the Publick would raise a Fund formaking and employing 've hundred such Frames in Lagado,and oblige the Managers to contribute in common theirseveral Collections.-- Jonathan Swift, _A Voyage to Laputa..._, 1726!!www.jaffebros.com/lee/gulliver/bk3/chap3-5.htmlLH === Subject: Re: Free the masses: Free the math!>Subject: Free the masses: Free the math!>Message-id: journal, instead of charging readers a subscription rate, science.journal.ap/index.html>>I am all for this, except that the authors seem, to me, to be charged>a>huge amount.>>their>public(non-student/faculty)-access to on-line journals subscribed to>by>these libraries.>>Here in my area, as an example, the university library has now cut off>the public's access to its internet terminals, and consequently to>member-only journal-searches.>>(Why?? ..You guessed it!... Budget cuts...)>That is why I love the internet, for the most part. Math information>(or>information), whether peer-reviewed or not even close, is available>in>many cases for FREE (technically, but not always in practice).>Hopefully, through PUBLIC libraries' books and internet terminals,>even>those of modest income will be forever able to learn some, at least,>of>the mysterious art of mathematics.>>(Gettin' socialistic about math...) minor journals charge, often by the word(!) but thought they were mostly used to pad a vita. I saw no notice of peerreview in your reference. Will acceptance for publication be strictly up to theeditors?MarvinMarvin Sebournosugeography@aol.com === Subject: Re: Factorial/Exponential Identity, In'nity> raf@tiki-lounge.com almost all and almost none is around one half.> Splitting the difference between almost all and almost none in a > real interval is almost anything in between.Unless some highly speci'c splitting mechanism is guaranteed.What do you think about this? How can this disparity be resolved?Parity. Boyee.Anyways, we've seen from one method that an established asymptoticvalue for n choice n/2 approaches zero. Yet, binary sequencesrepresenting numbers normal to base two have equal densities of onesand zeros, and almost all numbers in the unit interval areabsolutely normal, having 'nite measure.Proportion of sequences with equal zero-density and one-densityaccording to:Combinatorics: approx. 0Borel: approx. 1Is Borel wrong?It reminds me of using input values dependent on the divergentvariable in the Gamma function, except I haven't found that toactually disagree with anything besides diverging towards in'nity.Each integer is 'nite. If there were two in'nitely precise integersthen their quotient might be irrational.In a consideration of splitting the real numbers in the unit intervalinto two (equal) parts, half of them have a zero as the 'rst elementin their binary expansion, half don't. The same holds true for eachelement of the seqence.I thought that half of the sequence had half ones and half zeros justbecause, it was a moment of insight. I'm beginning to think that ithas to do with that half the elements of all the sequences are zerosand half the elements are ones.Unfortunately my space television antenna for receiving Galaxy 19intro to reality programming went down because of blackbodyinterference from the Warpgate 93 spaceseal pods. Makes me want tohaul out my alcohol-powered pro contractor graphite/chromolly sealclub. All hail red meat. Damn terrorists.The universe is in'nite.Where's Uncle Al when you need him? He'd have something to say. Would it offend half the people?Ross === Subject: Re: Factorial/Exponential Identity, > difference between almost all and almost none is around one half.> Splitting the difference between almost all and almost none in a > real interval is almost anything in between.Unless some highly speci'c splitting mechanism is guaranteed.What do you think about this? How can this disparity be resolved?Between what and what? === Subject: Re: Factorial/Exponential Identity, In'nity raf@tiki-lounge.com were two in'nitely precise integers> then their quotient might be irrational.Just what in hell is imprecise about an integer? === Subject: Re: Factorial/Exponential Identity, In'nityThe dis-parity is about a combinatoric expression evaluating theproportion of binary sequences with density of ones being one halfamong every binary sequence as near zero and the measure-theoreticevaluation of the set of absolutely normal numbers between zero andone as having measure one or near one, where absolutely normal numbershave density of ones being one half. You know that.Parity is a speci'c term with Parity appears to be a broadly appliedscienti'c principle.About the integers, there isn't anything imprecise about an integer. There's imprecision in representing an irrational as a ratio of twointegers. An in'nite sum (sum of in'nitely many) of ratios o'ntegers may be an absolutely precise equal thing to an irrational,eg, zeta(3) is irrational, e = 1/0! + 1/1! + 1/2! + ..., etcetera. There are also in'nite products of ratios of integers that equalirrational numbers, for example 2*(2*2/1*3)*(4*4/3*5)*(6*6/5*7)*... =pi. What shall we take 2*(2*4*6*...)^2 to be? Divide it by(3*5*7*...)^2, the quotient is pi. Agreeably, it's a bit morespeci'c than that.It's like considering the sets of integers as a binary sequence withno === Subject: Re: Factorial/Exponential Identity, In'nity raf@tiki-lounge.com combinatoric expression evaluating the> proportion of binary sequences with density of ones being one half> among every binary sequence as near zero and the measure-theoretic> evaluation of the set of absolutely normal numbers between zero and> one as having measure one or near one, where absolutely normal numbers> have density of ones being one half. You know that.There is a disparity between measurements in grams and measurements in metres which is of equal sequences. I do not> disrespect parity, yo. Parity appears to be a broadly applied> scienti'c principle.Parity with respect to binary sequences is a broadly applied scienti'c principle?About the integers, there isn't anything imprecise about an integer. > There's imprecision in representing an irrational as a ratio of two> integers. I beg to differ. Any such representation exactly represents one and only one rational, and, though there are equivalent repressentations, the nature of that equivalence is preciesly known: a/b = c/d <==> a*d = b*cAn in'nite sum (sum of in'nitely many) of ratios of> integers may be an absolutely precise equal thing to an irrational,> eg, zeta(3) is irrational, e = 1/0! + 1/1! + 1/2! + ..., etcetera. > There are also in'nite products of ratios of integers that equal> irrational numbers, for example 2*(2*2/1*3)*(4*4/3*5)*(6*6/5*7)*... => pi. What shall we take 2*(2*4*6*...)^2 to be? Divide it by> (3*5*7*...)^2, the quotient is pi. Agreeably, it's a bit more> speci'c than that.The issue with in'nite sums and in'nite products is their convergence, which is precisely de'ned. The value of a non-convergent expression for an in'nite sum or in'nite product is no more meaningful than the value of a quotient with zero as divisor, it is NaN! === Subject: Re: Factorial/Exponential Identity, In'nityRoss A. Finlayson a ratio of two> integers.I'll treasure that :-)-- Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.htmlNeedless to say, I had the last laugh. Alan Partridge, _Bouncing Back_ (14 times) === Subject: Re: Factorial/Exponential Identity, In'nity>> There's imprecision in representing an irrational as a ratio of two>> integers.Not when the two integers are both zero.At least, not precisely what I'd call imprecision.Lee Rudolph === Subject: Re: Web server question and 30 seconds arrive in average 3 requests. I want>to calculate the probability of waiting for more than 15 minutes so>that 80 requests arrive. Model it with a Poisson distribution.Doug === Subject: Re: Chi-square, Student T and f conditions under which the t, F and chi-square distributions > can yield the same results? > Are there any conditions under which the t, F and chi-square distributions can all be appropriate? === Subject: Re: Please check probability 2.73682 probability.>> Can a probability be greater than one?>> Doug>>Most de'nitely! I have it on good authority from James Harris thatprobablities can be much greater than one. The problem is thatmathematicians made an error in their de'nition of probability (just asthey did in de'ning algebraic integers). This is the soon-to-be-entitledcore error in probability and is certain to rock the mathematics communityto the core (although they will of course no doubt not listen).Hope this clears up any confusion you might have === Subject: Re: Fundamental Reason for High thy cheek, tear his head off and >down> his neck. [...] A real man> kills his enemies, takes his land and cattler, rapes his women,>enslaves> his children and contemplates how good life can be.>> In this evil world, if you> are not on top, some other part is and is humping you. The priceof> liberty is ef'ciently killing the enemies of liberty. The rule is>very> simple. Support and help your friends. Kill your enemies. That isthe> only way to survive.>> Do unto others, before they do unto you.>> Fascinating, even if it's off topic.>> Robert Kolker, who claims to be Jewish, advocates a philosophy> of life which sounds a lot like what we normally would associate> with Nazis and supremacists.>> If someone claimed the Jews believe what Kolker claims to> believe, that person would surely be labelled an anti-Semite.>> And yet, Kolker seems to be serious, and has received some support> from others in this thread.>> What gives?>>Actually, the masses have been brainwashed>>to give the German people a bad rap,>>for trying to defend themselves from>>the Bolsheviks.who were instigating>>con告ct and war, for power and riches in the 1900's.>> Please give examples. Stalin was no angel but except for his defeat>> in Finland never tried what the right wing Hitler did. All his crimes>> were internial>> Stalin did not invade Germany in June 1941, Hitler Invaded Russia,>> Stalin did however cooperate with Hitler in the occupation of Poland.>>As the Bolsheviks.were assassinating leaders and breaking>>up the meetings of political rivals,>> Please give examples including dates. For the most part it was the>> Nazi's that that broke up and attacked rivals.>>It is interesting to see that Thom does not comprehend,>that Germany, and many nations,>tried to control the class war instigations of the Bolsheviks>by many peaceful means, and by making treaties to>oppose the instigation of con告ct and war,>and when all measures failed, they went after the Bolsheviks>in the nations they were using as bases of operations, just as>America went after real terrorists, and imagined terrorists in Iraq.>>Note that the Germans were welcomed in most nations>as their local leaders had been bought or intimidated>by the Bolsheviks and were unable to maintain the>social, 'nancial and cultural integrity of their nations.>Even France had little opposition to the Germans.>>If FDR had joined with Germany, Spain, Japan, and other nations,>in going after the class war instigators, rather than backing them,>WWII would has lasted two months, and there would have been>no millions of deaths, no Cold War, no Korea, no Vietnam ,>no nuclear weapons, and no instigation of global religious war.>>Bush has also sold out to the religious war instigators,>and brought much harm to America and the world.>>And it is interesting to see that Thom does not know>that the Bolsheviks were assassinating leaders, and assaulting>people, and breaking up meetings, and that the Black Shirts>and Nazi were reactions to this.>>I suggest that he read some factual, concurrent history>of those times, rather than allow himself to be>brainwashed by present day spin motivated more by agenda,>than by facts or a respect for mankind.>> I see our Holocaust defender is still spewing vile.It is interesting to see that Lloyd Parkerconsiders it vile to post factual history,rather than parrot religious/ethnic propaganda;and to point out that the same group that instigatedthe class wars of the 1900'sis instigating the religious wars of the 2000's.One has to wonder why some people do this.Are they brainwashed,or do they support the people who instigatecon告ct and war for power and riches?????--Tom Potter http://tompotter.us === Subject: Re: Fundamental Reason for High Achievements of JewsTom Potter incredible nonsense from a dedicated anti-semite ...One has to wonder why some people do this.> Are they brainwashed,> or do they support the people who instigate> con告ct and war for power and riches?????--> Tom Potter http://tompotter.usGee, I don't get this. How do I get into this power elite? I'm usually considered quite bright and I am Jewish. But I have never been in the company of any Jew who was in this power elite. My late brother-in-law was rich, Jewish, but not one of the power elite. How do I get there. Why have the other Jews kept this a secret from me and all my relatively poor ancestors? Even the atomic bomb had those who blabbed about it. Why haven't I heard about this grand scheme? I want in. I could contribute a lot. I have lots of Christian relatives who would provide cover for me. I know a few fairly powerful politicians and could in吟ence them if it were worth my while. Why has all this been hidden from me for so many years? Could it be that Tom Potter is a troll who makes this all up out of whole cloth? Naw, not Tom Potter. Everybody knows he is honest to a fault.FK === Subject: Re: Fundamental Reason for High dedicated anti-semite ...> One has to wonder why some people do this.> Are they brainwashed,> or do they support the people who instigate> con告ct and war for power and riches?????--> Tom Potter http://tompotter.usGee, I don't get this. How do I get into this power elite? I'm usually > considered quite bright and I am Jewish. But I have never been in the > company of any Jew who was in this power elite. My late brother-in-law > was rich, Jewish, but not one of the power elite. How do I get there. > Why have the other Jews kept this a secret from me and all my relatively > poor ancestors? Even the atomic bomb had those who blabbed about it. Why > haven't I heard about this grand scheme? I want in. I could contribute a > lot. I have lots of Christian relatives who would provide cover for me. > I know a few fairly powerful politicians and could in吟ence them if it > were worth my while. Why has all this been hidden from me for so many > years? Could it be that Tom Potter is a troll who makes this all up out > of whole cloth? Naw, not Tom Potter. Everybody knows he is honest to a > fault.> FKfkasner makes a good point!EVERYONE, Black, White, Brown, Yellow, Protestent, Catholic, Jewish, Muslim, Buddhists, male, female, gay, rich, poor, etc.who has ever dealt with Tom Potter, on a personal level, knows that he is honest to a fault.If honesty be a grevious fault, then greviously have I paid for it, and will pay for it.(With apologies to the Bard.)--Tom Potter http://tompotter.us === Subject: Re: Fundamental Reason for High dedicated anti-semite ...>Careful, Kaz, these days the ones who always cry anti-Semite are now perceived to be the real bigots and racists at heart.Re呈ct on that and ask yourself why this came about.Hint: 50+ years of incessant and loud Jew propaganda about Jewish moral and intellectual superiority, ......perhaps?All good things do come to an end, Kaz,.......ahahahaha.... > One has to wonder why some people do this.> Are they brainwashed,> or do they support the people who instigate> con告ct and war for power and riches?????> Tom Potter >I don't know, nor care, what post preceded this one,but since ever mankind existed some people of/in anytribe have always and will always instigate con告ct and war for power and riches...... or what other reasons are there for killing each other?......and if the conditions wereright, Tom, you'd be in the forefront doing the same, giventhe personality you exhibit on the Usenet......ahahahaha...> Gee, I don't get this. How do I get into this power elite? I'm usually> considered quite bright and I am Jewish. But I have never been in the> company of any Jew who was in this power elite. My late brother-in-law> was rich, Jewish, but not one of the power elite. How do I get there.> Why have the other Jews kept this a secret from me and all my relatively> poor ancestors? Even the atomic bomb had those who blabbed about it. Why> haven't I heard about this grand scheme? I want in. I could contribute a> lot. I have lots of Christian relatives who would provide cover for me.> I know a few fairly powerful politicians and could in吟ence them if it> were worth my while. Why has all this been hidden from me for so many> years? >Very astute and SEEMINGLY factual, Kaz, BUT.....See, Kaz, apparently you really don't get it. It's very simple.It is not so-called riches and power that gets Jews into deep periodically and epically. A lot of goys have far more of each, yetit normally does not get them into trouble. Most have learned how to handle it: Discretely, smoothly and QUIETLY. But not the Jews. With the Jews it is the opposite. It is their ing,incessant **loudness about themselves**, advocating that they are richer, better, smarter and more lovable BECAUSE THE ARE JEWISH, from private events to general media stuff, (like i.e. reporting on thefront page or in headlines that it rained in Tel Aviv, but shoving a schoolbus accident report that killed 20 US-goy kids into the background......)that is what makes the goyim, which outnumber Jew almost a millionfold, so irate and belligerent towards them. --- It is a simple as that.We won't even have to touch that for 50 years US taxpayers gotforced to pay billions, annually, to the Jewish State... with NOTHING toshow for in return!Will it change? No. Why not?Because that would mean for Jews to become Un-Jewish....ahahahaha.... Of course Potter will come along now and give recital of his Not all Jews are... song .........aahahahaha........ahahahaha.........>> Could it be that Tom Potter is a troll who makes this all up out> of whole cloth? Naw, not Tom Potter. > Everybody knows he is honest to a fault.> FK>ahahahaha............fault, Kaz, what fault?.........honesty and morality isPotterian by DEFAULT...........ahahahahaha........but then it becomesmore evident with each post of yours that you, Kaz, are the Jewish mirrorimage of Potter.........ahahahah......So, keep on singing.....All of you!.........It's is a beautiful choir........accompanied by that clacking sound of shards of falling glass that comes from the stones we throw at each others houses of glass...ahahahaha......ahahahanson === Subject: BBP algorithmDoes anyone know of a derivation for the BBP === Subject: Re: the sum as an integral and so the integral.-- Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.htmlNeedless to say, I had the last laugh. Alan Partridge, _Bouncing Back_ (14 times) === Subject: Re: What is 0/0 ?jmfbahciv@aol.com don't you guys call> that unde'ned in the math biz?As I said in my 'rst response in this thread, 0/0 is normally consideredto be unde'ned.But another point is that 0/0 can be given meaning (and, IMO, in reasonableways) if we in the math biz choose to do so.David === Subject: Re: What is 0/0 ? David don't you guys call>> that unde'ned in the math biz?>>As I said in my 'rst response in this thread, 0/0 is normally considered>to be unde'ned.I remember. It doesn't hurt to say it often and say it loud ;-)./BAHSubtract a hundred and four for e-mail. === Subject: Re: What is 0/0 ? David W. Cantrell don't you guys call>> that unde'ned in the math biz?>>As I said in my 'rst response in this thread, 0/0 is normally considered>to be unde'ned.>>But another point is that 0/0 can be given meaning >(and, IMO, in reasonable>ways) if we in the math biz choose to do so.Sure it would be interesting to see what kinds of algebras youcould make, but that isn't going to apply in computing today.This propensity of doing something wrong just because there'sa rule against it might be a way of establishing territorialimperative among teenage males but it sure as hell would createhavoc in my bank account./BAHSubtract a hundred and four for e-mail. === Subject: Re: What is 0/0 ?> David W. Cantrell doesn't have meaning; don't you guys call>> that unde'ned in the math biz?>>As I said in my 'rst response in this thread, 0/0 is normally considered>to be unde'ned.>>But another point is that 0/0 can be given meaning>(and, IMO, in reasonable>ways) if we in the math biz choose to do so.>> Sure it would be interesting to see what kinds of algebras you> could make, but that isn't going to apply in computing today.> This propensity of doing something wrong just because there's> a rule against it might be a way of establishing territorial> imperative among teenage males but it sure as hell would create> havoc in my bank account.>The whole point is that it doesn't *have* to be unde'ned. The applicationdetermines what should be done with it. In bank accounts, divide by 0should generate an error message. But in hydrodynamics or number theory orcomplex variable theory or other areas, it might (note: *might*) makeperfect sense to simply remove all the removable singularities and not makea big deal about it. It all depends on the application.And that means that it isn't *always* wrong, and we don't need to *always*declare it to be unde'ned.Jon Miller === Subject: core error 'xed> 1. First the problematic de'nition:>> Algebraic integers are de'ned to be roots of monic polynomials with> integer coef'cient e.g. x^3 + 3x + 1 or x^234 - 34x^12 + 17, where> monic refers to the leading coef'cient.>> My assertion is that the over hundred year old de'nition excludes> numbers that have to be included to keep from having contradiction> i.e. mathematical inconsistency.Stupid, evil de'nition... It's time to destroy it!No de'nition - no problem! That's the easiest way to 'x everything.Let's never use the term algebraic integers again, let's just call themroots of monic polynomials with integer coef'cient!All right, no core error from now on! === Subject: Prime number generating functionHas anyone see this function: http://datashaping.com/Prime2.gif ?It's graph is shown at === Subject: Has anyone see this function: http://datashaping.com/Prime2.gif ? I would say it's more of a prime-testing function than a prime-generating function. And it only tests primes that are <=(v**2)/2.> Its graph is shown at Amling === Subject: Re: Prime number generating functionHehe, looks nice. Have you done any timing analysis of the function?(I have too little knowledge of this to do that myself...)-Panic === to prove the triangle inequality for the Lp-norm b |f| = (S|f(x)|^p dx)^(1/p) af(x) is a continous function on [a,b], and p is in [1,oo). I reallydon't get it, after writing several pages of inequalities. Can anyonegive me a hint about the main idea of the proof?Rene.-- Ren MeyerStudent of Physics & MathematicsZhejiang University, Hangzhou, China === Subject: Re: Problem with Lp-norm> I want to prove the triangle inequality for the Lp-norm b> |f| = (S|f(x)|^p dx)^(1/p)> af(x) is a continous function on [a,b], and p is in [1,oo). I really> don't get it, after writing several pages of inequalities. Can anyone> give me a hint about the main idea of the proof?You can do it without Holder's inequality (for a reference see Royden's_Real Analysis_ text). Of course you will aim for |f + g|^p <= (|f| + |g|)^p. The main hint would be to use the convexityof the function f(t) = t^p. Hugh === Subject: Re: Problem with Lp-norm Rene Meyer inequality for the Lp-norm b> |f| = (S|f(x)|^p dx)^(1/p)> af(x) is a continous function on [a,b], and p is in [1,oo). I really> don't get it, after writing several pages of inequalities. Can anyone> give me a hint about the main idea of the proof?This is often derived from Holder's inequality; do you know the latter? === Subject: Re: An Ownership Puzzle> On gold in theirpresence.> They all agree that the 'nal owner of the gold bar will be the personwho> is holding it at exactly one o'clock and they agree to the followingrules.> At twelve o'clock Mary will hold the gold bar and, since twelve thirtyis> half way between twelve o'clock and one o'clock, at twelve thirty Marywill> give the bar to Peter. Since twelve forty-'ve is half way betweentwelve> thirty and one o'clock, at twelve forty-'ve Peter will give the goldbar to> Paul. The half way time between twelve forty-'ve and one o'clock istwelve> 'fty two and thirty seconds at which time Paul hands the gold barback to> Mary. At the half way time between twelve 'fty-two (and thirtyseconds)> and one o'clock, Mary gives the gold bar to Peter and then at the nexthalf> way time Peter gives it to Paul, and so on. In this puzzle eachperson can> pass the gold bar to the next person in no time at all. This passingof the> gold bar continues in the order Mary, Peter, Paul, Mary, Peter, Paul,...> until exactly one o'clock and then stops. Who will be the 'nal ownerof> the gold bar?>> Since the speed at which the bar is being passed increases without> limit as the time approaches one o'clock, the relativistic mass will> also increase without limit, so the environs of the gold bar will> collapse into a black hole before one o'clock.>> This presumes the distances between Peter, Paul and Mary is non-zero> constant. That being the case, the bar will vaporise just before one.>> Now Peter, Paul and Mary had better don asbestos mitts, very thick mitts> because when the speed increases until the melting point of the bar is> reached due to air friction, the recoil will great. Big enuf to knock> them over, to blow them away.>> Since no information can escape from a black hole, we will never> know who got the gold bar.>> As that black circumstance is precluded by other practical concers, we're> forced to accept that Peter, Paul and Mary are moving closer and closer> together. That eventually the bar is squizzed between three palms with no> one having time to grasp or hold the bar, that all three palms are> holding the bar at one o'clock.>> Morrow of the story:> Peter, Paul and Mary best humorous responses. But these don't really addressthe puzzle, it would be like discussing the quantum uncertainty principle orvarious theories of quantisized space in response to a question about thetruth of the continuum hypothesis. This puzzle is purely mathematical, ittakes place in the ideal continuum space and time of mathematics. For theissue 'shfry raised, whenever the gold bar is swapped (for example attwelve thirty), at that time the gold bar is in the hands of the previousholder, not the new holder. Because this puzzle is taking place in theidealized Euclidean space and idealized time (modeled by the real line),there are no relativistic or other physical constraints: Peter, Paul andMary are not moving closer together at any time. So the question remains:who will be the 'nal owner of the gold === bar?Randyhttp://www.rlgerl.comSubject: Re: An Ownership >> Peter, Paul, and Mary each want to own the bar of gold in their> presence.> They all agree that the 'nal owner of the gold bar will be theperson> who> is holding it at exactly one o'clock and they agree to the following> rules.> At twelve o'clock Mary will hold the gold bar and, since twelvethirty> is> half way between twelve o'clock and one o'clock, at twelve thirtyMary> will> give the bar to Peter. Since twelve forty-'ve is half way between> twelve> thirty and one o'clock, at twelve forty-'ve Peter will give thegold> bar to> Paul. The half way time between twelve forty-'ve and one o'clockis> twelve> 'fty two and thirty seconds at which time Paul hands the gold bar> back to> Mary. At the half way time between twelve 'fty-two (and thirty> seconds)> and one o'clock, Mary gives the gold bar to Peter and then at thenext> half> way time Peter gives it to Paul, and so on. In this puzzle each> person can> pass the gold bar to the next person in no time at all. Thispassing> of the> gold bar continues in the order Mary, Peter, Paul, Mary, Peter,Paul,> ...> until exactly one o'clock and then stops. Who will be the humorous responses. But these don't really address> the puzzle, it would be like discussing the quantum uncertainty principleor> various theories of quantisized space in response to a question about the> truth of the continuum hypothesis. This puzzle is purely mathematical, it> takes place in the ideal continuum space and time of mathematics. For the> issue 'shfry raised, whenever the gold bar is swapped (for example at> twelve thirty), at that time the gold bar is in the hands of the previous> holder, not the new holder. Because this puzzle is taking place in the> idealized Euclidean space and idealized time (modeled by the real line),> there are no relativistic or other physical constraints: Peter, Paul and> Mary are not moving closer together at any time. So the question remains:> who will be the 'nal owner of the gold bar?>This reminds me of the Brower map where every boundry point is the boundryof three countries. It is an in'nite series but written in such a way thatthe map takes 1 year to complete so the implication is that the process hasended. Then there should have been a last country to extend its map (atleast one would think) - so which was the last country to extend its border?If the answer is none (it is an in'nite series), then is the map evercomplete? === Subject: Re: An gold in their>presence.<> They all agree that the 'nal owner of the gold bar will be the person>who<> is holding it at exactly one o'clock and they agree to the following>rules.<> At twelve o'clock Mary will hold the gold bar and, since twelve thirty>is<> half way between twelve o'clock and one o'clock, at twelve thirty Mary>will<> give the bar to Peter. Since twelve forty-'ve is half way between>twelve<> thirty and one o'clock, at twelve forty-'ve Peter will give the gold>bar to<> > Paul. The half way time between twelve forty-'ve and one o'clock is>twelve<> 'fty two and thirty seconds at which time Paul hands the gold bar>back to<> Mary. At the half way time between twelve 'fty-two (and thirty>seconds)<> and one o'clock, Mary gives the gold bar to Peter and then at the next>half<> way time Peter gives it to Paul, and so on. In this puzzle each>person can<> pass the gold bar to the next person in no time at all. This passing>of the<> gold bar continues in the order Mary, Peter, Paul, Mary, Peter, Paul,>...<> until exactly one o'clock and then stops. Who will be the 'nal owner>of<> the gold bar? responses. But these don't really address>the puzzle, it would be like discussing the quantum uncertainty principle or>various theories of quantisized space in response to a question about the>truth of the continuum hypothesis. This puzzle is purely mathematical, it>takes place in the ideal continuum space and time of mathematics. For the>issue 'shfry raised, whenever the gold bar is swapped (for example at>twelve thirty), at that time the gold bar is in the hands of the previous>holder, not the new holder. Because this puzzle is taking place in the>idealized Euclidean space and idealized time (modeled by the real line),>there are no relativistic or other physical constraints: Peter, Paul and>Mary are not moving closer together at any time. So the question remains:>who will be the 'nal owner of the gold bar?A similar problem occurs in the theory of Markov chains;there, instead of determinism, there is randomness. Butthe solution is still similar; the answer is not determined,and after one goes off the time scale in this manner, theprocess must be restarted, and this can be done in anymanner whatever.Or to put it in another manner, without assuming some formof at least approximate smoothness at 1, knowing f(t) for all t < 1 tells us nothing about f(1).-- This address is for information only. I do not claim that these viewsare those of the Statistics Department or of Purdue University.Herman Rubin, Department of Statistics, Purdue Universityhrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 === >> Peter, Paul, and Mary each want to own the bar of gold in their> presence.> They all agree that the 'nal owner of the gold bar will be the person> who> is holding it at exactly one o'clock and they agree to the following> rules.> At twelve o'clock Mary will hold the gold bar and, since twelve thirty> is> half way between twelve o'clock and one o'clock, at twelve thirty Mary> will> give the bar to Peter. Since twelve forty-'ve is half way between> twelve> thirty and one o'clock, at twelve forty-'ve Peter will give the gold> bar to> > Paul. The half way time between twelve forty-'ve and one o'clock is> twelve> 'fty two and thirty seconds at which time Paul hands the gold bar> back to> Mary. At the half way time between twelve 'fty-two (and thirty> seconds)> and one o'clock, Mary gives the gold bar to Peter and then at the next> half> way time Peter gives it to Paul, and so on. In this puzzle each> person can> pass the gold bar to the next person in no time at all. This passing> of the> gold bar continues in the order Mary, Peter, Paul, Mary, Peter, Paul,> ...> until exactly one o'clock and then stops. Who will be the 'nal owner> of> the gold bar?>> Since the speed at which the bar is being passed increases without> limit as the time approaches one o'clock, the relativistic mass will> also increase without limit, so the environs of the gold bar will> collapse into a black hole before one o'clock.>> This presumes the distances between Peter, Paul and Mary is non-zero> constant. That being the case, the bar will vaporise just before one.>> Now Peter, Paul and Mary had better don asbestos mitts, very thick mitts> because when the speed increases until the melting point of the bar is> reached due to air friction, the recoil will great. Big enuf to knock> them over, to blow them away.>> Since no information can escape from a black hole, we will never> know who got the gold bar.>> As that black circumstance is precluded by other practical concers, we're> forced to accept that Peter, Paul and Mary are moving closer and closer> together. That eventually the bar is squizzed between three palms with no> one having time to grasp or hold the bar, that all three palms are> holding the bar at one o'clock.>> Morrow of the story:> Peter, Paul and Mary best stay with Rosemary, Sage and Thyme.> really address> the puzzle, it would be like discussing the quantum uncertainty principle or> various theories of quantisized space in response to a question about the> truth of the continuum hypothesis. This puzzle is purely mathematical, it> takes place in the ideal continuum space and time of mathematics. For the> issue 'shfry raised, whenever the gold bar is swapped (for example at> twelve thirty), at that time the gold bar is in the hands of the previous> holder, not the new holder. Because this puzzle is taking place in the> idealized Euclidean space and idealized time (modeled by the real line),> there are no relativistic or other physical constraints: Peter, Paul and> Mary are not moving closer together at any time. So the question remains:> who will be the 'nal owner of the gold bar?>humerous? huhMaryHerc === Subject: Re: An Ownership Puzzlewhat gets me is as the problem is stated :1 o'clock WILL eventuateONE of them will be holding the bar at 1 o'clock!but there does seem an instantaneous period of in'nite swappingjust up to 1 o'clock making it hard to determine.could the problem be multi choice withA/ MaryB/ PeterC/ Paulas options for the answers?and does === it involve planch time intervals?HercSubject: Re: An Ownership IMPORTANT: Under NO circumstances will postings containing illegal or copyrighted material through this service be tolerated!! all for the humorous responses. But these don't really> address the puzzle. Because this puzzle is taking place in the> idealized Euclidean space and idealized time (modeled by the real line),> there are no relativistic or other physical constraints: Peter, Paul and> Mary are not moving closer together at any time. So the question> remains: who will be the 'nal owner of the gold bar?>Let p(n) be possessor at time t_n = 1 - 2^-np(0) = Petep(1) = Paulp(2) = Maryp(3) = Pete...lim(n->oo) t_n = 1lim(n->oo) p(n) doesn't exist because it's a cyclic sequence with frequency of 3.p(n) however, does has in'nitely many subsequences that do converge. === Subject: really> address the puzzle. Because this puzzle is taking place in the> idealized Euclidean space and idealized time (modeled by the real line),> there are no relativistic or other physical constraints: Peter, Paul and> Mary are not moving closer together at any time. So the question> remains: who will be the 'nal owner of the gold bar?>> Let p(n) be possessor at time t_n = 1 - 2^-n> p(0) = Pete> p(1) = Paul> p(2) = Mary> p(3) = Pete> ...> lim(n->oo) t_n = 1> lim(n->oo) p(n) doesn't exist> because it's a cyclic sequence with frequency of 3.> p(n) however, does has in'nitely many subsequences that do converge.Yes, p(n) does not converge but the gold bar has to be somewhere at oneo'clock. The question was, where is the gold bar at one o'clock? It has tobe somewhere in the range of this problem, the range being the setconsisting of the three participants. All three participants have agreed tostop passing the gold bar at one o'clock so the limit (n->oo) p(n) must beone of the three participants even though the subsequences do not converge.So the question remains: who will be the 'nal owner of the gold bar?Randyhttp://www.rlgerl.com === Subject: Re: [JSH] Simple principle in core error proof ... Worthless dribble deleted! ***> Yup, call me crazy, but I think the bastards are out to get me!!!I'll go for calling you crazy.Does anyone second the motion.You are like a broken record, replaying the same old nonsense and you havelied to yourself for so long, you believe your own incompetence.Please go get some psychotropic drugs or jump off a bridge, you ravinglunatic.How pathetic you have proven with your feeble attempts for fame, fortune andrecognition. You are so sad and an example of schooling gone horribly wrongin the US (as much as it hurts to admit that).Perhaps you should renounce your degree and go back to grade school and seeif people still think you are smart.Get a life! === Subject: Re: irreducible polynomial in R[X,Y] vanishing on 'nite set?Nntp-Posting-Host: a 'nite subset S of R^2 (where R denotes the real numbers), is>there an irreducible polynomial in R[X, Y] which vanishes on S and>nowhere else?>Mike Yes. First observe that there exists a slope lambda such that anyline with slope lambda passes through at most one point in S.This is because there are only 'nitely many slopes(y1 - y2)/(x1 - x2) where (x1, y1), (x2, y2) in S. By rotating S, we can assume no two points in Shave equal x-coordinates. Let T consist of these : x in T}.That is, f maps each x-coordinate to its corresponding y-coordinate. Set g(X, Y) = (Y - f(X))^2 + product (X - x)^2. x in Tg is monic in Y, and has no factors involving only X.Nor does it have two linear factors in Y.-- 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 === Subject: Re: Why is x^y + y^x > 1 for 0 < x < 1, 0 < y < 1? Ronald Bruck header says it all. The inequality is> assuredly true; why?--Ron BruckThe function is symmetric in x and y so we need only consider the upper triangle 0 < x <= y < 1. So we want to show for any 'xed c in (0,1) that x^c + c^x > 1 for x in (0,c]. Because c^x is strictly convex in x, it stays above its tangent line at (0,1). So x^c + c^x > x^c + 1 + [ln(c)]x (*)for x > 0, and in particular for x in (0,c]. Let f(x) denote the RHS of (*). We have f(0) = 1 and f(c) = c^c + 1 + ln(c^c). As we know from in'nitely many posts on sci.math, c^c >= (1/e)^(1/e). This implies f(c) > 1. But f is strictly concave down on (0,oo), which implies that on (0,c), f is above the secant line joining (0,f(0)) and (c,f(c)). This implies f > 1 on (0,c] and by (*) we're done. === Subject: Re: Why is x^y + y^x > 1 for 0 < x < 1, 0 < y < 1?The World Wide Wade header says it all. The inequality is>> assuredly true; why?[convexity-based solution deleted]Here is my approach (involving a 鮞ovely' lemma right below):Observe 'rst that x <= y is equivalent to x^(y-1) >= y^(x-1): indeed thelatter is equivalent to (y-1)*lnx >= (x-1)*lny, which, via division of both sides by the *positive* quantity (y-1)*(x-1), is in turn equivalent to(lnx)/(x-1) > = (lny)/(y-1); the result follows now from the negativity ofthe derivative of (lnx)/(x-1) for 0 < x < 1, easily seen to be equivalent to x < 1 + x*lnx for 0 < x < 1 -- an inequality easily established by way of h(1) = 0 and h'(x) = lnx < 0 for 0 < x < 1, where h(x) = 1 + x*lnx - x.Assume WLOG x <= y and x^(y-1) >= y^(x-1). There are two cases to consider:Case 1: y > 1/e. Set f(x) = x^y + y^x, so that f'(x) = y*x^(y-1) + (lny)*y^x > y*x^(y-1) - y^x = y*[x^(y-1) - y^(x-1)] > 0; we conclude that f(x) > f(0) = 1.Case 2: y <= 1/e. Set g(y) = x^y + y^x, so that g'(y) = (lnx)*x^y + x*y^(x-1) <= (lny)*x^y + x*x^(y-1) <= -x^y + x^y = 0 and therefore g(y) >= g(1/e) = x^(1/e) + 1/(e^x) = x*x^(1/e-1) + 1/(e^x) >= x*[(1/e)^(x-1)] + 1/(e^x) =(e*x+1)/(e^x); with r(x) = (e*x+1)/(e^x) and r'(x) = (e-e*x-1)/(e*x), we see that x <= y <= 1/e < 1 - 1/e yields r'(x) > 0, hence g(y) >= r(x) > r(0) = 1. baloglouAToswego.edu === Subject: MKC Set TheoriesI dedicate this thread to JSH and to the memory of Pertti Lounesto--Every system of set theory that was published during the lastcentury contains the standard axiom of extensionality, accordingto which collections are equal iff these are equi-membered.[1]AxAy[Az(z in x <-> z in y) -> x=y] Standard Extensionality--Nevertheless not all collections satisfy Standard Extensionality.It is a commonplace that *clubs* don't, for different clubs may beidentical in membership.--Correy Extensionality differs from Standard Extensionality byallowing both for sets (collections which are determined bytheir members); and for non-sets (collections which are notdetermined by their members).[2]C4 AxAy[Az(z in x <-> z in y) -> {(set x & set y) <-> x = y}] Correy Extensionality--Their novel features notwithstanding (in my next posting I'll saywhat these are), from the git-go set theories which combine CorreyExtensionality with the MK principle of Classi'cation (I'll callthese MKC theories),C3 EyAx[x in y <-> Set x & A] (with y not free in A) MK Classi'cationhave been ridiculed, scoffed at and misrepresented, not coincidentallyby some of the same people who led a successful campaign to run thelate Pertti Lounesto off of sci.math, and have led an unsuccessfulcampaign to silence JSH. Notes1. Various theories of collection have been proposed since the 1900s.What they all share is the axiom of extensionality, which asserts thatif x and y are collections then Az(z in x <-> z in y) -> x=y(Michael Potter, Different Systems of Set Theory, p. 1)2. If {a} and {b} are determined by their members, then {a}={b}C4 AxAy[Az(z in x <-> z in y) -> {(set x & set y) <-> x = y}] Correy ExtensionalityIn contrast, if {a} and {b} are not determined by their members,then ~({a}={b}) even when a=b, and it follows from C4 that {a}and {b} are non-sets. (Groupings that are like non-sets in thisregard are the solitaire club and the chess club, which remain different clubs even when they have the same membership.)--JohnThe road of excess leads to the palace of wisdom.William Blake (1757-1827) === Subject: Re: MKC Set Theories> I dedicate this thread to JSH and to the memory of Pertti Lounesto.To sum up so far: --There is one axiom that theories of collections proposed since the1900s all share: Standard Extensionality. AxAy[Az(z in x <-> z in y) -> x=y] Standard Extensionality--The domain of any theory whose axioms include StandardExtensionality excludes collections that are 鮦ot determinedby their members'. (Recall, if {a} and {b} are 骾eterminedby their members', then a=b <-> {a}={b}: this biconditionalfollows from C4 and 'rst-order logic without identity. Incontrast, if {a} and {b} are *not* determined by their members,then ~[a=b -> {a}={b}]. But a,b such that a=b & ~({a}={b})are excluded from the domain of every theory of collectionswhose axioms include Standard Extensionality.) The admissionof such collections thus marks a step in the direction of increasedmathematical generality--notwithstanding the giggles, poutsand moues of David Ullrich, Robin Chapman and Lee Rudolph.[1] Notes1. Perchance was it some such Trinity that inspired these linesof 餰he Triple Fool'? Who are a little wise, the best fools be. --John Donne, 餰he Triple Fool', st. 2John Correy === Subject: how to do curve 'tting for multiple curve 'ting for a single curve andjust two variables x and y... and I got very helpful answers...Now I met with another more complex problem. It turns out that I have abunch of those y=function(x) curves depending on the values of w and z, thusthey seem like the curves y=function(x, w, z)...I do have the vectors containing data for y, x, w, and z... how to do lot.-Walala === Subject: Re: how to do curve 'tting for multiple curve 'ting for a single curve and> just two variables x and y... and I got very helpful answers...Now I met with another more complex problem. It turns out that I have a> bunch of those y=function(x) curves depending on the values of w and z, thus> they seem like the curves y=function(x, w, z)...I do have the vectors containing data for y, x, w, and z... how to do this> multiple variables curve 'tting?In the case where your model can be written asy = a1*f1(x,w,z) + a2*f2(x,w,z) + ... + an*fn(x,w,z) + noisethat is, where the unknown parameters a1, a2, ..., an allappear linearly, then the techniques of linear least squaresare easily generalized to do the curve 't in one step.(It requires a linear algebra package to be able tosolve linear systems and, preferably, do matrixfactorizations). The functions fk(x,w,z) can be anythingat all so long as they have no free parameters that youare trying to estimate.In the case where your parameters occur nonlinearly, thenyou have a problem in nonlinear global minimization (ofyour error function), which requires iterative techniques.However, general nonlinear optimization packages areavailable on the web. - Randy === Subject: Re: how to do curve 'tting for help to do curve 'ting for a single curveand> just two variables x and y... and I got very helpful answers...>> Now I met with another more complex problem. It turns out that I have a> bunch of those y=function(x) curves depending on the values of w and z,thus> they seem like the curves y=function(x, w, z)...>> I do have the vectors containing data for y, x, w, and z... how to dothis> multiple variables curve 'tting?>> In the case where your model can be written as>> y = a1*f1(x,w,z) + a2*f2(x,w,z) + ... + an*fn(x,w,z) + noise>> that is, where the unknown parameters a1, a2, ..., an all> appear linearly, then the techniques of linear least squares> are easily generalized to do the curve 't in one step.> (It requires a linear algebra package to be able to> solve linear systems and, preferably, do matrix> factorizations). The functions fk(x,w,z) can be anything> at all so long as they have no free parameters that you> are trying to estimate.>> In the case where your parameters occur nonlinearly, then> you have a problem in nonlinear global minimization (of> your error function), which requires iterative techniques.> However, general nonlinear Randy,I've attached the data:Could you please help me take a look at this?when z=1.7527e+004, w= 0.3536 0.0077 0.0072 0.0077 0.3536 0.0077 0.0072 0.0077w is a parameter vector, the values here are used as a whole, they are notdata points. maybe I should extract some feature to use one value torepresent the whole vector in order to avoid parametrical vector curve'tting... oh, I do have a feature value for this parametric vector: 0.9314.x: 8.9289 3.8078 2.2907 1.5374 1.0899 0.8161 0.6354for the above x(7 data points), w(one scalar feature value, or one parametervector), z values(one scalar), we got y(7 data points):y: 0.0715 0.0176 -0.0078 -0.0225 -0.0350 -0.0430 -0.0496-------when z=1.6135e+004,w=0.3536 0.0076 0.0072 0.0076 0.3536 0.0076 0.0072 0.0076I also have a one-value feature extracted value for this parameter vector:0.9827.x(7 data ponits)=6.37951.86930.99230.64550.46120.34940.2753we got y(7 data points):0.0680-0.0131-0.0301-0.0449-0.0504-0.0506-0.0578So you see the family curves (x, y) are dependent on values of w and z. Andeach (x, y) has very nice shape as I have attached in previous image.Now what mathematical approach should I take to lot,-Walala === Subject: Re: how to do curve 'tting for multiple curve 'ting for a single curve and> just two variables x and y... and I got very helpful answers...>> Now I met with another more complex problem. It turns out that I have a> bunch of those y=function(x) curves depending on the values of w and z,thus> they seem like the curves y=function(x, w, z)...>> I do have the vectors containing data for y, x, w, and z... how to do this> multiple variables curve 'tting?First question: Do you have *any* idea what your function should look like?Are you looking for some polynomial?Basically, the idea is you choose a category of functions, e.g. polynomials,with a number of unknown coef'cients. For instance: Y = a*x + b*w + c*z.Then you must choose the coef'cients a, b, and c, such that the differencebetween y (observed) and Y ('tted) is the least possible. To do that youform an expression with the sum of the squared difference, i..e. SUM (y-Y)^2and minimize with respect to the unknown coef'cients.You can include higher order terms (i.e. x^2 and x*w, etc.), but that isreally grasping in thin air. What kind of relation do you expect? Withoutsome additional information this curve 'tting is basically meaningless. Imean, if you know that y is a bounded variable, then a polynomial relationis not a very good approximation.-Michael. === Subject: Re: how to do curve 'tting for multiple variables?There is no simple answer.If you want 't with polynomials of several a message asking for help to do curve 'ting for a single curveand> just two variables x and y... and I got very helpful answers...>> Now I met with another more complex problem. It turns out that I have a> bunch of those y=function(x) curves depending on the values of w and z,> thus> they seem like the curves y=function(x, w, z)...>> I do have the vectors containing data for y, x, w, and z... how to dothis> multiple variables curve 'tting?>> First question: Do you have *any* idea what your function should looklike?> Are you looking for some polynomial?>> Basically, the idea is you choose a category of functions, e.g.polynomials,> with a number of unknown coef'cients. For instance: Y = a*x + b*w + c*z.> Then you must choose the coef'cients a, b, and c, such that thedifference> between y (observed) and Y ('tted) is the least possible. To do that you> form an expression with the sum of the squared difference, i..e. SUM(y-Y)^2> and minimize with respect to the unknown coef'cients.>> You can include higher order terms (i.e. x^2 and x*w, etc.), but that is> really grasping in thin air. What kind of relation do you expect? Without> some additional information this curve 'tting is basically meaningless. I> mean, if you know that y is a bounded variable, then a polynomial relation> is not a very good approximation.>> -Michael.>> === Subject: Sampel Data attached! Re: how to do curve 'tting for multiple variables?> There is no simple answer.> If you want 't with polynomials of several variables,> see www.estlab.com>> Arto Huttunen>> 'ting for a single curve> and> just two variables x and y... and I got very helpful answers...>> Now I met with another more complex problem. It turns out that I havea> bunch of those y=function(x) curves depending on the values of w andz,> thus> they seem like the curves y=function(x, w, z)...>> I do have the vectors containing data for y, x, w, and z... how to do> this> multiple variables curve 'tting?>> First question: Do you have *any* idea what your function should look> like?> Are you looking for some polynomial?>> Basically, the idea is you choose a category of functions, e.g.> polynomials,> with a number of unknown coef'cients. For instance: Y = a*x + b*w +c*z.> Then you must choose the coef'cients a, b, and c, such that the> difference> between y (observed) and Y ('tted) is the least possible. To do thatyou> form an expression with the sum of the squared difference, i..e. SUM> (y-Y)^2> and minimize with respect to the unknown coef'cients.>> You can include higher order terms (i.e. x^2 and x*w, etc.), but that is> really grasping in thin air. What kind of relation do you expect?Without> some additional information this curve 'tting is basically meaningless.I> mean, if you know that y is a bounded variable, then a polynomialrelation> is not a very good approximation.>> this?when z=1.7527e+004, w= 0.3536 0.0077 0.0072 0.0077 0.3536 0.0077 0.0072 0.0077w is a parameter vector, the values here are used as a whole, they are notdata points. maybe I should extract some feature to use one value torepresent the whole vector in order to avoid parametrical vector curve'tting... oh, I do have a feature value for this parametric vector: 0.9314.x: 8.9289 3.8078 2.2907 1.5374 1.0899 0.8161 0.6354for the above x(7 data points), w(one scalar feature value, or one parametervector), z values(one scalar), we got y(7 data points):y: 0.0715 0.0176 -0.0078 -0.0225 -0.0350 -0.0430 -0.0496-------when z=1.6135e+004,w=0.3536 0.0076 0.0072 0.0076 0.3536 0.0076 0.0072 0.0076I also have a one-value feature extracted value for this parameter vector:0.9827.x(7 data ponits)=6.37951.86930.99230.64550.46120.34940.2753we got y(7 data points):0.0680-0.0131-0.0301-0.0449-0.0504-0.0506-0.0578So you see the family curves (x, y) are dependent on values of w and z. Andeach (x, y) has very nice shape as I have attached in previous image.Now what mathematical approach should I take to lot,-Walala === Subject: Primitive Recursion and Language TheoryQuick question: What are the language theoretic approaches*primitive* recursive languages? Recursively enumerable languageshave a nice non-algorithmic characterization in terms ofphase-structure (type-0) grammars.However, I haven't seen anything similar to characterize languageswhose characteristic function is primitive recursive. Are therecharaterizations that avoid referring to classes of functions? Anythoughts/references would be appreciated.Rex Butler === Subject: Re: Primitive Recursion and Language TheoryDistribution: inet theoretic approaches> *primitive* recursive languages? Recursively enumerable languages> have a nice non-algorithmic characterization in terms of> phase-structure (type-0) grammars.> However, I haven't seen anything similar to characterize languages> whose characteristic function is primitive recursive. Are there> charaterizations that avoid referring to classes of functions? Any> thoughts/references would be appreciated.Try looking up the Grzegorczyk hierarchy: it's a strati'cation ofprimitive recursive functions based on the depth of nestingof the recursions; it's purely syntactical. You can get a (nearly) identicalstrati'cation by looking at the depth of nesting of boundedloops in restricted programming languages. Dennis === Subject: Re: Determining temperature in a tank while adding water> I have a tank of water with a known temperature. I am going to add waterof a different known temperature.The 吶w rate of the water entering thetank is the same as the water leaving the tank. How do I set up thedifferential equation so that I can determine the temperature in the tank atany time t. I am assuming a uniform mixture of the water in the tank andneglecting heat gain or loss due to the surrounding environment.The temperature of the water leaving the tank is also the temperature of thewater in the tank, i.e. T(t). The temperature of the water entering the tankis T1. The heat added to the container is the temperature differencemultiplied by the amount of water exchanged (吶w rate) and the speci'cheat of water (4.2 J/gK). The total heat of the container is the temperaturetimes the total amount of water times the speci'c heat.Hope that helps.-Michael. === Subject: Re: Determining temperature in a tank while adding water> I have a tank of water with a known temperature. I am going to add water> of a different known temperature.The 吶w rate of the water entering the> tank is the same as the water leaving the tank. How do I set up the> differential equation so that I can determine the temperature in the tank at> any time t. I am assuming a uniform mixture of the water in the tank and> neglecting heat gain or loss due to the surrounding environment.The temperature of the water leaving the tank is also the temperature of the> water in the tank, i.e. T(t). The temperature of the water entering the tank> is T1. The heat added to the container is the temperature difference> multiplied by the amount of water exchanged (吶w rate) and the speci'c> heat of water (4.2 J/gK). The total heat of the container is the temperature> times the total amount of water times the speci'c heat.Or consider two solutions of salt in water at different concentrations instead of two different temperatures. Then you can deal directly with the amounts of salt in the tank as time passes. === Subject: Re: How Euclid did not prove the Pythagorean Theorem's converse>In http://www.oswego.edu/~baloglou/math/euclid-1.48.html I present a >geometrical argument that *at the same time* proves the Pythagorean>Theorem and illustrates how it fails for non-right angles (thus proving>its converse): this geometrical argument is a straightforward extension>of Euclid's proof of the Pythagorean Theorem, and argument for a right >angle, see http://www.oswego.edu/~baloglou/math/euclid-1.47.html, to the >case of an obtuse angle, the argument for an acute angle being similar.>>As you may (not) recall, Euclid's original proof of the converse of the >Pythagorean Theorem employs the Pythagorean Theorem itself, something that>I do not like that much*: my efforts to locate other proofs of the converse>in the literature led nowhere -- save for 鮛y' proof above, that is!Of course the converse of the Pythagorean Theorem is implicit in Euclid'sequivalents of the law of cosines (propositions II.12 (obtuse angle) and II.13 (acute angle)). It is interesting that proofs of these propositionsin the spirit of Euclid's proof of the Pythagorean Theorem are late: Heath (v. I, p. 404) is not aware of any such proof before Gregory of St. Vincent's Opus geometricum quadraturae circuli et sectionum coni (1647). baloglouAToswego.edu === Subject: Re: How Euclid did not prove the Pythagorean Theorem's converse> ... Euclid's original proof of the converse of the > Pythagorean Theorem employs the Pythagorean Theorem itself, something that> I do not like that much ...Why not? Seems perfectly reasonable to me. It's not like he's proving the inverse. ~ ChrisIn other words, you do not accept ordinary logic. In that case, you> better formulate the logical principles you do accept. For all anyone> knows, it cannot be proved in your logic, whatever it is. On the> other hand, it is likely that not much can be proved in your logic. I> certainly will not waste time on it (more than I have). Designing a> logic is not for the faint of heart, nor for the unsophisticated.Of course I accept ordinary logic. The converse of a theorem isindependent of the original theorem. Once you prove the theorem, thenyou can use it to prove the converse. === Subject: Re: Equivalent Binomial Random point, the mean and variance will remain> unchanged. That is, X1, X2 and X3 will have approximately the same> mean and variance, but is enough to let me state that they are> equivalent? If not, what are the conditions in order to state so?X1, X2, and X3 will have approximately the same mean, variance,skewness, kurtosis, etc; that is, their PMFs will be approximatelythe same (except, as you have noted) in the tails. How close theymust be before you declare them equivalent is a subjective matter:equivalence of this sort is a reference to the relation between> the Poisson and the Binomial distribution?Yes. === Subject: Re: Equivalent Binomial Random VariablesHi Mr. Koopman,> And my point also remains unchanged: that you should start by considering> what happens to the mean and variance when you increase n and decrease p> in a way that leaves n*p constant, which is what your values approximate.Are you making a reference to the relation between the Poisson and theBinomial distribution?If that's the case, there are two interesting sites about this fact:http://mathworld.wolfram.com/PoissonDistribution.htmlhttp Daniel Sadoc === Subject: Re: Core error, mathematicians, De Morgan on the topic of replying> to crackpots to the effect that doing so is necessary to prevent the> gullible public at large from believing them. That is Arturo Magidin, not Mr. Ullrich.Gib === Subject: Re: how about A1*X*B1+A2*X*B2=X?> Can you say something about A1*X*B1+A2*X*B2=X?Ah, that's interesting. Considering again X = e_{jk}, we 'nd that(with @ = tensor product) A1 @ B1 + A2 @ B2 = I @ I. Now I claim this implies for some scalars c and d, eitherA1 = c I, A2 = d I, c B1 + d B2 = IorB1 = c I, B2 = d I, c A1 + d A2 = INote that if, say, A1 is not a scalar multiple of I, there must be a vector u such that u and v = A1 u are linearly independent. Take a vector x such thatx.u = 0 and x.v = 1. Then for any vector w, B1 w + (x. A2 u) B2 w = (x.u) w = 0i.e. B1 w = - (x. A2 u) B2 wso B1 = - (x.A2 u) B2. So A1 @ B1 + A2 @ B2 = (-(x.A2 u) A1 + A2) @ B2 = I @ Iwhich implies B2 and B1 are multiples of I.> For the above problem, can I say it equals to > (A1+A2)*X*(B1+B2)=X...No, of course not. That would say A1 X B1 + A1 X B2 + A2 X B1 + A2 X B2 = X. Robert Israel israel@math.ubc.caDepartment of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada V6T 1Z2 === Subject: Re: 'nite groups every 'nite simple group G>>all isomorphic maximal subgroups>>are Aut(G)-conjugate?>>> No, but it is not easy to 'nd examples. I was about to give up, but>> then I found one!>>> Believe it or not, the alternating group A_{253} has two maximal subgroups>> isomorphic to PSL(2,23). One of them has dihedral D_{24} as point>> stabilizer, and the other has S_4, so they cannot be conjugate in>> S_{253}.>>Hi Derek,>>I have one question about your example.>The dihedral subgroup D_{24} of PSL(2,23) is extended to a subgroup>of PGL(2,23) of the same index 253. This means that PGL(2,23)>also has a permutational representation of degree 253.>Could it be that the 'rst of your subgroups is not maximal>but a subgroup of index 2 in a larger subgroup isomorphic to PGL(2,23)?No, the extension to PGL(2,23) lies in S_{253} but not in A_{253}. I justchecked that directly, but I have a computer list available with themaximal subgroups of A_n for n <= 1000, which is how I found the example.Incidentally, I am fairly certain that there are in'nitely many examples,although I have not proved it completely. There are many families ofsimple groups with non-isomorphic maximal subgroups of the same order.For example the groups PSp(4,p) for odd primes p have two non-isomorphicmaximal subgroups of order p^3(p-1)|PSL(2,p)|. If you form the permutationrepresentations on the cosets of those two subgroups, then I would expectto get isomorphic maximal subgroups of the appropriate alternating group,not conjugate in the symmetric group.Derek Holt. === Subject: Re: 'nite groups every 'nite simple group G>all isomorphic maximal subgroups>are Aut(G)-conjugate?> No, but it is not easy to 'nd examples. I was about to give up, but> then I found one!> Believe it or not, the alternating group A_{253} has two maximal subgroups> isomorphic to PSL(2,23). One of them has dihedral D_{24} as point> stabilizer, and the other has S_4, so they cannot be conjugate in> S_{253}.>>Hi Derek,>>I have one question about your example.>>The dihedral subgroup D_{24} of PSL(2,23) is extended to a subgroup>>of PGL(2,23) of the same index 253. This means that PGL(2,23)>>also has a permutational representation of degree 253.>>Could it be that the 'rst of your subgroups is not maximal>>but a subgroup of index 2 in a larger subgroup isomorphic to PGL(2,23)?>>No, the extension to PGL(2,23) lies in S_{253} but not in A_{253}. I just>checked that directly, but I have a computer list available with the>maximal subgroups of A_n for n <= 1000, which is how I found the example.>>Incidentally, I am fairly certain that there are in'nitely many examples,>although I have not proved it completely. There are many families of>simple groups with non-isomorphic maximal subgroups of the same order.>For example the groups PSp(4,p) for odd primes p have two non-isomorphic>maximal subgroups of order p^3(p-1)|PSL(2,p)|. If you form the permutation>representations on the cosets of those two subgroups, then I would expect>to get isomorphic maximal subgroups of the appropriate alternating group,>not conjugate in the symmetric group.Hmmm! After looking through Jim Heckman's proposed list, I see that thisfamily does not yield maximal subgroups for p=3,5,7, so maybe it never does!Derek Holt === Subject: Re: 'nite groups> ......>For example the groups PSp(4,p) for odd primes p have two non-isomorphic>maximal subgroups of order p^3(p-1)|PSL(2,p)|. If you form the permutation>representations on the cosets of those two subgroups, then I would expect>to get isomorphic maximal subgroups of the appropriate alternating group,>not conjugate in the symmetric group.Hmmm! After looking through Jim Heckman's proposed list, I see that this> family does not yield maximal subgroups for p=3,5,7, so maybe it never does!We could also consider the family of two parabolic subgroups of G_2(q)corresponding to the short and long roots of the Dynkin diagram. Theyare maximal, have the same order and, if I am not mistaken arenon-isomorphicunless q is a power of 3. But of course the hardest part would be to verify whether the corresponding permutational embeddings are maximal.I don't see how this can be done in general.Anvita === Subject: Re: 'nite >Is it true that in every 'nite simple group G>all isomorphic maximal subgroups>are Aut(G)-conjugate?>> No, but it is not easy to 'nd examples. I was about to give up, but> then I found one!>> Believe it or not, the alternating group A_{253} has two maximal> subgroups> isomorphic to PSL(2,23). One of them has dihedral D_{24} as point> stabilizer, and the other has S_4, so they cannot be conjugate in> S_{253}.>> Hi Derek,>> I have one question about your example.> The dihedral subgroup D_{24} of PSL(2,23) is extended to a subgroup> of PGL(2,23) of the same index 253. This means that PGL(2,23)> also has a permutational representation of degree 253.> Could it be that the 'rst of your subgroups is not maximal> but a subgroup of index 2 in a larger subgroup isomorphic to PGL(2,23)?Good catch! How about these, then? Hmm, let's see...1) A_{40} has 2 classes of maximal subgroups isomorphic toPSU(4,2), such that their nomalizers in S_{40} have pointstabilizers isomorphic to 3^{1+2}_+ : 2A_4 and 3^3 : S_4,respectively.2) A_{63} -> PSU(3,3) -> 4.S_4 and 4^2.S_3 .3) A_{156} -> PSp(4,5) -> 5^{1+2}_+ : (4 x A_5) and5^3 : (2 x A_5).2 .4) A_{253} -> M_{23} -> PSL(3,2^2) : 2 and 2^4 : A_7 .5) A_{400} -> PSp(4,7) -> 7^{1+2}_+ : (6 x PSL(2,7)) and7^3 : (3 x PSL(2,7)).2 .6) A_{495} -> M_{12} -> 2^{1+4}_+.S_3 and 4^2 : D_{12} .7) A_{820} -> PSp(4,3^2).2 -> (3^{1+2}_+)^2 : (8 x PSL(2,3^2))and 3^6 : (4 x PSL(2,3^2)).2 . (Actually, I'm not sure these 2classes of maximal subgroups are isomorphic. There's more than 1extension PSp(4,3^2).2 .)Unless I've missed some, that appears to exhaust the a prioripossibilities for alternating groups < A_{1000}.-- Jim Heckman === Subject: Re: 'nite groups Jim Heckman true that in every 'nite simple group G>>all isomorphic maximal subgroups>>are Aut(G)-conjugate?>> No, but it is not easy to 'nd examples. I was about to give up, but>> then I found one!>> Believe it or not, the alternating group A_{253} has two maximal>> subgroups>> isomorphic to PSL(2,23). One of them has dihedral D_{24} as point>> stabilizer, and the other has S_4, so they cannot be conjugate in>> S_{253}.>> Hi Derek,>> I have one question about your example.>> The dihedral subgroup D_{24} of PSL(2,23) is extended to a subgroup>> of PGL(2,23) of the same index 253. This means that PGL(2,23)>> also has a permutational representation of degree 253.>> Could it be that the 'rst of your subgroups is not maximal>> but a subgroup of index 2 in a larger subgroup isomorphic to PGL(2,23)?>>Good catch! How about these, then? Hmm, let's see...But my example works - both copies of PSL(2,23) are maximal.>1) A_{40} has 2 classes of maximal subgroups isomorphic to>PSU(4,2), such that their nomalizers in S_{40} have point>stabilizers isomorphic to 3^{1+2}_+ : 2A_4 and 3^3 : S_4,>respectively.Only one of those is maximal in A_{40}>2) A_{63} -> PSU(3,3) -> 4.S_4 and 4^2.S_3 .Only one is maximal>3) A_{156} -> PSp(4,5) -> 5^{1+2}_+ : (4 x A_5) and>5^3 : (2 x A_5).2 .Neither maximal.>4) A_{253} -> M_{23} -> PSL(3,2^2) : 2 and 2^4 : A_7 .Neither maximal>5) A_{400} -> PSp(4,7) -> 7^{1+2}_+ : (6 x PSL(2,7)) and>7^3 : (3 x PSL(2,7)).2 .Neither maximal>6) A_{495} -> M_{12} -> 2^{1+4}_+.S_3 and 4^2 : D_{12} .Neither maximal>7) A_{820} -> PSp(4,3^2).2 -> (3^{1+2}_+)^2 : (8 x PSL(2,3^2))>and 3^6 : (4 x PSL(2,3^2)).2 . (Actually, I'm not sure these 2>classes of maximal subgroups are isomorphic. There's more than 1>extension PSp(4,3^2).2 .)Neither maximal>Unless I've missed some, that appears to exhaust the a priori>possibilities for alternating groups < A_{1000}.>I expect my example is the only one.My stataments were all just based on consulting known lists of alternatinggroups up to degree 1000. If you want me to justify any of them, I willneed to 'nd a larger subgroup I suppose. Of course, lists like thatoften contain the odd error.Derek Holt.>Jim Heckman === Subject: Re: 'nite groupsBleh, :> Jim Heckman true that in every 'nite simple group G>>all isomorphic maximal subgroups>>are Aut(G)-conjugate?>> No, but it is not easy to 'nd examples. I was about to give up, but>> then I found one!>> Believe it or not, the alternating group A_{253} has two maximal>> subgroups>> isomorphic to PSL(2,23). One of them has dihedral D_{24} as point>> stabilizer, and the other has S_4, so they cannot be conjugate in>> S_{253}.>> Hi Derek,>> I have one question about your example.>> The dihedral subgroup D_{24} of PSL(2,23) is extended to a subgroup>> of PGL(2,23) of the same index 253. This means that PGL(2,23)>> also has a permutational representation of degree 253.>> Could it be that the 'rst of your subgroups is not maximal>> but a subgroup of index 2 in a larger subgroup isomorphic to PGL(2,23)?>>Good catch! How about these, then? Hmm, let's see...>> But my example works - both copies of PSL(2,23) are maximal.OK. Is there an easy way to see that the PGL(2,23) in the onecase lies in S_{253} but not in A_{253}? And the analogousquestion for the following cases?>1) A_{40} has 2 classes of maximal subgroups isomorphic to>PSU(4,2), such that their nomalizers in S_{40} have point>stabilizers isomorphic to 3^{1+2}_+ : 2A_4 and 3^3 : S_4,>respectively.>> Only one of those is maximal in A_{40}Ah, OK. I see now that all I really knew was that PSU(4,2) andits automorphism group have non-permutation-isomorphic primitivereps of degree 40.Again, is there an easy way to see that only one of the classesis maximal?>2) A_{63} -> PSU(3,3) -> 4.S_4 and 4^2.S_3 .>> Only one is maximalAnd again...>3) A_{156} -> PSp(4,5) -> 5^{1+2}_+ : (4 x A_5) and>5^3 : (2 x A_5).2 .>> Neither maximal.OK, but then don't both lie in Aut(PSp(4,5)) = PSp(4,5).2, whichwould then satisfy the maximal condition? Or are there evenlarger primitive groups of degree 156 in which at least one ofthem lies? Hmm..., if so, it looks like they would have to benormal extensions of PSL(4,5), right?>4) A_{253} -> M_{23} -> PSL(3,2^2) : 2 and 2^4 : A_7 .>> Neither maximalSo again if I understand correctly, at least one of these mustlie in a larger primitive group of degree 253, which it lookslike must thus be among normal extensions of A_{22} orPSL(2,23). Hmm..., must be the latter, since M_{23} isn't asubgroup of A_{22}, and so this probably reduces to yourexample. But wait a minute, M_{23} is too big to lie inPSL(2,23) either. I'm confused. :-(>5) A_{400} -> PSp(4,7) -> 7^{1+2}_+ : (6 x PSL(2,7)) and>7^3 : (3 x PSL(2,7)).2 .>> Neither maximalAnd here PSL(4,7)? (Or maybe even a primitive group with productaction and composite socle A_5 x A_5?)>6) A_{495} -> M_{12} -> 2^{1+4}_+.S_3 and 4^2 : D_{12} .>> Neither maximalAnd here A_{12} or PSO+(10,2) (more likely the former)?>7) A_{820} -> PSp(4,3^2).2 -> (3^{1+2}_+)^2 : (8 x PSL(2,3^2))>and 3^6 : (4 x PSL(2,3^2)).2 . (Actually, I'm not sure these 2>classes of maximal subgroups are isomorphic. There's more than 1>extension PSp(4,3^2).2 .)>> Neither maximalAnd here A_{41}, PSL(2,41) or PSL(4,3^2) (likely the latter)?>Unless I've missed some, that appears to exhaust the a priori>possibilities for alternating groups < A_{1000}.>> I expect my example is the only one.> My stataments were all just based on consulting known lists of alternating> groups up to degree 1000.Are any of these known lists available in books? I'm sure you'veguessed I'm working from the appendices of Dixon and Mortimer's_Permutation Groups_.> If you want me to justify any of them, I will> need to 'nd a larger subgroup I suppose. Of course, lists like that> often contain the odd error.Well, it would be cool if you could 'nd the larger subgroups.:-) I've given some suggestions above.-- Jim Heckman === Subject: Re: 'nite groups Jim Heckman :> Jim Heckman true that in every 'nite simple group G>all isomorphic maximal subgroups>are Aut(G)-conjugate?>> No, but it is not easy to 'nd examples. I was about to give up, but> then I found one!>> Believe it or not, the alternating group A_{253} has two maximal> subgroups> isomorphic to PSL(2,23). One of them has dihedral D_{24} as point> stabilizer, and the other has S_4, so they cannot be conjugate in> S_{253}.>> Hi Derek,>> I have one question about your example.> The dihedral subgroup D_{24} of PSL(2,23) is extended to a subgroup> of PGL(2,23) of the same index 253. This means that PGL(2,23)> also has a permutational representation of degree 253.> Could it be that the 'rst of your subgroups is not maximal> but a subgroup of index 2 in a larger subgroup isomorphic to PGL(2,23)?>>Good catch! How about these, then? Hmm, let's see...>> But my example works - both copies of PSL(2,23) are maximal.>>OK. Is there an easy way to see that the PGL(2,23) in the one>case lies in S_{253} but not in A_{253}? And the analogous>question for the following cases?Let x be an element of order 2 in PGL(2,23) - PSL(2,23). Then xhas two 'xed points and 11 2-cycles on the 24 points. It lies in exactly 11subgroups in the conjugacy class of maximal subgroups isomorphic to D_{48},one for each of its 11 2-cycles.So, when we move to the action on 253 points, it 'xes exactly 11 pointsand hence has 121 2-cycles, and is an odd permutation.of the maximal >>1) A_{40} has 2 classes of maximal subgroups isomorphic to>>PSU(4,2), such that their nomalizers in S_{40} have point>>stabilizers isomorphic to 3^{1+2}_+ : 2A_4 and 3^3 : S_4,>>respectively.>> Only one of those is maximal in A_{40}>>Ah, OK. I see now that all I really knew was that PSU(4,2) and>its automorphism group have non-permutation-isomorphic primitive>reps of degree 40.>>Again, is there an easy way to see that only one of the classes>is maximal?I can only go by the lists I have. They are basically compiled fromthe using list of primitive groups in Dixon & Mortimer, and thenchecking for containment, which is painstaking but do-able.The maximal primitive subgroups of A_40 are PSU(4,2) (with the3^3 : S_4 stabilizer) and PSL(4,3), which must contain theother PSU(4,2) (which is isomorphic to PSp(4,3)). >>2) A_{63} -> PSU(3,3) -> 4.S_4 and 4^2.S_3 .>> Only one is maximalA_63 has maximal primitive subgroups PSU(3,3), PSU(3,3).2 and PSL(6,2) -so that explains what is happening here.>And again...>3) A_{156} -> PSp(4,5) -> 5^{1+2}_+ : (4 x A_5) and>>5^3 : (2 x A_5).2 .>> Neither maximal.>>OK, but then don't both lie in Aut(PSp(4,5)) = PSp(4,5).2, which>would then satisfy the maximal condition? Or are there even>larger primitive groups of degree 156 in which at least one of>them lies? Hmm..., if so, it looks like they would have to be>normal extensions of PSL(4,5), right?The only maximal primitive subgroup is PSL(4,5).2 here, which must containeverything.>>4) A_{253} -> M_{23} -> PSL(3,2^2) : 2 and 2^4 : A_7 .>> Neither maximal>>So again if I understand correctly, at least one of these must>lie in a larger primitive group of degree 253, which it looks>like must thus be among normal extensions of A_{22} or>PSL(2,23). Hmm..., must be the latter, since M_{23} isn't a>subgroup of A_{22}, and so this probably reduces to your>example. But wait a minute, M_{23} is too big to lie in>PSL(2,23) either. I'm confused. :-(Three maximal primtiive subgroups, A_23, and the two PSL(2,23)'s.The A_23 (acting on pairs) contains both M_23's.>>5) A_{400} -> PSp(4,7) -> 7^{1+2}_+ : (6 x PSL(2,7)) and>>7^3 : (3 x PSL(2,7)).2 .>> Neither maximal>>And here PSL(4,7)? (Or maybe even a primitive group with product>action and composite socle A_5 x A_5?)Yes, both contained in PSL(4,7).A_400 also has maximal primitive subgroup isomorphic to S_20 wr C_2.>>6) A_{495} -> M_{12} -> 2^{1+4}_+.S_3 and 4^2 : D_{12} .>> Neither maximal>>And here A_{12} or PSO+(10,2) (more likely the former)?No, the only max. prim. subgp. of A_495 is PSO-(10,2).>>7) A_{820} -> PSp(4,3^2).2 -> (3^{1+2}_+)^2 : (8 x PSL(2,3^2))>>and 3^6 : (4 x PSL(2,3^2)).2 . (Actually, I'm not sure these 2>>classes of maximal subgroups are isomorphic. There's more than 1>>extension PSp(4,3^2).2 .)>> Neither maximal>>And here A_{41}, PSL(2,41) or PSL(4,3^2) (likely the latter)?Yes, I am sure it is the last - actually PSL(4,3^2).2^2>>Unless I've missed some, that appears to exhaust the a priori>>possibilities for alternating groups < A_{1000}.>> I expect my example is the only one.>> My stataments were all just based on consulting known lists of alternating>> groups up to degree 1000.>>Are any of these known lists available in books? I'm sure you've>guessed I'm working from the appendices of Dixon and Mortimer's>_Permutation Groups_.As I said, they come originally mainly from Dixon and Mortimer - I don't knowof any other written source. A few mistakes have been discovered in theDixon and Mortimer lists. I believe that there is now a very high degree ofcon'dence that the lists of primitive groups in GAP and Magma (bothreturned by the PrimitiveGroup function) are correct. They have beenindependentyl computed with extreme care.Derek Holt. === Subject: Re: 'nite groupsOn :> Jim Heckman true that in every 'nite simple group G>>all isomorphic maximal subgroups>>are Aut(G)-conjugate?>> No, but it is not easy to 'nd examples. I was about to give up, but>> then I found one!>> Believe it or not, the alternating group A_{253} has two maximal>> subgroups>> isomorphic to PSL(2,23). One of them has dihedral D_{24} as point>> stabilizer, and the other has S_4, so they cannot be conjugate in>> S_{253}.>> Hi Derek,>> I have one question about your example.>> The dihedral subgroup D_{24} of PSL(2,23) is extended to a subgroup>> of PGL(2,23) of the same index 253. This means that PGL(2,23)>> also has a permutational representation of degree 253.>> Could it be that the 'rst of your subgroups is not maximal>> but a subgroup of index 2 in a larger subgroup isomorphic to PGL(2,23)?>>Good catch! How about these, then? Hmm, let's see...>> But my example works - both copies of PSL(2,23) are maximal.OK. Is there an easy way to see that the PGL(2,23) in the onecase lies in S_{253} but not in A_{253}?>1) A_{40} has 2 classes of maximal subgroups isomorphic to>PSU(4,2), such that their nomalizers in S_{40} have point>stabilizers isomorphic to 3^{1+2}_+ : 2A_4 and 3^3 : S_4,>respectively.>> Only one of those is maximal in A_{40}Ah, OK. Is there an easy way to see this? (Same questionfor subsequent cases where this occurs>2) A_{63} -> PSU(3,3) -> 4.S_4 and 4^2.S_3 .>> Only one is maximal>>3) A_{156} -> PSp(4,5) -> 5^{1+2}_+ : (4 x A_5) and>5^3 : (2 x A_5).2 .>> Neither maximal.OK, but then don't both lie in Aut(PSp(4,5)) = PSp(4,5).2, whichwould then satisfy the condition?>4) A_{253} -> M_{23} -> PSL(3,2^2) : 2 and 2^4 : A_7 .>> Neither maximal>>5) A_{400} -> PSp(4,7) -> 7^{1+2}_+ : (6 x PSL(2,7)) and>7^3 : (3 x PSL(2,7)).2 .>> Neither maximal>>6) A_{495} -> M_{12} -> 2^{1+4}_+.S_3 and 4^2 : D_{12} .>> Neither maximal>>7) A_{820} -> PSp(4,3^2).2 -> (3^{1+2}_+)^2 : (8 x PSL(2,3^2))>and 3^6 : (4 x PSL(2,3^2)).2 . (Actually, I'm not sure these 2>classes of maximal subgroups are isomorphic. There's more than 1>extension PSp(4,3^2).2 .)>> Neither maximal>>Unless I've missed some, that appears to exhaust the a priori>possibilities for alternating groups < A_{1000}.> I expect my example is the only one.> My stataments were all just based on consulting known lists of alternating> groups up to degree 1000. If you want me to justify any of them, I will> need to 'nd a larger subgroup I suppose. Of course, lists like that> often contain the odd error.>> Derek Holt.>Jim Heckman-- Jim Heckman === true that in every 'nite simple group G>all isomorphic maximal subgroups>are Aut(G)-conjugate?>> No, but it is not easy to 'nd examples. I was about to give up, but> then I found one!>> Believe it or not, the alternating group A_{253} has two maximal> subgroups> isomorphic to PSL(2,23). One of them has dihedral D_{24} as point> stabilizer, and the other has S_4, so they cannot be conjugate in> S_{253}.>> Hi Derek,>> I have one question about your example.> The dihedral subgroup D_{24} of PSL(2,23) is extended to a subgroup> of PGL(2,23) of the same index 253. This means that PGL(2,23)> also has a permutational representation of degree 253.> Could it be that the 'rst of your subgroups is not maximal> but a subgroup of index 2 in a larger subgroup isomorphic to PGL(2,23)?>> Good catch! [...]Or not. On further thought, just because the relevantpermutation rep of PSL(2,23) is embedded in one of PGL(2,23) inS_{253} doesn't mean it's so embedded in A_{253}. Offhand, Idon't know an easy way to tell, but probably Derek will.-- Jim Heckman === Subject: what type of equation is this ?My apologies if this is a newbie type question.The Equation of the form Ut + H( Ux, x) = 0 is the Hamilton-Jacobi Equation in 1-D.What are equations of the following type called?Ut + H( U, Ux, x) = 0 and what are the numerical techniques used to solve it ? across a shock ? === Subject: Re: what type of equation is this question.>>The Equation of the form Ut + H( Ux, x) = 0 >>is the Hamilton-Jacobi Equation in 1-D.>>What are equations of the following type called?>>Ut + H( U, Ux, x) = 0 >>and what are the numerical techniques used >to solve it ? across a shock ?sometimes called Hamilton's principle or characteristic function inthis context. You're saying , essentially, that the Hamiltonian isexplicitly dependent on U itself. Just how is H dependent on U?I.e., what is H (U, Ux, x)? === Subject: Re: Limit of sequenceNever use indirect proof when it's not necessary.You easily 'nd that a-e0. Just let having dif'culty proving the following proposition on the limit>of a sequence xn:>>if a <= xn <= b for every n and xn -> x, then a <= x <= b>>Since xn -> x then I know that there is some N such that |xn - x| < e>whenever n > N. So I have>>xn - e < x < xn + e.>>By the initial condition I also have>>a - e <= xn - e <= b - e, and>>a + e <= xn + e <= b + e>>Now I try to combine into>>a - e <= xn - e < x < xn + e <= b + e. But that just tells me that>>a < x + e < b + 2e.>>Close, except I have a couple of e's that I don't really want :-)>>Any suggestions on how to prove this would be greatly appreciated!>>Tom>> How about indirect proof? If the theorem is not true, then either> x> b or x< a.>> If x> b, what happens if you pick e= (x-b)/2?> === Subject: isomorphism on abelian groupsif G is a 'nite abelian group of order n and phi: G->G is de'ned byphi(a)=a^m for all a in G, what's a necessary and suf'cient conditionfor phi such that it's an isomorphism from G onto itself ? === Subject: Re: isomorphism on abelian groupsNntp-Posting-Host: is a 'nite abelian group of order n and phi: G->G is de'ned by>phi(a)=a^m for all a in G, what's a necessary and suf'cient condition>for phi such that it's an isomorphism from G onto itself ? An isomorphism is a homomorphism which is bijective.For phi to be a homomorphism (also called automorphism when the domain and range are the same) you need *) phi(1) = 1 *) phi(x^(-1)) = phi(x)^(-1) for all x in G *) phi(xy) = phi(x) phi(y) for all x, y in G[The de'nition in your textbook may omit some of these.For example, the third with x = y = 1 gives phi(1) = phi(1)^2,from which we can derive 1 = phi(1) after multiplying by phi(1)^(-1).] For phi to be a bijection you need *) phi(x) = phi(y) implies x = y (injective) *) For all y in G there exists x in G with phi(x) = y (surjective) Play with these 've conditions, determining the restrictions on m such that all are satis'ed.Some of the 've are satis'ed for all m, but others are non-trivial.-- 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 === Subject: Re: 'nite abelian group of order n and phi: G->G is de'ned by> phi(a)=a^m for all a in G, what's a necessary and suf'cient condition> for phi such that it's an isomorphism from G onto itself ?It's surjective iff it's injective, so the question is,when does it have a trivial kernel?I'll let you think about this :-)-- Robin Chapman, === www.maths.ex.ac.uk/~rjc/rjc.htmlSubject: Re: isomorphism on IMPORTANT: Under NO circumstances will postings containing illegal or copyrighted material through this service be tolerated!! order n and phi: G->G is de'ned by> phi(a)=a^m for all a in G, what's a necessary and suf'cient condition> for phi such that it's an isomorphism from G onto itself ?>> It's surjective iff it's injective, so the question is,> when does it have a trivial kernel?>> I'll let you think about this :-)>Any 'nite abelian group is isomorphic to a direct product Z_p1^n1 x Z_p2^n2 x...x Z_pj^nk, for primes pj.of cyclic groups of prime power order. Any two such decompositionshave the same number of factors of each order.I'd surmise that m would have to be coprime to every pj.---- === Subject: Re: Andrica's Conjecture> Well, that takes care of that, but there are still some problems. > Here is the most important example: Let n = 22. Then p_n and p_(n+2) can be 2, as you say, but then> we can let p_(n+3) = 5 and p_(n+5) = 3; however, you state that> p_(n+5) can't equal 3. In other words, I have switched the 3 and> the 5 in the divisor list. The example here is kind of silly, because> for very small numbers there are very small intervals between prime> numbers. However, as numbers get larger, this is not the case at all,> and I could possibly switch the list so that p_(n+11) = 5. In this> case, n + 1 = (n + 11) - 10, and so p_(n+1) = 5. Note that this kind> of switching could happen basically anywhere on the list; for example,> if p_(n+7) = 3, then so does p_(n+1), or if p_(n+57) = 5, then so does> p_(n+37). In this way we can continue re-using the same primes over> and over again. Your argument that p_m and p_(m+P) must either be> equal or different and unequal to P does not take into account the> fact that the relationship between p_(m + p1) and p_(m + p2) is a> difference of a composite number. You may claim, Okay, well obviously that won't happen. You may> be able to swap around a couple of the prime numbers, but you can't> move them *that* far. Well, if so, prove it. Also, notice that if> you try to rede'ne p_(n+k) as the smallest prime that divides n+k but> doesn't divide n+j for j hcf(pm, p(m+M)) | hcf(pm, M) rather than hcf(pm, p(m+M))=hcf(pm, M)> The rest of the argument still follows anyway... (in fact the rest of the> argument becomes slightly I've just spotted -however it seems to be incomplete - was there a bit you accidentallyleft off? [it could be a problem with _my_ viewing of it thru Googlegroups??, if so, pls let me prime factorsis unimportant - I'm only using the pigeon-hole principle,effectively, [since every one has to be coprime to ALL the others] andshowing there's an === Subject: Re: Andrica's Conjecture> Hi which I've just spotted -> however it seems to be incomplete - was there a bit you accidentally> left off? [it could be a problem with _my_ viewing of it thru Google> groups??, if so, objection - the exact order of the prime factors> is unimportant - I'm only using the pigeon-hole principle,> effectively, [since every one has to be coprime to ALL the others] and> showing there's an over吶wThe problem is, you can't pigeonhole because your uniqueness argumentis broken. Relative primality is NOT an equivalence operator -- justbecause a and b are relatively prime and b and c are relatively primedoesn't mean than a and c are relatively prime. This is the problem-- you start by saying that several of the p_n are relatively prime tothe 'rst one, and then you claim that they're different from eachother. That's untrue; they can be the same, because after all, forP1, P2 primes > 2, p_(m + P2) = p_(m + P1 + C) for some _composite_number, and if p_(m+P1) | c, then we can let p_(m + P1) = p_(m + P2).> === Subject: Re: Andrica's ConjectureYou're (sort of) correct in what you say, though incorrect that what youcorrectly observe, negatively affects my proof. Let me explain why:There will exist factors with the properties you've found (presumably bysearching for speci'c (numerical) examples - which I'm always in favour of!:-), however you're missing a crucial facet of the proof. It's that oldchestnut again I call the any/all issue. I only need there to exist ANYprime factors with the characteristics I need - you're looking at anotherset - included in ALL the relevant prime factors - though with extra membersto my set, which extra members are therefore irrelevant to my proof. It'sthese extra members which have the property you demonstrate. This shows thelimitation of numerically examining a speci'c (mis-)interpretation of theproof [and the all/any issue is a common one]J === Subject: Re: cross-sectionphil a 3-dimensional solid be speci'ed if we know its> cross-sections, i.e., intersections with planes?>> Example: Given that every cross-section is a triangle, then the solid> is a tetrahedron. Proof?>> What if every cross-section is a square? Does the solid exist?I doubt it. I think that the only solid with all its cross-sections of thesame shape, is the sphere. Or, more generally, the ellipsoid, if you Larrosa CaestroA Corua (Espaa)ilarrosaQUITARMAYUSCULAS@mundo-r.com === Subject: Re: cross-sectionphil escribi en el know its> cross-sections, i.e., intersections with planes?>> Example: Given that every cross-section is a triangle, then the solid> is a tetrahedron. Proof?>> What if every cross-section is a square? Does the solid exist?>> philIf M and M' are the middpoints of opposite edges, any plan perpendicular tohte segment MM' produce a rectangular cross-section.Particularly, the meanplane of MM' produce a Corua (Espaa)ilarrosaQUITARMAYUSCULAS@mundo-r.com === Subject: Example: Given that every cross-section is a triangle, then the solid > is a tetrahedron. Proof?Nonsense. A tetrahedron will have cross-sections that are not triangular.-- Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email) === Subject: Re: cross-section Gerry Myerson every cross-section is a triangle, then the solid > is a tetrahedron. Proof?Nonsense. A tetrahedron will have cross-sections that are not > triangular.In particular, consider the plane parallel to a pair of opposite edges and equidistant from them, and how this plane intersects the tetrahedron. === Subject: Re: cross-section every cross-section is a triangle, then the solid> is a tetrahedron. Proof?> Nonsense. A tetrahedron will have cross-sections that are not> triangular.> In particular, consider the plane parallel to a pair of opposite> edges and equidistant from them, and how this plane intersects the> tetrahedron.I believe this sort of question is generally dealt with underthe topic geometric topology--a network search interesting points.I am fairly sure that there are some very counter-intuitive examples.-Mike === Subject: Re: every cross-section is a triangle, then the solid>> is a tetrahedron. Proof?>> Nonsense. A tetrahedron will have cross-sections that are not>> triangular.>> In particular, consider the plane parallel to a pair of opposite>> edges and equidistant from them, and how this plane intersects the>> tetrahedron.>>I believe this sort of question is generally dealt with under>the topic geometric topologyI think that belief is wrong. I usually at least glance at, and occasionally read with close attention, the papers posted at the ArXiv under the rubric Geometric Topology, and I very much doubtthat any example of this sort of question is dealt with in anyof the papers there. (The closest approximation I can think o's in some papers describing generalizations of normal surfacesin triangulated 3-manifolds.) Yet I think it would be generallyagreed, by those in the 'eld, that math.GT does, in fact, represent Geometric Topology (which I have seen de'ned astopology which is interested in concrete topological spaces andmaps, particularly homeomomorphisms, more than in homotopy types, homotopy equivalences, and so on) pretty well.>--a you to many interesting points.>I am fairly sure that there are some very counter-intuitive examples.The problem seems to me very untopological, but if a search string with topology must be used, I think combinatorialtopology might work better. I think it's a purely geometricquestion, though. Lee Rudolph === Subject: Re: Primes as number of solutions of a passes to two>integer points: (1,n) and (n,1). So, why we don't call what are the>numbers that the parabola only passes to two integer points, or passes>to any integer points?.>For example, what are the numbers n such that y=nx^2 has integer>solutions?Hint: any integer x will do.Yes, I'm in agreement with you that all integers x have this propierty(there are integers y, n such that y = n x^2), but I asked for n: whatare the integers n such that there are x, y integers such that y =nx^2?Because we see n prime as the integer such that the curve y = f(x,n)has only two integer solutions ((x,y)=(n,1) and (1,n)), then we couldinterest about the number of integer solutions of a curve. And Istarted with === Subject: Re: Primes as number of solutions of a diphantine equation.> I think there is merit in pursuing your idea, however in the form you have> presented it, there is not much you can do once you write n=xy but if you> use a mapping by which you tranform the original problem into a similar one,> you may make some progress.I will give you this hint: 'nd the mapping to tranform your useless> original equation into something more useful. then instead of working with> n=x*y, you work in the transformed space. You will 'nd that the function> that represents the product x*y in the transformed space has many> interesting properties and has the form:> alpha=x*(C-x)/(6*x+1) where C is a constant that depends on N. There is only> one such function for every N.What is alpha?What do you do?. Can you explain === Subject: Re: WHAT IS THE COINCIDENCE OF THIS was Re: To prove psychic powers, someone has to sit this test!> I thought we were going to concetrate on 1 issue. I have a moderated forum> for you to play on LInk is above and in my signature.signed up, waiting for con'rm, the issue is the new topic!Herc. I've sent you two invitations to rejoin the group and toinspect the method and conditions of ourproposed Trial and have not had a response. These were sent to bothyour Yahoo email and the Ozemail one.Have you lost interest in attempting to demonstrate your powers? Asyou say in the initial subject of this thread:To prove psychic powers, someone has to sit this test!That'll be you. We cannot proceed without your participation, and Iam not going to further invite others to participate if you are notgoing to attempt this.--Eric Hocking (moderator)You're invited to test of the paranormal at:http://www.twofromoz.freeserve.co.uk/sceptic/herctest/e_ hocking@yahoo.co.uk === Subject: Re: WHAT IS THE COINCIDENCE OF THIS was Re: To prove psychic powers, someone has to sit this test!>> Herc. I've sent you two invitations to rejoin the group and to> inspect the method and conditions> of our> proposed Trial and have not had a response. These were sent to both> your Yahoo email and the Ozemail one.You don't need to contact him via email! He's psychic. He should know tocontact you, and what your contact information is without you lifting a'nger to inform him. LOL!> Have you lost interest in attempting to demonstrate your powers? As> you say in the initial subject of this thread:> To prove psychic powers, someone has to sit this test!What powers? Psychics are predatory quacks looking for little old ladies toconn out of their life's savings for a feel-good bull session.> That'll be you. We cannot proceed without your participation, and I> am not going to further invite others to participate if you are not> going to attempt this.He isn't going to participate because psychics are frauds. Why do you thinkthey rely on newsgroups and 900 numbers? Why do you think the law requiresthem to have For entertainment purposes only tatooed to their every venue?So people will realize that they are just spinning new-aged feel-goodbull.Your sister has been trying to contact you... or perhaps it's an aunt orniece... She has good news... and so forth.-- Felony case 02-CR-0617 9/1/03: Oregon Department ofJustice V. Raymond Ronald Karczewski, Defendant.The defendant's name is NOT copyrighted. === Subject: Re: WHAT IS THE COINCIDENCE OF THIS was Re: To prove psychic powers, someone has to sit this test!>> Herc. I've sent you two invitations to rejoin the group and to> inspect the method and conditions> of our> proposed Trial and have not had a response. These were sent to both> your Yahoo email and the Ozemail one.You don't need to contact him via email! He's psychic. He should know to> contact you, and what your contact information is without you lifting a> 'nger to inform him. LOL!he foresaw the future, and knew he'd fail the test. === Subject: Re: ref. for in'nite seriesbmqtm4$q5kj6$1@ID-143665.news.uni-berlin.de...>> David Petry a crit dans le message reference for the proof that the in'nite series> 1/(n^2) elementary proof of this relation,> which I suspect is well known but I've never seen it.>> Factor (1+x)^N - (1-x)^N, for N an odd integer, as>> product ( w^k(1+x) - w^{-k}(1-x) ), k=-(N-1)/2..(N-1)/2> where w = exp( i pi / N )>> Then 'nd the coef'cient of x^3 for that expression, and> compare it to the same coef'cient using the Binomial Theorem> for the 'rst expression, and take a limit.>> I 'nd : Binomial(n,3)=n*Sum((cotan(k*Pi/n))^2,k=1..(n-1)/2)sin(x)<=x<= tan(x) donc (cotan(x))^2<=1/x^2<=1/(sin(x))^2=1+(cotan(x))^2thenSum((cotan (k*Pi/n))^2,k=1..(n-1)/2)<=Sum(1/(k*Pi/n))^2,k=1..(n-1)/2)<=(n -1)/2+ Sum((cotan(k*Pi/n))^2,k=1..(n-1)/2)then(Binomial(n,3)/(n^3))* Pi^2<=Sum(1/(k^2,k=1..(n-1)/2)<=(Pi/n)^2*((n-1)/2)+(Binomial(n ,3)/(n^3))*Pi^2and limit (Binomial(n,3)/(n^3))),n=oo)=1/6 andlimit((Pi/n)^2*((n-1)/2),n=00)=0 === Subject: Re: ref. for in'nite seriesDavid Petry a David Petry a crit dans le n*Binomial(n,3)=Sum((cotan(k*Pi/n))^2,k=1..(n-1)/2)> and ....> cotan(s/n)*(1/n) = 1/s>> Also, the left hand side of your === Binomial(n,3)=n*Sum((cotan(k*Pi/n))^2,k=1..(n-1)/2)Subject: Re: online math handbook web-based symbolic calculator, math handbook and computer algebra system. === www.mathHandbook.comSubject: Re: Data analysis software > > It plots and analyses any x-y data for peak location, peak height,> peak> width, semi-derivative, derivative, integral, semi-integral,> convolution,> deconvolution, curve 'tting, and separating overlapped peaks and> background.>> www.chemSoftware.com === Subject: Re: Two 06:27:10 = 3.>>> [ii] Let y = 3.>>> Do you understand that these are not necessarily equivalent because I>> haven't stated what the rest of the question is after this?>We could say that x = y.>We could say they are different in that x has two lines that cross; y>has two lines that don't.>Mathematically speaking, they are equal.>Are they equivalent? Depends on the de'nition of equivalent. Maybe you're trying to confuse us by pretending to be dense?Yes, _if_ [i] and [ii] are both true _then_ x = y. That wasn't> the question. The question is whether [i] and [ii] are > equivalent statements. They obviously are not.For example, suppose [i]. It follows that x^2 = 9.> Now suppose [ii]. Does that imply that x^2 = 9?> Of course it doesn't.>This>argument obvuscates the real argument.There's more than one argument in the universe. You got me> replying when you said that I'd said that At least one was a head> is the same statement as At least one was a tail. I never said> anything so ridiculous.> Okay, there is a lot of ambiguity in arguments. Not much in ourquestion.There is a relationship between heads and tails which is unique. Theyare on opposite sides of the coin.a)A coin was 告pped, it landed heads.a')A coin was 告pped, it landed tails.There is a relationship between a and a' which is unique. Equivalent?Complimentary? Equal? I don't know. When you 告p a coin, one happens,_OR_ the other.b)Two coins were 告pped and they landed HH.b')Two coins were 告pped and they landed TT.Same same b and b', except they each happen .25. When we say twocoins were 告pped, there is a relationship between 4 (four)outcomes. I don't know what it's called, but there are four eventstied together. If this relationship isn't de'ned (if it doesn't havea name) maybe we can de'ne it.When we 告p two coins, HH happens, _OR_ TT happens, _OR_ HT happens,_OR_ TH happens. We toss them thousands of times, and any one of thehappenings could have been the 'rst toss.Suppose that b' happened 'rst and:Two coins were 告pped and at least one is a tail. What are thechances for two tails?, _OR_Suppose that b happened 'rst and:Two coins were 告pped and at least one is a head. What are thechances for two heads?Bill and Jane only hear the statements. All they have to do to makethe proper bet is answer the questions correctly.On b' Bill bet there are two tails. Jane bet for one of each.On b Bill bet for two heads. Jane bet for one of each.Bill will win with either of these occurrances. What odds should they bet?Would both be the same, or would they be different?Eldon> ************************David C. Ullrich === Subject: Re: Less symbols, core error proofX-DMCA-Noti'cations: 15:46:52 -0400, Will Twentyman de'nition:>>> Algebraic integers are de'ned to be roots of monic polynomials with>> integer coef'cient e.g. x^3 + 3x + 1 or x^234 - 34x^12 + 17, where>> monic refers to the leading coef'cient.>>> My assertion is that the over hundred year old de'nition excludes>> numbers that have to be included to keep from having contradiction>> i.e. mathematical inconsistency.>>What part of the *de'nition* is inconsistent? For it to be >inconsistent would suggest that there are no algebraic integers.No, if the de'nition showed there were no algebraic integersthere would be nothing inconsistent about that (until we foundanother proof that there _is_ at least one algebraic integer).There's simply no way that this _de'nition_ can possibly beinconsistent. As always James is not saying exactly what hemeans - he means that the de'nition, together with otherfacts that he imagines are true, is === inconsistent.************************David C. UllrichSubject: wtwentyman@copper.net First the problematic de'nition:>>Algebraic integers are de'ned to be roots of monic polynomials with>integer coef'cient e.g. x^3 + 3x + 1 or x^234 - 34x^12 + 17, where>monic refers to the leading coef'cient.>>My assertion is that the over hundred year old de'nition excludes>numbers that have to be included to keep from having contradiction>i.e. mathematical inconsistency.>>What part of the *de'nition* is inconsistent? For it to be >>inconsistent would suggest that there are no algebraic integers.> No, if the de'nition showed there were no algebraic integers> there would be nothing inconsistent about that (until we found> another proof that there _is_ at least one algebraic integer).True. Of course, the fact that x+2 has solution -2 trivially shows that there is at least one algebraic integer.> There's simply no way that this _de'nition_ can possibly be> inconsistent. As always James is not saying exactly what he> means - he means that the de'nition, together with other> facts that he imagines are true, is inconsistent.Unfortunately, James has yet to take a class in which he 'nds out how mathematicians move from de'nition to properties. He seems to be convinced that we decide on the properties, and then construct the de'nition to 't. While that happens sometimes, as often we start with the de'nition and *then* explore the properties.-- Will Twentymanemail: wtwentyman at copper dot net === Subject: Re: Core error argument objection refuted, short Adjunct Assistant Professor at the University of Montana.Arturo Magidin was going through it in an e-mail reply to some questions Nora>sent. You can get it from the prime factorization of f and some Galois>Theory applied to the splitting 'eld, at least when the polynomial is>irreducible.>>What follows is almost certainly harder than it needs to be... That's>my usual m.o.What followed was my argument that f will be factored as f=u1*u2*u3,with u1, u2, u3 pairwise coprime, and each of a1, a2, a3 will bedivisible by u2*u3, u1*u2, and u1*u2, respectively. Some notes on thatargument: (1) Although I did not state so explicitly, it should be clear that I assuming that f was a rational prime throughout. The argument will go through, word for word, if we replace Q by the 'eld of de'nition of the polynomial and f by a prime element of its ring of integers (that is, f|ab -> f|a or f|b); so, for example, it applies to James's example of f=sqrt(2), m=1, because sqrt(2) is a prime element of Z[sqrt(2)], the ring of integers of Q(sqrt(2)), the 'eld of de'nition of the polynomial. (2) The argument should also work if f is a product of distinct primes, by analysing each prime separately. (3) The argument should also work if the ideal (f) is a product of distinct prime ideals, replacing divisibiilty of elements by divisibility of ideals throughout. (4) I believe the argument will also go through if we replace f with f^j for j>0, f a prime element; but there are some steps I used with j=1 which would no longer hold. For example, I discarded the possibility that (f)=p1^2*p2^2, because then there would be no way to split off (f)^2 into three elements; but if we are considering, say, f^3, then that would not be a problem. I think these dif'culties can be dealt with, but I haven't thought it through. =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 'gures few readers can criticize. A great many people are staggered to this extent, that they imagine there must be the inde'nite 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. -- A Budget of Paradoxes, Vol. 2 p. 129 by Augustus de Morgan = Magidinmagidin@math.berkeley.edu === Subject: Re: Question on algebrasX-DMCA-Noti'cations: an any algebra over the 'eld of real numbers.>>Choose x,y in A.>Call a 'nite sequence (x,x_1,x_2, ...,x_n) a ('nite) directed path >from x to y if x*x_1*...*x_n=y and x_j in A forall 1 <= j <=n.>Let P_{xy} be the set of all directed paths from x to y. >Let P'_{xy} subset P_{xy} be the set of all directed paths from>x to y without y being a member of any of the 'nite sequences>in P_{xy}.>>Question: Does there exist a set A which is a (possibly non-divisor)>algebra and has two elements x, y such that P'_{xy}, or>even P_{xy} = empty?. >>I have found an example algebra A' for which P_{xy} = not empty >forall x, y in A' No you haven't. If x = 0 and y <> 0 then P_{xy} is empty.>(to say the least) seemingly needs proving >-but, of course, why prove it if its already part of some more>general theorem?>>Warning: Please go easy on me if I've overlooked something obvious >as I am a physics student and not a mathematician. I'm sure path,>for example, probably has C. Ullrich === What is an example of an algebra that does not have the following> property: forall x, y in A exists z in A: x * z = y.>Every algebra A which contains more than one element is an example.Just let x = 0 and y be any non-zero element. For example, let A be thealgebra of all real numbers. === Subject: 'nite 'eld with q elements. I have learned that the number of monicirreducible polynomials of degree tfor a 'eld with q elements isI(t,q) = 1/t * the summation for divisors d of t of MoebiusMu(t/d)*q^d.Hence, the number of monic pairs of factors in F multiplying to a polynomialof degree t is:q^t - 1/t * the summation for divisors d of t of MoebiusMu(t/d)*q^d.Can someone help me simplyfy the power series expression:The summation as t goes from 0 to in'nity ofq^t - 1/t * the summation for divisors ==God made the integers, all else is the work of man.L. Kronecker, Jahresber. DMV 2, S. 19. === Subject: Re: Power series simply'cation of MoebiusMu expression>....> Can someone help me simplyfy the power series expression:The summation as t goes from 0 to in'nity ofq^t - 1/t * the summation for that you want t to go from 1, not 0, right? For at t = 0,all right of the minus is unde'ned.Now,sum{t= 1 to in'nity} 1/t^r sum{d|t} mu(t/d) q^d =polylog(q,r) /zeta(r),where polylog(q,r) = sum{t=1 to in'nity} q^t/t^r(for those r and q where the sum converges),and where I have otherwise shortened your notation.(And zeta(r) = polylog(1,r), of course {for r > 1}.)So, sum{t= 1 to in'nity} (q^t - 1/t sum{d|t} mu(t/d} q^d) =q/(1-q) - polylog(q,1)/zeta(1).But 1/zeta(r) -> 0 as r -> 1 from above.And, for -1 <= q < 1,polylog(q,1) = -log(1-q) (but this ends up not mattering).So, *IF* -1 <= q < 1,your sum (if t is from 1) is simplyq/(1-q).I have avoided being rigorous, however, and I may have misinterpretedyour === Subject: Re: Power series simply'cation of MoebiusMu expressionGlad math is a better subject for me than spelling:That would be simplify and simpli'cation...Help appreciated with this problem, learned that the number ofmonic> irreducible polynomials of degree t> for a 'eld with q elements is>> I(t,q) = 1/t * the summation for divisors d of t of MoebiusMu(t/d)*q^d.>> Hence, the number of monic pairs of factors in F multiplying to apolynomial> of degree t is:>> q^t - 1/t * the summation for divisors d of t of MoebiusMu(t/d)*q^d.>> Can someone help me simplyfy the power series expression:>> The summation as t goes from 0 to in'nity of>> q^t - 1/t * the summation for divisors d of t of ==> God made the integers, all else is the work of man.> L. Kronecker, Jahresber. DMV 2, S. 19.>> === Subject: Re: ordered pairs> Evil ordered pair (x,y) would be de'ned as>{{x}{x,y}}. I understand that a set has no order but therefore, wouldn't>that be the same as {{x,y} {x}}.>> Yes, it would. But the point is that {{x,y},{x}} = {{z,w},{z}} if and> only if x=z and y=w. So that (x,y) = (z,w) if and only if x=z and y=w,> so that (x,y)=(y,x) if and only if x=y. So it's not that the set is> now ordered, is that the set {{x}, {x,y}} can be used to say which of> x and y goes 'rst and which goes second.>Could a *variant* of Axiom of Choice be said to be assumed here, we only knowthe ordering by issuing a IS_SINGLETON function on the 2 members.Its almost a contextual ordering relying on the data itself, I've devised other schemesthat tend to rely on type checking.Herc === Subject: Re: ordered pairs Adjunct Assistant Professor at the University of Montana.|-|erc ordered pair (x,y) would be de'ned as>>{{x}{x,y}}. I understand that a set has no order but therefore, wouldn't>>that be the same as {{x,y} {x}}.>> Yes, it would. But the point is that {{x,y},{x}} = {{z,w},{z}} if and>> only if x=z and y=w. So that (x,y) = (z,w) if and only if x=z and y=w,>> so that (x,y)=(y,x) if and only if x=y. So it's not that the set is>> now ordered, is that the set {{x}, {x,y}} can be used to say which of>> x and y goes 'rst and which goes second.>>Could a *variant* of Axiom of Choice be said to be assumed here, we only know>the ordering by issuing a IS_SINGLETON function on the 2 members.No, no variant of the Axiom of Choice is being assumed.Given two sets, x and y, there is a set containing x and y (Axiom ofPairing).Therefore, there exists a set that contains exactly both of them,{x,y} (Axiom of speci'cation), and one that contains exactly x, {x}(Axiom of speci'cation).Applying the Axiom of Pairing again, you get that there is one setthat contains the set {x,y} and the set {x}. The Axiom ofspeci'cation gives you the set { {x,y}, {x} }.The fact that this is then used to ->de'ne<- an ordered pair hasnothing to do with ordering, and we DO NOT check to see if which oneis the singleton.We ->de'ne<- the 'rst element of the ordered pair A={ {x,y},{x} } tobe the unique element of intersection{ {x,y},{x} }. This intersectionexists by applying 'rst the axiom of of unions, which gives you theset S = {x: x is in some element of A}and then the axiom of speci'cation, which gives you the set I = {x in S: x is in all elements of A}.Then the unique element of I is the 'rst element of the orderedpair, and the second element of the ordered pair is de'ned to beeither the unique element of S-I, if one exists, or else the uniqueelement of x, if none exists.If x is equal to y, then the ordered pair becomesA = { {x,y}, {x} } = { {x,x},{x}} = {{x},{x}} = { {x} }.So S = {x}, and I={x}; x is the 'rst element, x is the secondelement.If x is different from y, then S = {x,y} and I={x}; so the 'rstelement is the unique element of I, and the second element is theunique element of S-I = {y}. No need to test to see if something is a singleton. =It's not denial. I'm just very selective about what I accept as reality. --- Calvin (Calvin and Hobbes) Arturo Magidinmagidin@math.berkeley.edu === Subject: Re: Quick Math Guide to core error issuesIn alt.math.undergrad James Harris but I was in a weird mood the> last couple of days, partly out of EXTREME FRUSTRATION at my> situation. I've found that I can have fun with postings, which makes> me feel better.Translation: weird mood = drunk and/or in the manic phase of (one of)your disorders> Oh well, maybe someday you'll have reason to give me your name, but> it's not a big deal. In any event, unlike with Nora Baron, I won't> put quotes around your name.How chivalrous of you. So you're going to be slightly less obnoxiousin your dealings with Penny than with Nora -- at least until it's clearyou can't snow her into agreeing with you. Then you'll be calling hera liar, too.-- 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 === Subject: FunktorWhat is that? What is the precise de'nition?Why is it said that fundamental 'eld (Puankare's 'eld) is a functor? Andwhat is the result? === is that? Looks like a Germanic spelling of functor.>What is the precise de'nition?In category theory a functor F from a category C to a category Dassigns to each object A of C an object FA of D, and to each arrowf: A -> B of C an arrow Ff fA -> FB of D such that identitiesand composition are preserved by F.> Why is it said that fundamental 'eld (Puankare's 'eld)What?> is a functor? And> what is the result?Result?Like for instance Forfar 4, East Fife 5?-- Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.htmlNeedless to say, I had the last laugh. Alan Partridge, _Bouncing Back_ (14 times) === Subject: Re: FunktorRobin Chapman that fundamental 'eld (Puankare's 'eld)>>What?> is a functor? AndPuankare' is probably meant to be Poincare'. I don't knowwhat Poincare's 'eld is, but the original poster mightmean the fundamental group of a topological space, whichwas (according to MathWorld) introduced by Poincare'.Under all these assumptions: when someone says that thefundamental group is a functor, he/she means that notonly there exists a fundamental group pi(X) for everytopological space, but that there actually is a functor pi from the category of topological spaces tothe category of groups such that pi(X) for every topologicalspace X is the fundamental group of X. So, in particular,a homomorphism f : X -> Y of topological spaces givesrise to a group homomorphism pi(f) : pi(X) -> pi(Y) andthis behaves nicely with respect to function compositionand identities.-- Peter van Rossum, | Universal law of linearity: for allDept. of Mathematics, New Mexico | f : R -> R and for all x, y in R:State University, Las Cruces, NM, USA. | f(x + y) = f(x) + f(y) === category theory a functor F from a category C to a category D> assigns to each object A of C an object FA of D, and to each arrow> f: A -> B of C an arrow Ff fA -> FB of D such that identities> and composition are preserved by F.>>Why is it said that fundamental 'eld (Puankare's 'eld)> What?Cannot answer the original question, but I think this is phonetic transcription of Poincare-- Vale ! Christianus Auriocus === Subject: Re: Need help for this integralphil calculate the value of the integral >>int_{-infty} ^infty exp(ikx) Ln(1/Abs(x-x')) dx.>>Is it possible to calculate the integral analytically? >>Can anyone give me hints for how to solve such case?Can you give me any sense in which the integral exists?The integrand is going to in'nity as x does.-- This address is for information only. I do not claim that these viewsare those of the Statistics Department or of Purdue University.Herman Rubin, Department of Statistics, Purdue Universityhrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 === Subject: Re: Need help for this integral> phil >>int_{-infty} ^infty exp(ikx) Ln(1/Abs(x-x')) dx.>>Is it possible to calculate the integral analytically? >>Can anyone give me hints for how to solve such case?Can you give me any sense in which the integral exists?> The integrand is going to in'nity as x does.How aboutlimit a->0 integral (x=-oo..oo) exp(ikx - a|x-x'|) ln(1/|x-x'|) dx === Subject: Re: Need help <>sSHfTy;{Dhe&:+?b`9fUj5A~$gIYlYT0/$-asR-K~3S3[]q.R3YSmpR|$- GiZp>UN2a}!Fmw+%h}YL`!h_XXr5Q>_nGsY2_>int_{-infty} ^infty exp(ikx) Ln(1/Abs(x-x')) dx.>>Is it possible to calculate the integral analytically? >>Can anyone give me hints for how to solve such case?Can you give me any sense in which the integral exists?> The integrand is going to in'nity as x does.Let's try x'=0, k=1. We have convergence at 0, so how abouta principal value where we integrate from -X to X, then let Xincrease to in'nity? Here is what I get with Maple:> k := 1; k := 1> fp := exp(I*k*x)*log(1/x); fm := exp(I*k*x)*log(1/(-x)); /1 fp := exp(I x) ln|-| x/ / 1 fm := exp(I x) ln|- -| x/> 'nt := int(fp,x=0..X)+int(fm,x=-X..0);'nt := Pi + I exp(I X) ln(X) + I Ei(1, -I X) - I exp(-I X) ln(-X) - Pi exp(-I X) - I Ei(1, I X)> simplify(%) assuming X>0; -2 ln(X) sin(X) + 2 Si(X)> limit(Si(X),X=in'nity); 1 - Pi 2 So the 2 Si(X) term converges, and we are left with bigger and biggeroscillations. So not even this principal value exists.-- G. A. Edgar http://www.math.ohio-state.edu/~edgar/ === Subject: Re: Tough Probability question...Jonathan Miller club for people>with>>high IQ scores. To qualify, your IQ must be at least 132, putting you>in>>the>>top 2% of the general population. If a group of 10 people are chosen at>>random, what is the probability that at least two of them qualify for>>Mensa?>> IQ tests are allegedly designed so that>> (1) distribution of IQ scores may be treated as normal,>> Why normal? Log-normal would be more appropriate.>No it wouldn't. The scoring of the tests is designed so that the scores are>symmetric about the mean (subject to measurement error). Log-normal has an>upward drift over time (oops, I'm sampling over time rather than population>here.)>I really don't think we mere mathematicians want to get bogged down in the>quagmire of the right way to measure intelligence.>Unless, of course, someone comes up with a compelling argument that it>exists (or doesn't).>Jon MillerWhy is there any concern over the distribution of IQ?This is a straight binomial problem, and it makes nodifference what the distribution of IQ happens to be.-- This address is for information only. I do not claim that these viewsare those of the Statistics Department or of Purdue University.Herman Rubin, Department of Statistics, Purdue Universityhrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 === Subject: Re: Tough Probability question...> Why is there any concern over the distribution of IQ?>> This is a straight binomial problem, and it makes no> difference what the distribution of IQ happens to be.I have the bad habit of answering questions asked rather than the questionsthat should have been asked. And of wandering off on tangents.OP's question has been answered many posts back (Randy Poe's post, plusanother one that even gives more detail) and the rest is just playing games.Which (IMHO) is allowed, even in a math ng. I am just assuming that theother posts are offered in the same vein.Jon Miller === Subject: Re: Tough Probability question...This problem can be solved with the Bernoulli experiment.think of the problem as hit / no-hit or 0 and 1n = total number of triesk = number of hitsp = possiblity for a hitnCr(n,k) = combinations of k in n nCr -> on my TI-89 this function is called that waynCr(n,k) * p^k * (1-p)^(n-k)for your problem:P(A) = at least 2P(NOT A) = none or exactly 1P(A) = 1 - P(NOT A)1 - (0.98^10) + (10 * (0.02^1 * (1-0.02)^(10-1))) = 0.0161776407 approx. 1.6 % === Subject: Re: Tough Probability question...> Anyone know how to attack the following? Mensa is a club for people with> high IQ scores. To qualify, your IQ must be at least 132, putting you in the> top 2% of the general population. If a group of 10 people are chosen at> random, what is the probability that at least two of them qualify for> Mensa?> So far I have: Approx pop of US is 292,000000 but Im not sure how to> proceed.Now do I 'gure out the chances of 2 people being 132 or above from> the 10 or problem, it is often simpler to 'nd the probability> of the opposite case. So, what is the probability that NONE of the> group qualify for Mensa, and what is the probability that ONE person> quali'es. These two answers, combined with the one you want, cover> all the possibilities...I don't think that the population of the US is relevant to the> answer...Isn't mensa an international organization anyway?To this hint and my own, I'll add a pedantic note: Technicallythis is sampling without replacement in the sense thatafter you take one person out of the pool, the probabilitiesare slightly changed. However, nobody would solve it thatway. Treat it as sampling with replacement in the sensethat the probability of any given person having IQ 132(or above) is exactly 2%. The pool is large enough tobe considered in'nite. - Randy === Subject: Re: >>> Anyone know how to attack the following? Mensa is a club for people> with>> high IQ scores. To qualify, your IQ must be at least 132, putting you> in>> the top 2% of the general population. If a group of 10 people are> chosen>> at random, what is the probability that at least two of them qualify> for>> Mensa?>> So far I have: Approx pop of US is 292,000000>>Did the question say anything about the USA?> >>There are other countries in the world, you know.>> Well obviously us furreiners are too stupid to qualify for Mensa. Duh.It is largely true that youse furriners is too stupid to score above 131 on> ours IQ tests, but I think Mensa allows other methods of intelligence> estimation. So you might be able to make it in, anyways. If'n ya wanna,> o'course.Further question. What is the probability that a randomly selected> president of the US quali'es for Mensa? Of course, does he really have to> be that intelligent, or can he just act the part?> We'll go a little further... Due to the system of elections, the selection test is obviouslyconducted and evaluated by the population. What does that say about theintellegence of them?> Jon Miller Jeroen Boschma === Subject: Re: Tough Probability question... Jim Ferry club for people with>high IQ scores. To qualify, your IQ must be at least 132, putting you in >the>top 2% of the general population. If a group of 10 people are chosen at>random, what is the probability that at least two of them qualify for>Mensa?> IQ tests are allegedly designed so that > (1) distribution of IQ scores may be treated as normal,> Why normal? Log-normal would be more appropriate.>Ask the designers of the tests, not me! > (1) the mean IQ score is 100,> (3) the standard deviation of IQ scores is 15. === Subject: pls help arith prob!please help me with the following simple problem that is frustrating meimmensely!:An old car has to travel a 2-mile route, uphill and down. Because it is soold, the car can climb the 'rst mile-the ascent-no faster than an averagespeed of 15mph. How fast does the car have to travel the 2nd mile (thedescent-where it can go faster) in order to achieve an average speed of 30mph for the entire trip?thank you very very much! === Subject: Re: pls help with the following simple problem that is frustrating me>immensely!:>>An old car has to travel a 2-mile route, uphill and down. Because it is so>old, the car can climb the 'rst mile-the ascent-no faster than an average>speed of 15mph. How fast does the car have to travel the 2nd mile (the>descent-where it can go faster) in order to achieve an average speed of 30>mph for the entire trip?>>thank you very very much!>> Complete solution e-mailed to the address you had the integrity toprovide. === Subject: Re: pls help arith me with the following simple problem that is frustrating me> immensely!:An old car has to travel a 2-mile route, uphill and down. Because it is so> old, the car can climb the 'rst mile-the ascent-no faster than an average> speed of 15mph. How fast does the car have to travel the 2nd mile (the> descent-where it can go faster) in order to achieve an average speed of 30> mph for the entire trip?thank you very very much!What have you done so far? If s is the speed during the second half,can you 'nd a formula for the total time of the whole trip? === please help me with the following simple problem that is frustrating me> immensely!:>> An old car has to travel a 2-mile route, uphill and down. Because it is so> old, the car can climb the 'rst mile-the ascent-no faster than an average> speed of 15mph. How fast does the car have to travel the 2nd mile (the> descent-where it can go faster) in order to achieve an average speed of 30> mph for the entire trip?>> thank you very very much!Is this a Newtonian or an Einsteinian problem?--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 correcting both erasures and errors ofReed-Solomon codes (appeared in IEEE Transactions on Communications,vol. 51, no. algorithm, (Algorithm 2), todecode both erasures and errors, using an algorithm based on theEuclidean algorithm together with Berlekamp-Massey algorithm.I have tried to implement the pseudocode in MATLAB, and used Example 1to verify if my implementation works. The output of my implementationdoes not correspond at all with the output given in the example. My'rst problem is that the polynomial OMEGA^(b) is not computedaccording to the pseudocode.In the pseudocode, OMEGA^(b)(x) is multiplied by x, in line 41, butwhen I look at the output given in Example 1, the code is notmultiplied by x.Did anyone implement this algorithm? Any suggestions would be greatlyappreciatedJaco Versfeld === Subject: Shannon Marie C K10 1 3 11 = 25 Shannon was the 6th of 17 people to provide stats today, she wasthe 10th of over 150 people to provide sweety dothn't know her parent's years ofbirth.25+ Dad 28 8 /12525+ Mom 30 8 /123156 Shannon 24 7 82 205/160 9288Shannon 85 Marie 46 Jack 2525+ Sis 21 9 88 265/101 11539 Mom was likely born on day 242 (First Samuel 6) and mom was bornwith 123 days remaining in the year (Numbers 6). The parents were bornon days and in months adding to 74 (a factor of 666). Shannon was born330 days after dad's birthday, it's a combination of the 6th and 66thprimes (13 and 317). Shannon was born a total of 658 days after herparent's birthdays, it's the number of verses in Bible Book 6,prettier as Book 6 contains 24 chapters while Shannon was born on the24th. Her name adds to 156, it's a combination of 66 plus the 66thnon-prime (90). Her odd valued letters add to 78 and also her evenvalued letters add to 78 (6 times the 6th prime). Her given namescontain an average of 6 letters. Her repeating letters add to 45 (NewTestament Book 6). Her unrepeated letters exceed her repeating lettersby 66. The sisters were born on days of the year averaging 235, prettyas the 184th prime (1097) and the 184th non-prime (235) averages 666.Shannon's 'rst name adds to 184.78% of her middle name while hermiddle name adds to exactly 184% of her last name, again, the 184thprime and the 184th non-prime averages 666. Her initials, middle andlast letters add together for 108 (the 'rst 6 primes in primepositions).1-50 - Genesis51-90 - Exodus91-117 - Leviticus118-153 - Numbers154-187 - Deuteronomy188-211 - Joshua930-957 - Matthew958-973 - Mark974-997 - Luke998-1018 - John1019-1046 - Acts1047-1062 - Romans 123 <-Numbers 6, it is three times the 13th prime (41+41+41), keeping in mind that 13 is the 6th prime 188 <-the opening chapter of Book 6 is 6x6x6 short of the 404 verses of Bible Book 66, it is the 6th prime squared (13x13) short of the 357 verses of Daniel (also in part about 666) 193 <-Book 6 chapter 6 is the 44th prime, while 44 is in turn 66.666...% of 66 211 <-the terminating chapter of Book 6 is approximately 66.6% of the 66th prime (317) 357 <-the opening chapter of Book 6 plus the 6th prime squared is the 357 verses of Daniel (in part about 666) 404 <-the 6th prime squared (13x13) plus the 6th prime squared (13x13) plus 66 adds to the 404 verses of Bible Book 661062 <-666 plus 6x66 is a combination of the 658 verses of Bible Book 6 plus the 404 verses of Bible Book 66, and is the terminating chapter of New Testament Book 61070 <-666 plus the 404 verses of Book 66 is the 1070 verses of Job (Book 6+6+6)1213 <-Exodus terminates at chapter 90 (66th non- prime) with 1213 verses (the 198th or the 66+66+66th prime)1292 <-the 658 verses of Book 6 plus twice the 66th prime (317) is the 1292 verses of Isaiah (the Book contains 66 chapters) The parents were born on days 28 and 30, together these Bible Bookscontain 343 (7x7x7) verses and differ in length by 51 (17+17+17)verses. The parents were born on days of the month adding to 58 (the 7primes up to 17). The kids were born on days and in months and yearsadding to 231 (77+77+77).Primes Non-Primes 2 1 3 4 5 6 7 8 11 9 13 10 17 12 19 14 23 15 29 16 31 18 37 20 41 21 43 22 47 24 53 <-16th-> 25 --- --- 381 225 The last name adds to 25 (16th non-prime) and dad was born with 125days remaining in the year. Mom Jack (25) and her kids were born ondays of the month averaging 25 (16th non-prime). The parents were bornin months adding to 16 and the kids were born in months adding to 16.The family was born in months adding to 32 (16+16), Bible Book 32contains 48 (16+16+16) verses. The kids are separated by 6.16 years.Shannon has 16 letters, her vowels add to 32 (16+16). Her odd valuedletters add to 78 and also her even valued letters add to 78, it's acombination of the 16th prime (53) and the 16th non-prime (25). Hergiven names add to the 62nd and 32nd non-primes, together for 94(16+16p+16np) while her last name adds to the 16th non-prime. Hergiven names add together for 131 (16+16th prime) while her full nameadds to 156 (the 'rst 16 primes minus the 'rst 16 non-primes).Primes 2 61 3 67 5 71 7 73 11 79 13 83 17 89 19 97 23 101 29 103 31 107 37 109 41 113 43 127 47 131 <-32nd 53 137 59 139 Shannon was born 45 days closer to the end of the year than to thebeginning of the year. Shannon's repeating letters add to 45. The kidswere born on days of the month adding to 45. The females were born ondays 30, 24 and 21, together these Bible Books contain 1732 verses,it's 4 times the 433 verses of Romans, Bible Book 45. Shannon and dadgenerally have their birthdays on days of the year adding to 445. Thekids are together 13045 days old. There are 45 chapters in the Biblethat contain the length of 17 verses (pretty as 198 is the 153rdnon-prime, 198 exceeds it's 153rd non-prime position by 45, while 153is 1 through 17 and is the 117th non-prime, it's the terminatingchapter of Numbers and is the number of 'sh in the net in John 21).Primes 2 179 419 3 181 421 5 191 431 7 193 433 11 197 439 13 199 443 17 211 449 19 223 457 23 227 461 29 229 463 31 233 467 37 239 479 41 241 487 43 251 491 47 257 499 53 263 503 59 269 509 61 271 521 67 277 523 71 281 541 73 283 547 79 293 557 83 307 563 89 311 569 97 313 571 101 317 577 103 331 587 107 337 593 109 347 599 113 349 601 127 353 607 131 359 613 137 367 617 139 373 619 149 379 631 151 383 641 157 389 643 <-117th 163 397 647 167 401 653 173 409 659 On average the parents generally have their birthdays 117 dayscloser to the end of their years than to the beginning of their years.Psalm 117 brings Psalms up to 1929 verses, or three times the 117thprime (643). The family was born on days 28, 30, 24 and 21, togetherthese Bible Books contain 1929 verses (3 times the 117th prime and isthe running total of Psalms up to Psalm 117).Primes Non-Primes 2 1 3 4 5 6 7 8 11 9 13 10 17 12 19 14 23 15 29 16 31 18 37 20 41 21 43 22 47 24 53 25 59 <-17th-> 26 --- --- 440 251 Shannon adds to 85, she and her sister were born in years averaging85, it's 5 times 17 and is the 17th prime plus the 17th non-prime (59and 26), Ruth with 85 verses is the 17th shortest Book in the Bible.The kids were born in years adding to 170 (Deuteronomy 17). The 9different letters in Shannon's given names add to 102 (6x17 and is17+17p+17np) and she is missing 17 letters from her given names. Herprimes add to 51 (3x17), her squares and cubes add together for 17.Her consonants add to 132 (Numbers 7). Her little sister is 14.77years old.Primes Non-Primes 2 1 3 4 5 6 7 <-4th-> 8 <-Bible Book 8 contains 11 4 chapters, pretty as 13 8 is the 4th non-prime 17 19 -- 77 <-the 'rst 8 primes plus 8 more adds to the 85 verses of Bible Book 8 Primes In Prime Primes Positions 1 2 2 3 <- 3 3 5 <- 5 4 7 5 11 <- 11 6 13 7 17 <- 17 8 19 9 2310 2911 31 <- 3112 3713 41 <- 4114 4315 4716 5317 59 <- 5918 6119 67 <- 67 <-the 8th prime in prime positionR U T H <-Book 818 21 20 8 = 67 Both parents were born in the 8th month. Dad was born on the 28thwhile the parents were born on days of the month adding to 58 (Exodus8). Shannon adds to 85, she and her sister were born in yearsaveraging 85, there are 85 verses in Bible Book 8, Ruth (it's the'rst 8 primes plus 8 more). The little sister was born in 88 while Iam 9288 days older than Shannon. Shannon's name begins with the 19thletter of the alphabet (8th prime), her 'rst 8 letters add to 98(Leviticus 8). Shannon's consonants plus their positions togetherexceed her vowels plus their positions by 118 (88th non-prime). Book 8terminated at chapter 236 (twice the 88th non-prime), prettier as 236is the 185th non-prime while Book 8 contains 85 verses (it's the 'rst8 primes plus 8 more).Lucas 1 3 4 7 11 18 29 -- 73 <-the Lucas numbers up to 29 add to the 73 verses of Bible Book 29J O E L <-Bible Book 2910 15 5 12 = 42 <-29th non-primeC O P P E R <-29th element3 15 16 16 5 18 = 73 <-Book 29 and is the Lucas numbers up to 29, there is a copper riding a horse on the 1973 Canadian 25 cent pieceC E N T <-made out of 29th element3 5 14 20 = 42 <-29th non-prime The parents were born on days of the month averaging 29. Theparents were born on days of the month adding to 58, it's the 42ndnon-prime while 42 in turn is the 29th non-prime, while Bible Book 29is Joel (42). The last of the kids was born on day 265 (First Samuel29). The kids were together born 209 days closer to the end of theiryears than to the beginning of their years. Shannon was born anaverage of 329 days after her parent's birthdays. The family was bornon days 28, 30, 24 and 21, together these Bible Books contain 1929verses. Shannon was born with 160 days remaining in the year while thelittle sister was born 60 days further into her year than Shannon,perhaps one or more of the parents was born in 60. Anyway, dad waslikely born on day 240 (60+60+60+60).187 Dar 17 2 57 48/317 00Daryl 60 Shawn 65 Kabatoff 62187 Marcia 6 8 80 219/147 8571Marcia 45 Veronica 87 Acevedo 55248 Shannon 24 7 82 205/160 9288Shannon 85 Marie 46 Acevedo-Kabatoff 55-62 If you people think that you have the right to use my abusiveparents as tools and arrest and torture me, then I think that I shouldhave the right to ask women to marry me, or to marry Marcia and me,our last names add together for the 117 verses of Song of Solomon,it's the Bible's Book of Love. The nubile sweety was born on the 6thand has a 6 lettered 'rst name). Isaiah is the Book with 66 chapters,pretty as it is Book 23, or the 6th prime plus the 6th non-prime(13+10=23). Isaiah 4, 12 and 20 (adds to 6x6) each contains 6 verses.Isaiah 4:1 is about Marcia (and me), and 6 other women who are capableof feeling shame rather than pride, greed or lust, or who limit theirlove for traditions and for people who abide by their traditions. Youpeople have Egyptian penises on the roofs of your churches and linedcity streets with representations of penises, and had me tortured foryears for saying so, others just sat back in silence while they weredoing this to me, and similarly you remain silent and compassionlessnow that the arrests and torture have ceased. You people spentmillions of dollars having me tortured, and then annually you spendbillions on your decorated trees, I begged and begged for assistanceto 呈e the country (they tortured me for years at the U of S) and youpeople are so cheap that you can't even offer to buy me a cookie whenI bust my ass to show you evidence that your very name is a gift fromGod!!! Should Matthew's sister marry me, great, but if Marcia marriesme and then Matthew's sister marries Marcia and me, then Matthew isgoink to win himself a shiny new Cadillac!!! Good luck and may Godbless you!!!Daryl Shawn KabatoffBox 7134Saskatoon SaskatchewanCanadaS7K 4J1Isaiah 45:4, Ephesians 3:15 - God gives you your name!!!What a wonderful weddink there will beWhat a wonderful day for you and meChurch bells will chimeYou will be mineIn apple blossom time... === Subject: Re: Shannon Marie Jack - July 24th was the 6th of 17 people to provide stats today, she was>the bit>of a space cadet, the nubile sweety dothn't know her parent's years of>birth.<<The following (courtesy of Waxy.org) is sort of an unof'cial FAQexplaining the psychotic nonsense posted to Usenet by Shawn DarylKabatoff AKA Dar, AKA Probababbilities. And now AKA marcia andme.WARNING: Read below before even thinking about responding to thistwit.http://www.waxy.org/archive/2002/05/21/dar_kaba.shtml #000643Usenet has the tendency to provide a public forum for those who wouldnormally be scribbling in a closet. For example, take Daryl ShawnKabatoff. For the last few years, he's methodically gatheredstatistics from various sources, ranging from local newspaperobituary pages to the food court of the Saskatoon Midtown Plaza mall.With all the raw data he's collected, he's attempting to prove dailythat our full names are in mathematical harmony with our birthdays.His rants normally focus on a single individual he's met or readabout, starting with calculations related to their birthdate and fullnames, blending in whatever other personal information about theirfamily members, spouses, birthplace, and career he's been able tozealotry, and personal torment. I've never seen anything like it.With all the prime numbers, Fibonacci sequences and biblicalreferences, it's like reading the notebooks of Maximillian Cohen andJohn Nash combined. Unsurprisingly, several posts unfold to reveal ahistory of painful mental illness. If you have some time, take a look.I've detailed his posting history and a several sample posts below. Usenet Posting History:January 27, 1999 to July 5, 2000 as Catsco@home.comDecember 9, 2000 to May 4, 2001 as s.kabatoff@sk.sympatico.caOct 30, 2001 to Oct 31, 2001 as kabatoff@the.link.caJanuary 20, 2002 to April 17, 2002 as s_kabatoff@hotmail.com (originalposts have been removed from Google Groups archive)April 26, 2002 to Present as dar_kabatoff@hotmail.comSelected Posts:Tessa Lynne SmithDastageer Sakhizai and Helen SmithBrett David MakiAndrew Meredith CottonKathryn Lee HippersonAmanda Dawn NewtonMona Marie EtcheverryTony Peter NusplLisa Charlene McMillanGrant Allyn Wood Comments scarier still is that saskatoon is my hometown, though not my currentresidence. and every single place he's mentioned in his posts (mostnotably nervous harold's and the roastary) were either places i'vebeen (as it's a small city of 200K) or hangouts, ie. the two placesmentioned. chances are i could email some friends back home and 'ndout if they know of him, they (my friends that is) being of thebroadway-centred slacker ilk. myself, too, until i got out of there.eh, anyways. thought it odd to see all this. midtown mall. i ate mymeals there, whilst waiting several days in line for star wars episodeone, at the theatre across the street.posted by andy raad on May 22, 2002 06:20 PMFascinating. It's like he's trying to take chaos and bind it intowhatever rules he can 'nd, religious, logical and otherwise. Numbersand math have a reliable pattern, something that can always be provento true or false. People and religion do not. It reminds me of DarrenAronofsky's movie Pi. It's the story of an paraniod genius who istrying to 'nd a pattern in Pi. A group that takes interest in hiswork is convinced that the existence of Pi, a number whose existencecan be proven but no quanti'ed, is proof of the existence of God.Kabatoff's hunt for patterns in something as random as name selectionis a way to reconcile his deeply logical thought process with hiscon告cting religious views.posted by matt on May 23, 2002 Daryl yesterday,asking him if he'd be willing to create a numerological analysis forme. I also asked him if he had seen either Pi or A Beautiful Mind, andwhat he thought of them. If he replies, I'll be sure to post it.posted by Andy Baio on May pumpkin pies). I rubbedpumpkin pie all over my breasts for him, and my breasts turned orange.I am a pumpkin for Shawn.posted by Trisha Blondie on July 24, 2002 10:41 PMUm, that's swell. So, you're in love with him?posted by Andy Baio Jehovah Witness that shot himselfand the lemon tarts were very bad, they were not only sour but wererubbery as well. Shawn said that the guy was some kind of JehovahWitness prophet, he saw in advance that the lemon tarts at his funeralwere to be very very bad, and so he shot himself. Shawn said that henever ate pumpkin pie at a funeral but would like to some day. Shawnlikes pumpkin pie and so I have been practicing to make very goodpumpkin pies.posted by Trisha Blondie on July 25, 2002 02:49 PMShawn said that the lemon tarts were sour, bitter don't think this guy takes notes. I think he has Total Recall, andit has driven him insane...posted by Todd Smith on December thousands of dollars a daytormenting Daryl... We got a deal on tormenting that 'scal year, itonly came to about 37cents a Kabatoff attempts to portray himself as a victim, but in fact heis a violent predatory pedophile who is well known to his local lawenforcement. In his post to multiple newsgroups with the subjectCollecting Mail For The Coming Anti-Christ, he encourages mothers tosend him photos of their naked daughters. Mr Kabatoff explains, Ipersonally did not want photographs being mailed to (the comingAnt-Christ) that were of underage children unless the parent wassigning consent. He is banned from virtually all the shopping mallsin his community because he stalks young people and sexually harassesthem. He has an extensive arrest record which includes sexualmolestation charges. He's been hospitalized in mental institutionsseveral his contact with young girls in many posts. Search newsgrouparchives for posts by him containing the word nubile. As part of hisharrassment, he provides personal details in a public forum, such asthe real names of real children, in these wanted Callie in my bed or Iwanted her and her sister dead+or+in+my+bed&hl=en&lr=&ie=UTF-8&selm=asqm35%24tjq5j%241% 40ID-136124.news.dfncis.de&rnuHe not only curses children and prays for their death in his posts, healso enjoys attending the funerals of young people: And so, sincenubile sweeties are found in greatest abundance at the funerals ofhigh school students, then it is the funerals of high school studentsthat make the very very best funerals, especially if there is food...I stuff my face (and my pockets) with all the good food and look atall the pretty nubile sweeties and have the time of my nubile+sex&hl=en&lr=&ie=UTF-8&scoring=d&selm=LfXN8.63042% 24R53.25142039%40twister.socal.rr.com&rnum=1 Many of his posts and crossposts his off-topic threatening and offensivemissives to countless newsgroups. Some people HAVE problems and somefolks ARE problems. Don't dismiss Mr. Kabatoff as a harmless nut. Whenhe sends these posts to any newgroup, please University of Saskatchewan.He'd hang out in the Arts computer lab and all you'd see is screens ofnumbers racing by on his laptop. I have an original copy of hisCollecting Mail for the Coming Anti-Christ pamphlet, and have seenhim be hauled away by campus security on more than one occasion. Myfriends and I refer to him as Crazy Number Man.posted by Mr. Somebody on Shawn for over two years with biggaps in between. He has seen Pi and didn't like it and didn't think itresembled him at all. (Wrong, it 'ts him to a tee) He doesn't havetotal recall and has stated that he travels with a lap top to notateitems. Also, he uses cut n' paste a lot if you read all the waythrough his ramblings. He is anti-social as shown by his angrystatements towards those who, by his own admission, have been kind(but not kind enough) to him. Still, he's intelligent and seems to beable to take a joke on occassion. That's where I came in. group(Unsolicited e-mail is deleted from the server unread if it comes from anyone not already in my addressbook. I'll never even see it) === Subject: Suzanne Marcus - January 15th 1951Friday September 15th 2000 259/107 15916M A R C U S13 1 18 3 21 19 = 75 I stopped at my brother's gallery, Vision Images at 14224 StonyPlain Road Edmonton, and met Suzanne, she is visiting from Israel andis originally from the UK. Suzanne provided stats for her three kids.there was a 4th child but he or she had died, Suzanne would notdiscuss the matter.175 Suzanne 15 1 51 15/350 +2225Suzanne 100 Marcus 75143 Yoash 13 11 72 318/48 5748Yoash 68 Marcus 75130 Shira 6 10 74 279/86 6440Shira 55 Marcus 75103 Ohad 29 9 78 272/93 7894Ohad 28 Marcus 75 Suzanne was born Susan (74) Marcus (75), her name at birth added tothe 149 verses of Bible Book 48. Her initials add to 32, Bible Book 32is Jonah (48) with 48 verses. Her 'rst kid was born with 48 daysremaining in the year. Her 'rst kid's day, month and year of birthadds to 96 (48+48), and I am 5748 days older than him. Her kids wereborn on days of the month adding to 48. Suzanne's even valued lettersadd with their positions for 96 (48+48). Suzanne's even valued lettersin even positions add to 32 (Book 32 contains 48 verses) and add withtheir positions for 48, her name exceeds her 'rst kid's name by 32.The 'rst and last kids are males, these brothers have 'rst namesaveraging 48. Suzanne adds to 100 and exceeds her 'rst son's 'rstname by 32 (Book 32 contains 48 verses). Shira's 279th day of birthexceeds her 130 valued name by the 149 verses of Bible Book 48.Primes Non-Primes Lucas 2 1 1 3 4 3 5 6 4 7 8 7 11 9 11 13 10 18 17 12 29 19 14 47 23 15 76 29 16 123 31 18 199 37 20 322 41 21 521 43 22 843 47 <-15th-> 24 <-15th-> 1364 <-Jeremiah is Book 24 with 1364 verses Suzanne was born on the 15th, her last name adds to 75 (5x15). Herrepresented letters add to 120 (1 through 15). Her unrepeated lettersadd to 65 and her Fibonacci valued letters add to 65 (Exodus 15), it'sthe 47th non-prime while 47 in turn is the 15th prime. The sons wereborn on days 13 and 29, these Bible Books together contain 1015verses. Mom and the 'rst kid have 'rst names adding together for 168(Deuteronomy 15). Mom and the kids have 'rst names adding to 251(First Samuel 15). Shira's names average 65 (Exodus 15), it's the 47thnon-prime while 47 in turn is the 15th prime (65 is the 15th non-primein prime position). Shira was born with 86 days remaining in the year,it is 15 plus the 15th prime plus the 15th non-prime, or simply15+15p+15np. The last two kids have 'rst names adding to 55 and to28, together these Bible Books contain 280 verses (the number ofverses in Bible Book 15). I meet mom on the 15th.Primes Non-Primes 2 1 3 4 5 6 7 8 11 9 13 10 17 12 19 14 23 15 29 16 31 18 37 20 41 21 43 22 47 24 53 25 59 26 61 27 67 28 71 30 73 32 79 33 83 34 89 35 97 36 101 38 103 39 107 40 109 42 113 44 127 45 131 46 137 48 139 49 149 50 151 <-36th-> 51---- ---5350 1917 Suzanne was born in 51, her kids have 'rst names adding togetherfor 151. The kids have 'rst names adding to 68, 55 and 28,corresponding to Exodus 18, Exodus 5 and Genesis 28, together for 51.The kids have vowels in their 'rst names adding together for 42(Bible Book 42 contains 1151 verses). Mom and the kids were born ondays of the year that are the 9th, 252nd, 220th and 214th non-primenumbers, together for 695, the are 695 verses in Second Samuel and 95verses in Bible Book 51. Suzanne Marcus (75) and her kids were born in years adding to 275,prettier as mom's full name adds to 175. The Marcus (75) kids wereborn an average of 75.45 years into the century. The last kid's name adds to the 27th prime, and the last two kidshave names differing in value by 27. The last two kids have 'rstnames adding together for the 83 verses of Bible Book 55, while Shiraadds to 55.Primes 2 61 3 67 5 71 7 73 11 79 13 83 17 89 19 97 23 101 29 103 <-27th 31 107 37 109 41 113 43 127 47 131 53 137 59 139 The kids are separated by 2146 days. The 'rst two kids were bornin years adding to 146. There are 146 verses in Bible Book 30, thekids were born in months adding to 30, the daughter's name adds to130. The kids were born on days of the year adding to 869, correspondingto Bible Book 28 (1 through 7) chapter 7, it is Hosea (the Mexicanprophet). The kids were together born with 227 days remaining in theiryears (the 7x7th prime). Mom and the kids are together 45807 days old. Mom's even valued letters add to 72, she 'rst gave birth in 72 andlast gave birth on day 272, her name exceeds Ohad's name by 72. Thelittle brother's name adds to 72.027% of big brother's name (who wasborn in 72). The brothers have 'rst names adding to the 49th and 19thnon-primes, together for 68 (the value of the 'rst brother's 'rstname).Primes Non-Primes Fibonacci Lucas 2 1 0 1 3 4 1 3 5 6 1 4 7 8 2 7 11 9 3 11 13 10 5 18 17 12 8 29 19 14 13 47 23 15 21 76 29 16 34 123 31 18 55 199 37 20 89 322 41 <-13th-> 21 <-13th-> 144 <-13th-> 521 --- --- 238 154 <-Lamentations Suzanne has 13 letters, her last name begins with the 13th letterof the alphabet and adds to 75 (13+13p+13np). She 'rst gave birth onthe 13th, last gave birth on the 29th (29 chapters in Bible Book 13).The 'rst of the kids has a name adding to 143 (11x13), the second hasa name adding to 130 (Numbers 13), the last has a name adding to 103(Leviticus 13). Ohad's 272nd day of birth exceeds his 103 valued nameby 169 (13x13). Mom and the kids were born on days of the month addingto 63 (Exodus 13). The kids were born in years adding to 224 (Judges13). The 'rst two kids were together born with 134 days remaining intheir years (Numbers 17, the 'rst of the chapters to contain thelength of 13 verses).Non-Primes 1 57 110 158 207 255 303 4 58 111 159 208 256 304 6 60 112 160 209 258 305 8 62 114 161 210 259 306 9 63 115 162 212 260 30810 64 116 164 213 261 30912 65 117 165 214 262 31014 66 118 166 215 264 31215 68 119 168 216 265 31416 69 120 169 217 266 31518 70 121 170 218 267 31620 72 122 171 219 268 318 <-252nd21 74 123 172 220 270 31922 75 124 174 221 272 32024 76 125 175 222 273 32125 77 126 176 224 274 32226 78 128 177 225 275 32327 80 129 178 226 276 32428 81 130 180 228 278 32530 82 132 182 230 279 32632 84 133 183 231 280 32733 85 134 184 232 282 32834 86 135 185 234 284 32935 87 136 186 235 285 33036 88 138 187 236 286 33238 90 140 188 237 287 33339 91 141 189 238 288 33440 92 142 190 240 289 33542 93 143 192 242 290 33644 94 144 194 243 291 33845 95 145 195 244 292 33946 96 146 196 245 294 34048 98 147 198 246 295 34149 99 148 200 247 296 34250 100 150 201 248 297 34351 102 152 202 249 298 34452 104 153 203 250 299 34554 105 154 204 252 300 34655 106 155 205 253 301 34856 108 156 206 254 302 350 Suzanne is 49.66 years old, she and the 'rst kid were born inyears adding to 123 (Numbers 6). Mom and the kids were born on days ofthe year that are the 9th, 252nd, 220th and 214th non-prime numbers,together for the 695 verses of Second Samuel, it is 666 plus 6 plusthe 6th prime (13) plus the 6th non-prime (10). Mom and the kids wereborn in years that are the 36th (6x6th), 52nd, 53rd and 57thnon-primes, together for 198 (66+66+66). The 'rst of the kids wasborn on the 13th (6th prime), followed by a kid on the 6th, followedby a kid on the 29th (6+6p+6np). The 'rst of the kids was born in 72(6x6+6x6 or 66+6), the second was born in 74 (a factor of 666),actually in 1974 (3 times the 658 verses of Bible Book 6). The 'rstkid's name adds to 143, chapter 666 brings Ecclesiastes up to 143verses. The brothers have names averaging 123 (Numbers 6). Yoash's'rst name adds to 90.666..% of his last name (90 is the 66thnon-prime). The kids were born in years averaging 74.666... Today thekids are together 27666 days old, prettier as Daniel is in part about666 and is Bible Book 27. The kids are separated by 6x357.666... days(357 verses in Daniel, it's in part about 666).1-50 - Genesis51-90 - Exodus91-117 - Leviticus118-153 - Numbers154-187 - Deuteronomy188-211 - Joshua930-957 - Matthew958-973 - Mark974-997 - Luke998-1018 - John1019-1046 - Acts1047-1062 - Romans 123 <-Numbers 6, it is three times the 13th prime (41+41+41), keeping in mind that 13 is the 6th prime. Numbers 6 is 3 times the 6th prime in prime position 188 <-the opening chapter of Book 6 is 6x6x6 short of the 404 verses of Bible Book 66, it is the 6th prime squared (13x13) short of the 357 verses of Daniel (also in part about 666) 193 <-Book 6 chapter 6 is the 44th prime, while 44 is in turn 66.666...% of 66 211 <-the terminating chapter of Book 6 is approximately 66.6% of the 66th prime (317) 357 <-the opening chapter of Book 6 plus the 6th prime squared is the 357 verses of Daniel (in part about 666) 404 <-the 6th prime squared (13x13) plus the 6th prime squared (13x13) plus 66 adds to the 404 verses of Bible Book 661062 <-666 plus 6x66 is a combination of the 658 verses of Bible Book 6 plus the 404 verses of Bible Book 66, and is the terminating chapter of New Testament Book 61070 <-666 plus the 404 verses of Book 66 is the 1070 verses of Job (Book 6+6+6)1213 <-Exodus terminates at chapter 90 (66th non- prime) with 1213 verses (the 198th or the 66+66+66th prime)1292 <-the 658 verses of Book 6 plus twice the 66th prime (317) is the 1292 verses of Isaiah (the Book contains 66 chapters) The 6440 days I am older than Shira is 5 times the 1288 verses ofNumbers, or 23 times the 280 verses of Ezra. I am 35x184 days older,the 184th prime (1097) and the 184th non-prime (235) averages 666. Iam 8x805 days older than Shira (805 is the 666th non-prime). The kidswere born on days of the century adding to 82683, pretty as chapter683 is Isaiah 4. Isaiah 4, 12 and 20 (adds to 6x6) each contain 6verses. Isaiah 4 is in part about 7 women feeling shame, pretty as itis chapter 683, this 683 is the 124th prime while chapter 124 in turnis Numbers 7. Numbers 7 (124) is the 7x7th prime (227) short of thenumbers up to the 17th non-prime (351). Numbers 17 (134) is 217 shortof the numbers up to the 17th non-prime (351), prettier as 217 is the170th non-prime while chapter 170 is Deuteronomy 17. Also at my brother's gallery was a Canadian Caucasian male whodressed as a Hindu and was actually a Hindu. The Hindu handed me asmall mauve colored lea呈t called Mantra Chanting, on the top of thelea呈t was a picture of the Hindu god Shiva, contents as follows: Mantra Chanting Om namah Sivaya Om namah Sivaya Om namah Sivaya Om namah Sivaya We will sing traditional Indian prayers that worship the different deities which represent the different aspects of life, such as love, prosperity, wisdom, playfulness, death, masculine-feminin etc... Mantras that are the names of these divine beings or qualities. The Indian melodies naturally lead into a deeper state of consciousness. We will move from slow, meditative to wild, ecstatic singing. The chants are interwoven by longer periods of silence. Sundays starting Sept 3rd 8 p.m. at Vision Images 14224 Stony Plain Road On donation To inform please call 487-7578 Suzanne is in town because she is involved in an Anti-Christiancult, she is a disciple of some local kid named John de Ruiter whotraveled to India and supposedly learned the truth (some kind of truththat does not involve Jesus). When I 'rst saw Suzanne she was sittingwith her back to the wall, she did not know the people in the room,she appeared to be uncomfortable, so I approached her and asked herwhat she was doing with these Hindus. Brother Randal's quest forspirituality involved 'rst opening his heart and doors to dead NorthAmerican Indians and now to East Indian Hindus. My parents had hiredHindus to repeatedly chemically lobotomize me, now I travel toEdmonton and 'nd my brother involved in Hinduism, and I'm pretty surethat he now embraces Hinduism just to continue to be abusive to me,and his company may be the only one involved in all of Alberta thatpromotes Hinduism with actual Hindu prayer meetings, and on Sunday. Icame to Edmonton to assist my brother's business, but then decidedagainst it as I do not wish to see him prosper and use his facilitiesto spread Hinduism or any other Anti-Christian religion. My previousattempts to assist my brother just opened doors for him to shovelabuse my way, it's high time I learned my lesson that my enemies arecoming out of my own household (Micah 7:6, Matthew 10:36, Luke 12:53).Randal and Suzanne are both seekers of truth, but are wanting truthwithout having to accept Jesus as their God and Creator of Heaven andEarth. Suzanne's quest for truth moved her from the UK to Israel, andnow to Edmonton where she could listen to a group of Hindus chantpraises to Siva, and make Shira known to Marcia and me. Marcia andShira differ in age by 2131 days (the 321 prime), they were born inyears adding to the 154 verses of Lamentations.187 Dar 17 2 57 48/317 00Daryl 60 Shawn 65 Kabatoff 62187 Marcia 6 8 80 219/147 8571Marcia 45 Veronica 87 Acevedo 55172 Shira 6 10 74 279/86 6440Shira 55 Acevedo-Kabatoff 55-62 Anyway, if you people think that you have the right to use myabusive parents as tools and arrest and torture me, then I think thatI should have the right to ask women to marry me, or to marry Marciaand me, our last names add together for the 117 verses of Song ofSolomon, it's the Bible's Book of Love. The nubile sweety was born onthe 6th and has a 6 lettered 'rst name). Isaiah is the Book with 66chapters, pretty as it is Book 23, or the 6th prime plus the 6thnon-prime (13+10=23). Isaiah 4, 12 and 20 (adds to 6x6) each contains6 verses. Isaiah 4:1 is about Marcia (and me), and 6 other women whoare capable of feeling shame rather than pride, greed or lust, or wholimit their love for traditions and for people who abide by theirtraditions. You people have Egyptian penises on the roofs of yourchurches and lined city streets with representations of penises, andhad me tortured for years for saying so, others just sat back insilence while they were doing this to me, and similarly you remainsilent and compassionless now that the arrests and torture haveceased. You people spent millions of dollars having me tortured, andthen annually you spend billions on your decorated trees, I begged andbegged for assistance to 呈e the country (they tortured me for yearsat the U of S) and you people are so cheap that you can't even offerto buy me a cookie when I bust my ass to show you evidence that yourvery name is a gift from God!!! Should Shira marry me, great, but ifMarcia marries me and then Shira marries Marcia and me, then Yoash andOhad are both goink to win themselves a shiny new Cadillac!!! And ifShira turns out to be some sort of sexual acrobat then her mom willwin a shiny new Cadillac too. Good luck and may God bless you!!!Daryl Shawn KabatoffBox 7134Saskatoon SaskatchewanCanadaS7K 4J1Isaiah 45:4, Ephesians 3:15 - God gives you your name!!!What a wonderful weddink there will beWhat a wonderful day for you and meChurch bells will chimeYou will be mineIn apple blossom time... === Subject: Inverting the Laplace trasformI have some problems of inverting the Laplace transform of this functionF(s)=sh(k*s)/s^2 ; k=constsh(x) is hyperbolic sinusObviously, F(s) has a simple pole at s=0. Now by de'nition to recover f(t)we need to take the residue at s=0 from this expression:F(s)*e^(s*t)Result is k. But this is not correct. Where is my error? === Subject: Re: Inverting the problems of inverting the Laplace transform of this function>F(s)=sh(k*s)/s^2 ; k=const>sh(x) is hyperbolic sinus>Obviously, F(s) has a simple pole at s=0. Now by de'nition to recover f(t)>we need to take the residue at s=0 from this expression:>F(s)*e^(s*t)>Result is k. But this is not correct. Where is my error?Do you have any reason to think that this F(s) should be a Laplacetransform? Note that if f(t) is an exponentially bounded function(the kind of function for which the Bromwich inversion formula is valid) its Laplace transform F(s) satis'es |Lf(s)| <= A/(Re(s)-a) for some constants a and A when Re(s) > a. Even if you allowdistributions involving a 'nite number of derivatives of such functions,the result will be bounded by a polynomial in |s|. But your F hasno such bound. So I doubt it's the Laplace transform of anythingsensible.Robert Israel israel@math.ubc.caDepartment of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada V6T 1Z2 === Subject: minimization appreciate any help.g(t,c_i, f_i(t)), i=1..n where c_i is a parameter non-linear to g andf_i(t) known functions.I want to 'nd c_i so that g(t)=g(t,c_i,f_i(t))=:g_i(t) for all iWhat I have tried so far is to minimize integral (sum_i,j (g_i(t)-g_j(t))^2) dtor equivalently minimizeintegral ((sum_i g_i(t)^2)-(1/n)*(sum_i g_i(t))^2) dtSo Ive differentiated the above term with respect to c_j and set itto 0:int (g_j(t)) dt = 1/n * int (sum_i g_i(t)) dt.But this is not very helpful since I cant solve for the cs.Any suggetions? Or any === Subject: Re: Boolean axioms come from? Are these simply highly reliable patternsIt depends on what you want to deduce from them. It seems to me thatthe axioms and de'nitions are chosen so that interesting theorems maybe deduced. History works back to them, logic works forward from them.> that emerge out of empirical reality?Can axiom be thought of as a pattern or template, that given one form> of truth can imply another?Can an axiom be modeled therefore as an edge in a directed graph?> Given some truth (state) and an applicable axiom it moves me to> another truth (state)?I think of trees (upside ones with the leaves at the top) with nodeslike this A B C | / | / * | DAt * a rule has been applied to three previous theorems A, B, C toproduce a new theorem D. Here the number three is not signi'cant. I't's 0, D as an axiom. 1 and 2 are common.If this is true, doesn't it imply that all transformations can be> modeled by a Turing machine?A Turing Machine can con'rm that a deduction in a formal system iscorrect (if it is) but it cannot discover all invalid to be removed if you're e-mailing me. === Subject: Re: Boolean Algebra - Arithmetic Relationship> I think of trees (upside ones with the leaves at the top) with nodes> like this A B C> | /> | /> *> |> DAt * a rule has been applied to three previous theorems A, B, C to> produce a new theorem D. Here the number three is not signi'cant. If> it's 0, D as an axiom. 1 and 2 are common.Are rules, operations, and axioms essentially different forms of thesame thing?Is it possible to de'ne a grammar where any syntactically correctstatement is also semantically meaningful and 鮠rue'? Where I can'twrite a gramatically correct statement that is is false?-Steve === Subject: Re: Considering study of mathematics or physics after age 50X-Cise: tanbanso@iinet.net.auX-CompuServe-Customer: YesX-Coriate: admin@interspeed.co.nzX-Ecrate: tanandtanlawyers.comX-Punge: Micro$oftX-Sanguinate: themvsguy@email.comX-Terminate: SPA(GIS)X-Tinguish: Mark Grif'th X-Treme: C&C,DWSIn said:>I'm in my mid-'fties. Will my age be (perceived as) an impediment to>either undergraduate or graduate studies?By whom? The only place where it would seem relevant is in 'nding agood thesis advisor,which might not be relevant for a masters.>- how one chooses between/among programs in applied mathematics and>physics?Based on your own aptitudes and interests.>- level of effort/time required? Substantial. But if you have the interest, money, talent and time, Idon't see why not. Certainly if I had the money I would seriouslyconsider going back to school, 'rst for some review, second to get upto date and third for a PhD.-- Shmuel (Seymour J.) Metz, SysProg and JOATUnsolicited bulk E-mail will be subject to legal action. I reservethe right to publicly post or ridicule any abusive E-mail.Reply to domain Patriot dot net user shmuel+news to contact me. Donot reply to === Subject: Re: homoeomorphims between different dimensions? <3f8f75ef$3$fuzhry+tra$mr2ice@news.patriot.net> X-Cise: tanbanso@iinet.net.auX-CompuServe-Customer: YesX-Coriate: admin@interspeed.co.nzX-Ecrate: tanandtanlawyers.comX-Punge: Micro$oftX-Sanguinate: themvsguy@email.comX-Terminate: SPA(GIS)X-Tinguish: Mark Grif'th X-Treme: C&C,DWSIn Robin Chapman isomorphic to Z. Now is that a homework question?No, it's an obvious counterexample. -- Shmuel (Seymour J.) Metz, SysProg and JOATUnsolicited bulk E-mail will be subject to legal action. I reservethe right to publicly post or ridicule any abusive E-mail.Reply to domain Patriot dot net user shmuel+news to contact me. Donot reply to === Subject: Re: homoeomorphims said:>>It's isomorphic to Z. Now is that a homework question?No, it's an obvious counterexample.Counterexample to what? -- Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.htmlNeedless to say, I had the last laugh. Alan Partridge, _Bouncing Back_ (14 times) === Subject: Re: homoeomorphims between different at 12:10 PM, Robin Chapman isomorphic to Z. Now is that a homework question?>>No, it's an obvious counterexample.> Counterexample to what?> I think he missed the adjective local, or may not know aboutthe concept of homology at a point.Just to complete the thought: The i'th homology group of the space X at the point p is de'ned to be the relative group H_i(X, X {p}). If X is locally contractible at p, then one can replace this group by the following: H_i(U, dU) (two steps: 'rst is via excision, to H_i(U, U {p}) for U any neighborhood of p, and the second is the isomorphism between H_i(U, U{p}) and H_i(U, dU) [dU = boundary of U] for U a contractible neighborhood). This yields local homology for open subsets of R^n to be Z in dimension n, zero everywhere else.Dale === Subject: Re: Naive Q: Set theory, logic - which <1xUcb.14254$O85.6040@pd7tw1no> <3f79e264$7$fuzhry+tra$mr2ice@news.patriot.net> <3f82ebb8$3$fuzhry+tra$mr2ice@news.patriot.net> X-Cise: tanbanso@iinet.net.auX-CompuServe-Customer: YesX-Coriate: admin@interspeed.co.nzX-Ecrate: tanandtanlawyers.comX-Punge: Micro$oftX-Sanguinate: themvsguy@email.comX-Terminate: SPA(GIS)X-Tinguish: Mark Grif'th X-Treme: C&C,DWSIn 06:10 PM, Robert J. Kolker said:>However, Goedel numbering schemes are somewhat arbitrary. They are >merely artifacts for self reference, hence any theorems proven about>a particular set of numbers used as Goedel encoding are unlikely to>be of any fundemental importance in number theory.Fundamental importance is a separate issue. An unimportant statementabout natural numbers is still a statement about natural numbers.-- Shmuel (Seymour J.) Metz, SysProg and JOATUnsolicited bulk E-mail will be subject to legal action. I reservethe right to publicly post or ridicule any abusive E-mail.Reply to domain Patriot dot net user shmuel+news to contact me. Donot reply to === Subject: Re: Naive Q: Set theory, logic - which comes 'rst? <1xUcb.14254$O85.6040@pd7tw1no> <3f79e264$7$fuzhry+tra$mr2ice@news.patriot.net> <3f82ebb8$3$fuzhry+tra$mr2ice@news.patriot.net> <3f8c413c$18$fuzhry+tra$mr2ice@news.patriot.net> <3f8fd096$5$fuzhry+tra$mr2ice@news.patriot.net> X-Cise: tanbanso@iinet.net.auX-CompuServe-Customer: YesX-Coriate: admin@interspeed.co.nzX-Ecrate: tanandtanlawyers.comX-Punge: Micro$oftX-Sanguinate: themvsguy@email.comX-Terminate: SPA(GIS)X-Tinguish: Mark Grif'th X-Treme: C&C,DWSIn PM, Torkel Franzen said:> Different how?The general usage of the term true has nothing to do withconstructing models.-- Shmuel (Seymour J.) Metz, SysProg and JOATUnsolicited bulk E-mail will be subject to legal action. I reservethe right to publicly post or ridicule any abusive E-mail.Reply to domain Patriot dot net user shmuel+news to contact me. Donot reply to === Subject: Re: Naive Q: Set theory, logic - which comes 'rst?Cc: nobodyShmuel (Seymour J.) usage of the term true has nothing to do with> constructing models. What does constructing models have to do with the observation orassumption that an arithmetical sentence is true? === Subject: Re: Naive Q: Set theory, logic - which comes 'rst? <3f79e264$7$fuzhry+tra$mr2ice@news.patriot.net> <3f82ebb8$3$fuzhry+tra$mr2ice@news.patriot.net> <3f8c413c$18$fuzhry+tra$mr2ice@news.patriot.net> <3f8fd096$5$fuzhry+tra$mr2ice@news.patriot.net> tanbanso@iinet.net.auX-CompuServe-Customer: YesX-Coriate: admin@interspeed.co.nzX-Ecrate: tanandtanlawyers.comX-Punge: Micro$oftX-Sanguinate: themvsguy@email.comX-Terminate: SPA(GIS)X-Tinguish: Mark Grif'th X-Treme: C&C,DWSIn Wikstr?m) said:>Here is a de'nition which I hope will satisfy you: The natural>numbers are the things obtainable from the two operations (the 'rst>of which is actually a constant) 0:N and s:N->N.That's still not a de'nition. >This is an example of an inductive de'nition.No. You have neither de'ned 0 and s not given any axioms for them.>I have (see above).above is some numenclature from Peano and the claim This is anexample of an inductive de'nition.>I hope we agree that the Peano Postulates are consistent.I hope that they are ;-)>Here you have an example of a statement about natural numbers >which we agree is true, but which cannot be proven from the >Peano Postulates.My hoping that they are consistent does not make them consistent. Myagreeing that they are consistent would not make them consistent.>I will show how the Peano Postulates can be proven from the>following de'nition:>The natural numbers are the things obtainable from the two>operations 0:N and s:N->N.That's too imprecise to be a de'nition, and you would need moremachinery to get Peano's Postulates.>This de'nition is complete if we understand operation the right>way. Namely, there should be no sence of equality for the things we>obtain by theese operations other than that two expressions built up>from signs denoting theese operations denote the same thing iff they>are equal. This is vaguely formulated, but I hope it is clear what I>mean.I know what you mean, but how are you going to formulate it rigorouslywithout presupposing something equivalent to Peano's Postulates?-- Shmuel (Seymour J.) Metz, SysProg and JOATUnsolicited bulk E-mail will be subject to legal action. I reservethe right to publicly post or ridicule any abusive E-mail.Reply to domain Patriot dot net user shmuel+news to contact me. Donot reply to === Subject: Re: Open set de'nitionX-Cise: tanbanso@iinet.net.auX-CompuServe-Customer: YesX-Coriate: admin@interspeed.co.nzX-Ecrate: tanandtanlawyers.comX-Punge: Micro$oftX-Sanguinate: themvsguy@email.comX-Terminate: SPA(GIS)X-Tinguish: Mark Grif'th X-Treme: C&C,DWSIn said:>1.- The two concepts agree when the topology involved is that of all>open subsets of R. That is any open set in the topology is open in>the usual, elementary sense, that is the set is a neighborhood of all>its points.That's always true; you can de'ne a topolog either in terms ofneighborhoods or in terms of open sets. Don't confuse the concept ofneighborhood witht he special case of open interval.>2.- For other topologies (say the collection of all subsets of R)a>set may be open according to one de'nition, closed according to the>other, or even both open and closed. The 2 de'nitions are>therefore unrelated.No. If you have two topologies on R, each has its own neighborhoods.The open sets of any topology are de'ned by its neighborhoods, andvice versa. If you are using a nonstandard topology for R then aneighborhood of a real x might not contain any open interval around x,and an open interval might not contain any neighborhood of its points.>There must be some general utility in de'ning open sets as the>elements of a properly de'ned topology.Sure. There are lots of topological spaces of interest besides thereal line. Although properly de'ned topology is redundant; if it'snot properly de'ned then it is not a topology.>Can someone please outline the reason? The most obvious example is to look at the plane rather than the line.You can no longer use open intervals as the basis for the standardtopology. You could use products of intervals, but it is oftenconvenient to use distance instead, which leads to the next example.If you have a metric space, you can de'ne a topology where the opensets are unions of open balls.Frequently it is convenient to de'ne a topology on a space offunctions. See any book on Functional Analysis for examples. Thesespaces are very important for both Mathematics and Physics, and havebeen used to prove important results in the theory of differentialequations.-- Shmuel (Seymour J.) Metz, SysProg and JOATUnsolicited bulk E-mail will be subject to legal action. I reservethe right to publicly post or ridicule any abusive E-mail.Reply to domain Patriot dot net user shmuel+news to contact me. Donot reply to === polynomials Well as I understand it, the resolvent cubic has roots aa'+bb', ab+a'b' and ab'+a'b. It should be a cubic since any automorphism that permutes the roots of the quartic, a, a', b, b' will permute the three values above.Bill.Michael don't see why the root of the> resolvent is equal to aa'+bb'.-Michael.>>OK, someone has pointed out the solution to me. I feel a bit stupid for>>not knowing it. I should.>>In a case like the one I mention, the cubic resolvent equation has a>>rational root, which is easily calculated. This leads to the evaluation>>I'm after, since that root is precisely the value aa' + bb' where the>>a's and b' are the conjugate pairs of the original roots of my quartic.>>Bill.> === Subject: are available if I want to study the foundations,> ie how newton and leibniz actually conceived calculus,You can read Newton himself. The Principia, for example, is availablein English.Leibniz? I don't know.Generally, see E Hairer, G and invalid to be removed if you're e-mailing me. === Subject: the foundations,>>ie how newton and leibniz actually conceived calculus,> You can read Newton himself. The Principia, for example, is available> in English.Leibniz? I don't know.Generally, see E Hairer, G Wanner Analysis by Its History Springer.> Look at Dover's The History of the Calculus and Its Conceptual Developmentby Carl B. BoyerOrigins in antiquity, medieval contributions, work of Newton, Leibniz, rigorous formulation. Treatment is verbal.Price $11.95url: http://store.yahoo.net/doverpublications/ by-subject-science-and-mathematics-mathematics-history-of-mathe matics-1.htmlor, for just the book,http://store.yahoo.net/doverpublications/0486605094. htmlMartin Cohen === Subject: Re: foundations of calculus tanbanso@iinet.net.auX-CompuServe-Customer: YesX-Coriate: admin@interspeed.co.nzX-Ecrate: tanandtanlawyers.comX-Punge: Micro$oftX-Sanguinate: themvsguy@email.comX-Terminate: SPA(GIS)X-Tinguish: Mark Grif'th X-Treme: C&C,DWSIn said:>sheesh - i was hoping that the rest of the world wasn't going to>following america's> descent-into-idiocy-by-reading-secondary-or-abridged-sources.. .. just>read the damn Principia - sheesh....And I was hoping that the rest of the world wasn't going to followAmerica's descent into idiocy by confusing origins with publicity. Thesecondary sources can be very useful in telling you where to look, andyou would have done well to consult them before making a fool ofyourself. The roots of Calculus go back well before Newton.-- Shmuel (Seymour J.) Metz, SysProg and JOATUnsolicited bulk E-mail will be subject to legal action. I reservethe right to publicly post or ridicule any abusive E-mail.Reply to domain Patriot dot net user shmuel+news to contact me. Donot reply to === Subject: Re: foundations of calculus> In >sheesh - i was hoping that the rest of the world wasn't going to>following america's> descent-into-idiocy-by-reading-secondary-or-abridged-sources.. .. just>read the damn Principia - sheesh....And I was hoping that the rest of the world wasn't going to follow> America's descent into idiocy by confusing origins with publicity. The> secondary sources can be very useful in telling you where to look, and> you would have done well to consult them before making a fool of> yourself. The roots of Calculus go back well before Newton.ro你nd I quote the OP:##what texts, if any, are available if I want to study thefoundations,##ie how newton and leibniz actually conceived calculusI made no alethic errors in my post. Yours was completely irrelevantto the OP.(a) the OP did not ask for the roots of Calculus which, as youastutely notice, go back well before Newton. The OP didn't ask aboutorigins. The OP didn't ask about publicity. To 'nd out what the OP_did_ ask for, either read the OP, or see (b), below.(b) the OP speci'cally asked for how Newton/Leibniz thought of theirtopic. I stand by my response: to understand what a person thought oftheir chosen topic, there is no place better to go than the personhimself.(c) almost unfailingly, secondary sources are crap. This, combinedwith the increasing practice of 2ndary sources being the _only_ sourceused exacerbates the idiocy problem I mentioned initially.(d) wrt Newton speci'cally, the only good secondary source I've seenis by (if I recall the name correctly - it's been awhile) DanaDensmore. It will be clear to anyone at all familiar with this bookthat my recognition of this as a good secondary source is completelyconsonant with (c), above.confuse origins with publicity? lol - good onecdj === Subject: Vito Rizzuto - February 21st 1946Friday April 26th 2002 116/249 16504R I Z Z U T O18 9 26 26 21 20 15 = 135 I am posting Vito Rizzuto's stats again because Shriner/FreemasonDon Ocean is repeatedly calling me a pedophile. I have never sexuallyassaulted anybody, I have never been charged with sexual assault, Ihave never been arrested for sexual assault, and I am not sexuallyattracted to children. In 1988 I criticized the phallic worship in theProtestant and Catholic churches and was repeatedly arrested andtortured at the U of S for years. Ruby would have me arrested forfailing to kiss her God-damned ass and wear the clothes she was alwaystrying to force upon me (and because Protestants and Catholics wereupset with my words and lobbied her to shut me up), Ruby would have mearrested and chemically lobotomized, and then she would come to thepsychiatric ward and force her choice of clothes upon me there.Eventually I found myself internet access at the U of S and postedCollecting Mail For The Coming Anti-Christ, in the essay I spoke indefense of people to wear their own choice of clothes, and thisincluded defending the rights of women and girls to go topless if theywanted. Now Don Ocean calls me a pedophile, and as a result of DonOcean, somebody in Hawaii has begun doing the same. First the fellowlibels me in the WaxyOrg (aka MauiCop) this fellow quotes his own materialposted as asbeing truthful, saying that I have been repeatedly arrested for sexualassault and that I was a pedophile. Now as a result, people inSaskatoon are calling me a pedophile and are threatening to beat me upand kill me. The Saskatoon police are not in the habit of chargingpeople for assault when they give me beatings (in fact they arrestedme after James De Witt brutally assaulted me at the Seventh DayAdventist Church, I was brutally assaulted and then the policearrested me and took me to the U of S to be tortured by Hindus), andthe doctors will not give me adequate pain relievers when these peoplecrack and break my ribs. The situation is quite unfair, and now VitoRizzuto will have his stats posted daily until the situation isresolved.203 NicoloNicolo 68 Rizzuto 135225 LibertinaLibertina 90 Rizzuto 135201 Vito 21 2 46 52/313 +4014Vito 66 Rizzuto 135177 MariaMaria 42 Rizzuto 135 Mom's 'rst name adds to 90 (66th non-prime), Exodus contains 1213verses (66+66+66th prime) and terminates at chapter 90 (66thnon-prime). Vito adds to 66, mom and the little sister have 'rstnames averaging 66. The kids have 'rst names adding together for 108(the 'rst 6 primes in prime positions). The kids have 'rst namesdiffering in value by the 24 chapters of Bible Books 6 and 10 (6thnon-prime). Dad has a 6 lettered 'rst name, there are 24 letters inall the 'rst names, the number of chapters in Books 6 and 10 (6thnon-prime). All 'rst names add together for 266. Dad and Vito have'rst names adding together for 134, corresponding to Numbers 17 with13 verses (the 6th prime). Mom and Vito have 'rst names averaging 78(6 times the 6th prime). Dad and Vito have full names adding togetherfor the 404 verses of Bible Book 66, Revelation. Vito was born on the21st, corresponding to Ecclesiastes (chapters 660 to 671). Vito hasconsonants adding to 132 (66+66). Primes In Prime Primes Positions 1 2 2 3 <- 3 3 5 <- 5 4 7 5 11 <- 11 6 13 7 17 <- 17 8 19 9 2310 2911 31 <- 3112 3713 41 <- 41 --- 108 Vito Rizzuto (135) was hot for Cammalleni (83), the names differ invalue by 52, pretty as Vito was born on the 52nd day of the year.Giovanna (83) Cammalleni (83) was born with names adding to the 23rdprime and to the 23rd prime, together for 46, and she gets a husbandthat was born in 46.166 Giovanna 48Giovanna 83 Cammalleni 83 Vito married Giovanna (83) Cammalleni (83). She was born with 18(6+6+6) letters adding to 166. Both of her names added to the 83verses of Second Timothy (the 16th Book of the New Testament). Hernames added to 83 and 83, corresponding to Exodus 33 and Exodus 33,together for 66. At birth, Vito and Giovanna had 29 letters in theirnames, or 6 plus the 6th prime (13) plus the 6th non-prime (13), thereare 29 (6+6p+6np) chapters in Bible Book 13 (the 6th prime), there are29 (6+6p+6np) verses in chapter 666 (Ecclesiastes 7). At birth Vitoand Giovanna had 29 letters adding together for 367 (First Chronicles29). Vito's sister's 'rst name adds to 42 (the 29th non-prime), BibleBook 29 is Joel (42). Now Giovanna's name adds to 218 (twice the 29thprime). Nicolo's name adds to 203 (7x29). Leonardo's name adds to 219,or 3 times the 73 verses of Bible Book 29. Libertina was born in 73(the length of Book 29 and is the Lucas numbers up to 29). Leonardoand Libertina have 'rst names adding together for 174 (6x29). Dad andthe 'rst two kids have 'rst names adding together for 218 (twice the29th prime). The males were born in years adding to 182 (Deuteronomy29 with 29 verses).201 Vito 21 2 46 52/313 +4014Vito 66 Rizzuto 135218 Giovanna 48Giovanna 83 Rizzuto 135203 Nicolo 67Nicolo 68 Rizzuto 135219 Leonardo 69Leonardo 84 Rizzuto 135225 Libertina 73Libertina 90 Rizzuto 135Lucas 1 3 4 7 11 18 29 -- 73 <-the Lucas numbers up to 29 add to the 73 verses of Bible Book 29J O E L <-Bible Book 2910 15 5 12 = 42 <-29th non-primeC O P P E R <-29th element3 15 16 16 5 18 = 73 <-Book 29 and is the Lucas numbers up to 29, there is a copper riding a horse on the 1973 Canadian 25 cent pieceC E N T <-made out of 29th element3 5 14 20 = 42 <-29th non-prime The have three kids, the 'rst and last of the kids bear Vito'sparent's names, so the daughter's 'rst name adds to 90 (66thnon-prime). The kids have 'rst names adding together for 242 (FirstSamuel 6), all names in the family add together for 1066. The kidswere born in 67, 69 and 73, these are the 19th prime, 50th non-primeand the 21st prime, together for 90 (66th non-prime and the value ofthe daughter's 'rst name). Mom and her sons have 'rst names addingtogether for 235... the 184th prime (1097) and the 184th non-prime(235) averages 666. The brothers have names averaging 211, it isapproximately 66.6% of the 66th prime (317) and is the terminatingchapter of Bible Book 6. Book 6 chapter 6 (193) plus the terminatingchapter of Book 6 (211) adds together for the 404 verses of Bible Book66. Daughter's 'rst name not only adds to 90 (66th non-prime), buther 'rst name adds to 66.666...% of her last name. This is a familyof 5, the 4014 days dad is older than me is the 959 verses of BibleBook 5 short of the 666th prime (4973).Primes Non-Primes 2 1 3 4 5 6 7 8 11 9 13 10 17 12 19 14 23 15 29 16 31 18 37 20 41 21 43 22 47 24 53 25 59 26 61 27 67 28 71 30 73 32 79 33 83 34 89 35 97 36 101 38 103 39 107 40 109 42 113 44 127 45 131 46 137 48 139 49 149 50 151 51 157 52 163 54 167 55 173 56 179 57 181 58 191 60 193 62 197 63 199 64 211 65 223 <-48th-> 66 227 68 229 69 233 70 239 72 241 74 251 75 257 76 263 77 269 78 271 80 277 81 281 82 283 84 293 85 307 86 311 87 313 88 317 <-66th-> 90 Vito adds to 66 (48th non-prime). Vito's 'rst name adds to48.888...% of his last name, God gives him a wife that was born in 48.Vito and his wife have 'rst names adding together for the 149 versesof Bible Book 48, Galatians. Vito's 201 valued name exceeds his 52ndday of birth by the 149 verses of Bible Book 48. Rizzuto (135) was hotfor Cammalleni (83), the 83 value of mom's maiden name is 61.48% ofthe 135 value of Rizzuto. The males were born in years adding to 182,the females in years adding to 121 (66.48%). The kids are missing 15letters from their 'rst names, these missing letters add to 248. The4014 days dad is older than me is 18 times the 48th prime (223),prettier as I was born on the 48th day of the year and with 317 daysremaining in the year (66th prime).1-50 - Genesis51-90 - Exodus91-117 - Leviticus118-153 - Numbers154-187 - Deuteronomy188-211 - Joshua930-957 - Matthew958-973 - Mark974-997 - Luke998-1018 - John1019-1046 - Acts1047-1062 - Romans 123 <-Numbers 6, it is three times the 13th prime (41+41+41), keeping in mind that 13 is the 6th prime 188 <-the opening chapter of Book 6 is 6x6x6 short of the 404 verses of Bible Book 66, it is the 6th prime squared (13x13) short of the 357 verses of Daniel (also in part about 666) 193 <-Book 6 chapter 6 is the 44th prime, while 44 is in turn 66.666...% of 66 211 <-the terminating chapter of Book 6 is approximately 66.6% of the 66th prime (317) 357 <-the opening chapter of Book 6 plus the 6th prime squared is the 357 verses of Daniel (in part about 666) 404 <-the 6th prime squared (13x13) plus the 6th prime squared (13x13) plus 66 adds to the 404 verses of Bible Book 661062 <-666 plus 6x66 is a combination of the 658 verses of Bible Book 6 plus the 404 verses of Bible Book 66, and is the terminating chapter of New Testament Book 61070 <-666 plus the 404 verses of Book 66 is the 1070 verses of Job (Book 6+6+6)1213 <-Exodus terminates at chapter 90 (66th non- prime) with 1213 verses (the 198th or the 66+66+66th prime)1292 <-the 658 verses of Book 6 plus twice the 66th prime (317) is the 1292 verses of Isaiah (the Book contains 66 chapters) Vito is 4014 days older than me, his name adds to 201 (Joshua 14),his mom and daughter share the same 225 valued name (Judges 14). Thekids have odd valued letters in their 'rst names adding together for140. The letters that are neither prime nor square in the kids' givennames add to 196 (14x14). Vito and his daughter have names differingin value by 14. All 'rst names add to 391 (314th non-prime). Dad's name adds to 67+67+67. The 'rst of the kids was born in 67and has names differing in value by 67. These 'rst three familymembers have 'rst names adding to 66, 83 and 68, corresponding toExodus 16, 33 and 18, together for 67. This 67 is the 19th prime, thesecond kid was born in 69 (Exodus 19) and has a name adding to 219.The brothers were born in years adding to 136 (Numbers 19). Vito andthe last of the kids were born in years adding to 119. Perhaps mom was19 years old when she gave birth in 67 (the 19th prime). Mom's nameadds to twice 109 (Leviticus 19) while dad's name adds to 201 (3 timesthe 19th prime). The parents have names adding together for 419(Nehemiah 6 with 19 verses). Vito and his kids were born in yearsadding to 255 (First Samuel 19). Vito and his kids have 'rst namesaveraging 77 (the primes up to 19). The kids were born in years addingto 5909 (19x311). Libertina's last name adds to 150% of her 'rst name(150 chapters in Bible Book 19). Vito was born a multiple of 19 daysinto the century (16853=19x887). Vito's vowels add to 69 (Exodus 19).The 2460 verses of Bible Book 19 is19x19+19x19+19x19+19x19+19x19+19x19+19x19 minus 67 (the 19th prime). Vito's names differ in value by 69 and his second kid was born in69. Vito was born on the 21st and his third kid was born in 73 (21stprime). Vito was born on the 21st and his name adds to 201, and he waslikely 21 years old when the 'rst of the kids was born. Vito was born in 46, his 201 valued name exceeds it's 155thnon-prime position by 46. The kids have prime and square valuedletters in their 'rst names adding together for 46. Vito was born on day 52, it's the number of chapters in Bible Book24, while his daughter gets a name that exceeds his by 24. Vito and Iwere together born 530 days closer to the beginning of our years thanto the end of our years (Psalm 52). This 530 is a combination of the'rst three perfect numbers (6, 28 and 496), they have factors thatadd to form themselves:Perfects 6 - 1, 2, 3 28 - 1, 2, 4, 7, 14496 - 1, 2, 4, 8, 16, 31, 62, 124, 248 The males have 'rst names adding together for 218, and mom's nameadds to 218. Mom was born with 18 letters and took a last name thatbegins with the 18th letter of the alphabet, it is a last name thatadds to 135 (Numbers 18). Vito and his sister have 'rst names addingtogether for 108 (Leviticus 18). Rizzuto adds to 135 (the 103rd non-prime), the 11 different lettersutilized in the construction of the 'rst names for the kids addtogether for 103.3x3x3x3x3x3 3x3x3 103 <- the 3x3x3rd prime----------- 859 <- the number of verses in Bible Book 3 The parents were born in 46 and 48, Bible Books 46 and 48 contain437 and 149 verses. These Books contain an average of 293 verses whilethe 437 is 293.28% of the 149. The 437 and 149 are the 353rd non-primeand 35th prime, and so it is pretty that there would be 35 letters inthe family 'rst names, and pretty that the last name would add to135. Mom and her sons have 'rst names adding together for 235. Thebrothers have 'rst names adding together for 152 (Numbers 35).Libertina Kabatoff adds to 152 (Numbers 35), prettier as 293 is the62nd prime while Kabatoff adds to 62. Rizzuto adds to 135, or 57 plus the 57th non-prime (78). The mainBooks of end-times prophecy are Daniel with 357 verses and Revelationwith 404 verses, or 57 plus the 57th prime (269) plus the 57thnon-prime (78).Primes Non-Primes 2 1 3 4 5 6 7 8 11 <-5th-> 9 Vito and his sister Maria have 'rst names adding to 66 and 42,together these Bible Books contain 1555 verses. Vito has 11 lettersand a 'rst name adding to a multiple of 11, his kids have 'rst namesadding together for 11x11+11x11 (11 is the 5th prime). Then Vitomarries Giovanna (83) Cammalleni (83), there are 83 verses in BibleBook 55, and she soon 'nds herself in a family of 5. The 5th of 5family members has a name adding to 225, prettier as 25 is not only5x5 but is 5 plus the 5th prime (11) plus the 5th non-prime (9),keeping in mind that Bible Book 5 contains 959 verses. Perhaps mom was25 (5x5 or 5+5p+5np) years old when she gave birth to the 5th of 5family members. Libertina's 'rst name adds to a multiple of 5 andalso a multiple of 9 (5th non-prime). Libertina's (the 5th of 5 familymembers) 'rst 5 letters add together for dad's 46th year of birth. Myname adds to 187 (the terminating chapter of Bible Book 5), it is5x5x5 plus twice the 5th prime in prime position (31). If Libertinatook my 62 (twice the 5th prime in prime position) valued last name,then her names would have an average value of 76 (55th non-prime).Lamentations is Bible Book 25 with 154 verses, the 154th prime is 887while Vito was born on the 19x887th day of the century, pretty becauseif Libertina married me then he would be lamenting. Vito and his kidsalready have 'rst names adding together for 308, or twice the 154verses of Lamentations. Note that Bible Books 5 and 5x5 differ inlength by 805 verses (the 666th non-prime). And Old Testament Book 9(the 5th non-prime) and New Testament Book 9 (the 5th non-prime)together contain 959 verses (the number of verses of Book 5). Primes In Prime Primes Positions 1 2 2 3 <- 3 3 5 <- 5 4 7 5 11 <- 11 6 13 7 17 <- 17 8 19 9 2310 2911 31 <- 3112 3713 41 <- 4114 4315 4716 5317 59 <- 59 --- 167 Esther Book 17 Vito (66) was born on day 52, it is an average of 59 (the 17thprime). His sister's name adds to 177 (3 times the 17th prime). Vitoand his sister have names averaging 189 (the 'rst 17 primes minus the'rst 17 non-primes). Vito and Giovanna have names differing in valueby 17 (7th prime, the primes up to 7 add to 17). Giovanna's name addsto 218 (Book 7 chapter 7). Vito and Giovanna were born with last namesadding together for 218 (Book 7 chapter 7). The 'rst of the kids getsa 'rst name adding to a multiple of 17 and he was born in 67 (Exodus17). The second gets a 'rst name adding to 7 times the 7th non-prime(12). The brothers have 'rst names adding to 68 and 84 (a span of17). The daughter gets a name adding to 225 (Book 7 chapter 7+7). Thekids were born in 67, 69 and 73, corresponding to Exodus 17, 19 and23, together for 59 (the 17th prime). Libertina's names differ invalue by 45 (45 chapters contain the length of 17 verses), she mighttake my name and end up with 17 letters.Primes Non-Primes 2 1 3 4 5 6 7 8 11 9 13 10 17 12 19 14 23 15 29 16 31 18 37 20 41 21 43 22 47 24 53 25 59 <-17th-> 26 --- --- 440 251 I wanted 17 French fry girls at my weddink, they would throw frenchfries high up into the air, the french fries would fall to the groundand get dirty, and nobody would ever eat french fries again. And Iwanted 59 big nosed Greeks with their big noses throwing hamburglersat us from across the street. And I wanted American Noel Nibblettblowing his bugle and leading a marching regiment of cadets up anddown the street while American Don Ocean and his Shriner friends ridecircles around them on their little motorscooters. Scientists haverecently discovered that tomatoes contain properties that help toprevent prostate cancer, in men, and since A&W allows one to take asmuch ketchup as they wanted, the Great A&W Rootbear was on the fasttrack to becoming an international symbol of health and fertility...so of course I wanted the Great A&W Rootbear to be the best man at myweddink. My weddink was soon approaching and it was goink to be aglorious affair, probababbly.187 Dar 17 2 57 48/317 00Daryl 60 Shawn 65 Kabatoff 62187 Marcia 6 8 80 219/147 8571Marcia 45 Veronica 87 Acevedo 55207 Libertina 73Libertina 90 Acevedo-Kabatoff 55-62 Anyway, if you people think that you have the right to use myabusive parents as tools and arrest and torture me, then I think thatI should have the right to ask women to marry me, or to marry Marciaand me, our last names add together for the 117 verses of Song ofSolomon, it's the Bible's Book of Love. The nubile sweety was born onthe 6th and has a 6 lettered 'rst name). Isaiah is the Book with 66chapters, pretty as it is Book 23, or the 6th prime plus the 6thnon-prime (13+10=23). Isaiah 4, 12 and 20 (adds to 6x6) each contains6 verses. Isaiah 4:1 is about Marcia (and me), and 6 other women whoare capable of feeling shame rather than pride, greed or lust, or wholimit their love for traditions and for people who abide by theirtraditions. You people have Egyptian penises on the roofs of yourchurches and lined city streets with representations of penises, andhad me tortured for years for saying so, others just sat back insilence while they were doing this to me, and similarly you remainsilent and compassionless now that the arrests and torture haveceased. You people spent millions of dollars having me tortured, andthen annually you spend billions on your decorated trees, I begged andbegged for assistance to 呈e the country (they tortured me for yearsat the U of S) and you people are so cheap that you can't even offerto buy me a cookie when I bust my ass to show you evidence that yourvery name is a gift from God!!! Should Libertina marry me, great, butif Marcia marries me and then Libertina marries Marcia and me, thenNicolo and Leonardo are both goink to win themselves a shiny newCadillac!!! And if Libertina turns out to be some sort of sexualacrobat then Vito and Giovanna are both goink to win themselves ashiny new Cadillac too. Good luck and may God bless you!!!Daryl Shawn KabatoffBox 7134Saskatoon SaskatchewanCanadaS7K 4J1Isaiah 45:4, Ephesians 3:15 - God gives you your name!!!What a wonderful weddink there will beWhat a wonderful day for you and meChurch bells will chimeYou will be mineIn apple blossom time...Note that every day Freemason Don Ocean libels me and calls me apedophile (or such) on the usenet, then I will repost the stats forthe following people: Daniel Bruner, Angel Cadwell, Brittanie Cecil,Carl Koopang, Jay Larson, Brian Lott, Adam Millikan, Cody Milliken,Christopher Ridsdale, Vito Rizzuto, Melissa Schultz, Erin Sorenson,Ann Wigdahl, Michael Winkler, or maybe more (more or less). === Subject: Re: Vito Rizzuto - February 26th 2002 116/249 16504>>R I Z Z U T O>18 9 26 26 21 20 15 = 135>> I am posting Vito Rizzuto's stats again because Shriner/Freemason>Don Ocean is repeatedly calling me a pedophile. I have never sexually<<The following (courtesy of Waxy.org) is sort of an unof'cial FAQexplaining the psychotic nonsense posted to Usenet by Shawn DarylKabatoff AKA Dar, AKA Probababbilities. And now AKA marcia andme.WARNING: Read below before even thinking about responding to thistwit.http://www.waxy.org/archive/2002/05/21/dar_kaba.shtml #000643Usenet has the tendency to provide a public forum for those who wouldnormally be scribbling in a closet. For example, take Daryl ShawnKabatoff. For the last few years, he's methodically gatheredstatistics from various sources, ranging from local newspaperobituary pages to the food court of the Saskatoon Midtown Plaza mall.With all the raw data he's collected, he's attempting to prove dailythat our full names are in mathematical harmony with our birthdays.His rants normally focus on a single individual he's met or readabout, starting with calculations related to their birthdate and fullnames, blending in whatever other personal information about theirfamily members, spouses, birthplace, and career he's been able tozealotry, and personal torment. I've never seen anything like it.With all the prime numbers, Fibonacci sequences and biblicalreferences, it's like reading the notebooks of Maximillian Cohen andJohn Nash combined. Unsurprisingly, several posts unfold to reveal ahistory of painful mental illness. If you have some time, take a look.I've detailed his posting history and a several sample posts below. Usenet Posting History:January 27, 1999 to July 5, 2000 as Catsco@home.comDecember 9, 2000 to May 4, 2001 as s.kabatoff@sk.sympatico.caOct 30, 2001 to Oct 31, 2001 as kabatoff@the.link.caJanuary 20, 2002 to April 17, 2002 as s_kabatoff@hotmail.com (originalposts have been removed from Google Groups archive)April 26, 2002 to Present as dar_kabatoff@hotmail.comSelected Posts:Tessa Lynne SmithDastageer Sakhizai and Helen SmithBrett David MakiAndrew Meredith CottonKathryn Lee HippersonAmanda Dawn NewtonMona Marie EtcheverryTony Peter NusplLisa Charlene McMillanGrant Allyn Wood Comments scarier still is that saskatoon is my hometown, though not my currentresidence. and every single place he's mentioned in his posts (mostnotably nervous harold's and the roastary) were either places i'vebeen (as it's a small city of 200K) or hangouts, ie. the two placesmentioned. chances are i could email some friends back home and 'ndout if they know of him, they (my friends that is) being of thebroadway-centred slacker ilk. myself, too, until i got out of there.eh, anyways. thought it odd to see all this. midtown mall. i ate mymeals there, whilst waiting several days in line for star wars episodeone, at the theatre across the street.posted by andy raad on May 22, 2002 06:20 PMFascinating. It's like he's trying to take chaos and bind it intowhatever rules he can 'nd, religious, logical and otherwise. Numbersand math have a reliable pattern, something that can always be provento true or false. People and religion do not. It reminds me of DarrenAronofsky's movie Pi. It's the story of an paraniod genius who istrying to 'nd a pattern in Pi. A group that takes interest in hiswork is convinced that the existence of Pi, a number whose existencecan be proven but no quanti'ed, is proof of the existence of God.Kabatoff's hunt for patterns in something as random as name selectionis a way to reconcile his deeply logical thought process with hiscon告cting religious views.posted by matt on May 23, 2002 Daryl yesterday,asking him if he'd be willing to create a numerological analysis forme. I also asked him if he had seen either Pi or A Beautiful Mind, andwhat he thought of them. If he replies, I'll be sure to post it.posted by Andy Baio on May pumpkin pies). I rubbedpumpkin pie all over my breasts for him, and my breasts turned orange.I am a pumpkin for Shawn.posted by Trisha Blondie on July 24, 2002 10:41 PMUm, that's swell. So, you're in love with him?posted by Andy Baio Jehovah Witness that shot himselfand the lemon tarts were very bad, they were not only sour but wererubbery as well. Shawn said that the guy was some kind of JehovahWitness prophet, he saw in advance that the lemon tarts at his funeralwere to be very very bad, and so he shot himself. Shawn said that henever ate pumpkin pie at a funeral but would like to some day. Shawnlikes pumpkin pie and so I have been practicing to make very goodpumpkin pies.posted by Trisha Blondie on July 25, 2002 02:49 PMShawn said that the lemon tarts were sour, bitter don't think this guy takes notes. I think he has Total Recall, andit has driven him insane...posted by Todd Smith on December thousands of dollars a daytormenting Daryl... We got a deal on tormenting that 'scal year, itonly came to about 37cents a Kabatoff attempts to portray himself as a victim, but in fact heis a violent predatory pedophile who is well known to his local lawenforcement. In his post to multiple newsgroups with the subjectCollecting Mail For The Coming Anti-Christ, he encourages mothers tosend him photos of their naked daughters. Mr Kabatoff explains, Ipersonally did not want photographs being mailed to (the comingAnt-Christ) that were of underage children unless the parent wassigning consent. He is banned from virtually all the shopping mallsin his community because he stalks young people and sexually harassesthem. He has an extensive arrest record which includes sexualmolestation charges. He's been hospitalized in mental institutionsseveral his contact with young girls in many posts. Search newsgrouparchives for posts by him containing the word nubile. As part of hisharrassment, he provides personal details in a public forum, such asthe real names of real children, in these wanted Callie in my bed or Iwanted her and her sister dead+or+in+my+bed&hl=en&lr=&ie=UTF-8&selm=asqm35%24tjq5j%241% 40ID-136124.news.dfncis.de&rnuHe not only curses children and prays for their death in his posts, healso enjoys attending the funerals of young people: And so, sincenubile sweeties are found in greatest abundance at the funerals ofhigh school students, then it is the funerals of high school studentsthat make the very very best funerals, especially if there is food...I stuff my face (and my pockets) with all the good food and look atall the pretty nubile sweeties and have the time of my nubile+sex&hl=en&lr=&ie=UTF-8&scoring=d&selm=LfXN8.63042% 24R53.25142039%40twister.socal.rr.com&rnum=1 Many of his posts and crossposts his off-topic threatening and offensivemissives to countless newsgroups. Some people HAVE problems and somefolks ARE problems. Don't dismiss Mr. Kabatoff as a harmless nut. Whenhe sends these posts to any newgroup, please University of Saskatchewan.He'd hang out in the Arts computer lab and all you'd see is screens ofnumbers racing by on his laptop. I have an original copy of hisCollecting Mail for the Coming Anti-Christ pamphlet, and have seenhim be hauled away by campus security on more than one occasion. Myfriends and I refer to him as Crazy Number Man.posted by Mr. Somebody on Shawn for over two years with biggaps in between. He has seen Pi and didn't like it and didn't think itresembled him at all. (Wrong, it 'ts him to a tee) He doesn't havetotal recall and has stated that he travels with a lap top to notateitems. Also, he uses cut n' paste a lot if you read all the waythrough his ramblings. He is anti-social as shown by his angrystatements towards those who, by his own admission, have been kind(but not kind enough) to him. Still, he's intelligent and seems to beable to take a joke on occassion. That's where I came in. group(Unsolicited e-mail is deleted from the server unread if it comes from anyone not already in my addressbook. I'll never even see it) === Subject: Re: Vito Rizzuto - February 21st 1946Protestants and Catholics were upset with me saying that they had Egyptianpenises at the Vatican and on the roofs of their churches, and lobbied myabusive parents to have me treated. My parents quickly and complied andthen Protestants and Catholics sat on psychiatric appeal panel hearings andrepeatedly denied my release and repeatedly gave permission to predominantlyHindu psychiatrists to torture me. While this was goink on, Catholic Italianmobsters such as the Rizzuto family were no doubt tithing big bucks to theCatholic church. and were in turn hearing assurances that they were sure tobe goink to heaven. God is set to rub in your faces and spread youpeople out like the dung that you are. You honor traditions in place ofGod's Commandments, then periodically He takes away one of your children(see Exodus 20:5 and Hosea 4:6), and then you respond by giving yet moremoney to the churches (churches that teach you to turn trees into decoratedidols) for the favor of them burying your smitten kid and giving youadditional assurance that your support of their church results in yoursmitten kid goink to heaven. Italian Catholic Vito Rizzuto, you are ignorantand compassionless, you only have ears for traditions and you only havecompassion for the people that abide by your traditions. -Daryl S. Kabatoff> Friday April 26th 2002 116/249 16504>> R I Z Z U T O> 18 9 26 26 21 20 15 = 135>> I am posting Vito Rizzuto's stats again because Shriner/Freemason> Don Ocean is repeatedly calling me a pedophile. I have never sexually> assaulted anybody, I have never been charged with sexual assault, I> have never been arrested for sexual assault, and I am not sexually> attracted to children. In 1988 I criticized the phallic worship in the> Protestant and Catholic churches and was repeatedly arrested and> tortured at the U of S for years. Ruby would have me arrested for> failing to kiss her God-damned ass and wear the clothes she was always> trying to force upon me (and because Protestants and Catholics were> upset with my words and lobbied her to shut me up), Ruby would have me> arrested and chemically lobotomized, and then she would come to the> psychiatric ward and force her choice of clothes upon me there.> Eventually I found myself internet access at the U of S and posted> Collecting Mail For The Coming Anti-Christ, in the essay I spoke in> defense of people to wear their own choice of clothes, and this> included defending the rights of women and girls to go topless if they> wanted. Now Don Ocean calls me a pedophile, and as a result of Don> Ocean, somebody in Hawaii has begun doing the same. First the fellow> libels using> the name of Thomas (aka MauiCop) this fellow quotes his to quote the libel as> being truthful, saying that I have been repeatedly arrested for sexual> assault and that I was a pedophile. Now as a result, people in> Saskatoon are calling me a pedophile and are threatening to beat me up> and kill me. The Saskatoon police are not in the habit of charging> people for assault when they give me beatings (in fact they arrested> me after James De Witt brutally assaulted me at the Seventh Day> Adventist Church, I was brutally assaulted and then the police> arrested me and took me to the U of S to be tortured by Hindus), and> the doctors will not give me adequate pain relievers when these people> crack and break my ribs. The situation is quite unfair, and now Vito> Rizzuto will have his stats posted daily until the situation is> resolved.>> 203 Nicolo> Nicolo 68 Rizzuto 135>> 225 Libertina> Libertina 90 Rizzuto 135>> 201 Vito 21 2 46 52/313 +4014> Vito 66 Rizzuto 135>> 177 Maria> Maria 42 Rizzuto 135>> Mom's 'rst name adds to 90 (66th non-prime), Exodus contains 1213> verses (66+66+66th prime) and terminates at chapter 90 (66th> non-prime). Vito adds to 66, mom and the little sister have 'rst> names averaging 66. The kids have 'rst names adding together for 108> (the 'rst 6 primes in prime positions). The kids have 'rst names> differing in value by the 24 chapters of Bible Books 6 and 10 (6th> non-prime). Dad has a 6 lettered 'rst name, there are 24 letters in> all the 'rst names, the number of chapters in Books 6 and 10 (6th> non-prime). All 'rst names add together for 266. Dad and Vito have> 'rst names adding together for 134, corresponding to Numbers 17 with> 13 verses (the 6th prime). Mom and Vito have 'rst names averaging 78> (6 times the 6th prime). Dad and Vito have full names adding together> for the 404 verses of Bible Book 66, Revelation. Vito was born on the> 21st, corresponding to Ecclesiastes (chapters 660 to 671). Vito has> consonants adding to 132 (66+66).>> Primes> In Prime> Primes Positions> 1 2> 2 3 <- 3> 3 5 <- 5> 4 7> 5 11 <- 11> 6 13> 7 17 <- 17> 8 19> 9 23> 10 29> 11 31 <- 31> 12 37> 13 41 <- 41> ---> 108>> Vito Rizzuto (135) was hot for Cammalleni (83), the names differ in> value by 52, pretty as Vito was born on the 52nd day of the year.> Giovanna (83) Cammalleni (83) was born with names adding to the 23rd> prime and to the 23rd prime, together for 46, and she gets a husband> that was born in 46.>> 166 Giovanna 48> Giovanna 83 Cammalleni 83>> Vito married Giovanna (83) Cammalleni (83). She was born with 18> (6+6+6) letters adding to 166. Both of her names added to the 83> verses of Second Timothy (the 16th Book of the New Testament). Her> names added to 83 and 83, corresponding to Exodus 33 and Exodus 33,> together for 66. At birth, Vito and Giovanna had 29 letters in their> names, or 6 plus the 6th prime (13) plus the 6th non-prime (13), there> are 29 (6+6p+6np) chapters in Bible Book 13 (the 6th prime), there are> 29 (6+6p+6np) verses in chapter 666 (Ecclesiastes 7). At birth Vito> and Giovanna had 29 letters adding together for 367 (First Chronicles> 29). Vito's sister's 'rst name adds to 42 (the 29th non-prime), Bible> Book 29 is Joel (42). Now Giovanna's name adds to 218 (twice the 29th> prime). Nicolo's name adds to 203 (7x29). Leonardo's name adds to 219,> or 3 times the 73 verses of Bible Book 29. Libertina was born in 73> (the length of Book 29 and is the Lucas numbers up to 29). Leonardo> and Libertina have 'rst names adding together for 174 (6x29). Dad and> the 'rst two kids have 'rst names adding together for 218 (twice the> 29th prime). The males were born in years adding to 182 (Deuteronomy> 29 with 29 verses).>> 201 Vito 21 2 46 52/313 +4014> Vito 66 Rizzuto 135>> 218 Giovanna 48> Giovanna 83 Rizzuto 135>> 203 Nicolo 67> Nicolo 68 Rizzuto 135>> 219 Leonardo 69> Leonardo 84 Rizzuto 135>> 225 Libertina 73> Libertina 90 Rizzuto 135>> Lucas> 1> 3> 4> 7> 11> 18> 29> --> 73 <-the Lucas numbers up to 29 add to> the 73 verses of Bible Book 29>> J O E L <-Bible Book 29> 10 15 5 12 = 42 <-29th non-prime>> C O P P E R <-29th element> 3 15 16 16 5 18 = 73 <-Book 29 and is the Lucas> numbers up to 29, there> is a copper riding a> horse on the 1973> Canadian 25 cent piece>> C E N T <-made out of 29th element> 3 5 14 20 = 42 <-29th non-prime>> The have three kids, the 'rst and last of the kids bear Vito's> parent's names, so the daughter's 'rst name adds to 90 (66th> non-prime). The kids have 'rst names adding together for 242 (First> Samuel 6), all names in the family add together for 1066. The kids> were born in 67, 69 and 73, these are the 19th prime, 50th non-prime> and the 21st prime, together for 90 (66th non-prime and the value of> the daughter's 'rst name). Mom and her sons have 'rst names adding> together for 235... the 184th prime (1097) and the 184th non-prime> (235) averages 666. The brothers have names averaging 211, it is> approximately 66.6% of the 66th prime (317) and is the terminating> chapter of Bible Book 6. Book 6 chapter 6 (193) plus the terminating> chapter of Book 6 (211) adds together for the 404 verses of Bible Book> 66. Daughter's 'rst name not only adds to 90 (66th non-prime), but> her 'rst name adds to 66.666...% of her last name. This is a family> of 5, the 4014 days dad is older than me is the 959 verses of Bible> Book 5 short of the 666th prime (4973).>> Primes Non-Primes> 2 1> 3 4> 5 6> 7 8> 11 9> 13 10> 17 12> 19 14> 23 15> 29 16> 31 18> 37 20> 41 21> 43 22> 47 24> 53 25> 59 26> 61 27> 67 28> 71 30> 73 32> 79 33> 83 34> 89 35> 97 36> 101 38> 103 39> 107 40> 109 42> 113 44> 127 45> 131 46> 137 48> 139 49> 149 50> 151 51> 157 52> 163 54> 167 55> 173 56> 179 57> 181 58> 191 60> 193 62> 197 63> 199 64> 211 65> 223 <-48th-> 66> 227 68> 229 69> 233 70> 239 72> 241 74> 251 75> 257 76> 263 77> 269 78> 271 80> 277 81> 281 82> 283 84> 293 85> 307 86> 311 87> 313 88> 317 <-66th-> 90>> Vito adds to 66 (48th non-prime). Vito's 'rst name adds to> 48.888...% of his last name, God gives him a wife that was born in 48.> Vito and his wife have 'rst names adding together for the 149 verses> of Bible Book 48, Galatians. Vito's 201 valued name exceeds his 52nd> day of birth by the 149 verses of Bible Book 48. Rizzuto (135) was hot> for Cammalleni (83), the 83 value of mom's maiden name is 61.48% of> the 135 value of Rizzuto. The males were born in years adding to 182,> the females in years adding to 121 (66.48%). The kids are missing 15> letters from their 'rst names, these missing letters add to 248. The> 4014 days dad is older than me is 18 times the 48th prime (223),> prettier as I was born on the 48th day of the year and with 317 days> remaining in the year (66th prime).>> 1-50 - Genesis> 51-90 - Exodus> 91-117 - Leviticus> 118-153 - Numbers> 154-187 - Deuteronomy> 188-211 - Joshua>> 930-957 - Matthew> 958-973 - Mark> 974-997 - Luke> 998-1018 - John> 1019-1046 - Acts> 1047-1062 - Romans>> 123 <-Numbers 6, it is three times the 13th> prime (41+41+41), keeping in mind that> 13 is the 6th prime>> 188 <-the opening chapter of Book 6 is 6x6x6 short> of the 404 verses of Bible Book 66, it is the> 6th prime squared (13x13) short of the 357> verses of Daniel (also in part about 666)>> 193 <-Book 6 chapter 6 is the 44th prime,> while 44 is in turn 66.666...% of 66>> 211 <-the terminating chapter of Book 6 is> approximately 66.6% of the 66th prime (317)>> 357 <-the opening chapter of Book 6 plus the 6th> prime squared is the 357 verses of Daniel> (in part about 666)>> 404 <-the 6th prime squared (13x13) plus the 6th> prime squared (13x13) plus 66 adds to the> 404 verses of Bible Book 66>> 1062 <-666 plus 6x66 is a combination of the 658> verses of Bible Book 6 plus the 404 verses> of Bible Book 66, and is the terminating> chapter of New Testament Book 6>> 1070 <-666 plus the 404 verses of Book 66 is the> 1070 verses of Job (Book 6+6+6)>> 1213 <-Exodus terminates at chapter 90 (66th non-> prime) with 1213 verses (the 198th or the> 66+66+66th prime)>> 1292 <-the 658 verses of Book 6 plus twice the> 66th prime (317) is the 1292 verses of> Isaiah (the Book contains 66 chapters)>> Vito is 4014 days older than me, his name adds to 201 (Joshua 14),> his mom and daughter share the same 225 valued name (Judges 14). The> kids have odd valued letters in their 'rst names adding together for> 140. The letters that are neither prime nor square in the kids' given> names add to 196 (14x14). Vito and his daughter have names differing> in value by 14. All 'rst names add to 391 (314th non-prime).>> Dad's name adds to 67+67+67. The 'rst of the kids was born in 67> and has names differing in value by 67. These 'rst three family> members have 'rst names adding to 66, 83 and 68, corresponding to> Exodus 16, 33 and 18, together for 67. This 67 is the 19th prime, the> second kid was born in 69 (Exodus 19) and has a name adding to 219.> The brothers were born in years adding to 136 (Numbers 19). Vito and> the last of the kids were born in years adding to 119. Perhaps mom was> 19 years old when she gave birth in 67 (the 19th prime). Mom's name> adds to twice 109 (Leviticus 19) while dad's name adds to 201 (3 times> the 19th prime). The parents have names adding together for 419> (Nehemiah 6 with 19 verses). Vito and his kids were born in years> adding to 255 (First Samuel 19). Vito and his kids have 'rst names> averaging 77 (the primes up to 19). The kids were born in years adding> to 5909 (19x311). Libertina's last name adds to 150% of her 'rst name> (150 chapters in Bible Book 19). Vito was born a multiple of 19 days> into the century (16853=19x887). Vito's vowels add to 69 (Exodus 19).> The 2460 verses of Bible Book 19 is> 19x19+19x19+19x19+19x19+19x19+19x19+19x19 minus 67 (the 19th prime).>> Vito's names differ in value by 69 and his second kid was born in> 69. Vito was born on the 21st and his third kid was born in 73 (21st> prime). Vito was born on the 21st and his name adds to 201, and he was> likely 21 years old when the 'rst of the kids was born.>> Vito was born in 46, his 201 valued name exceeds it's 155th> non-prime position by 46. The kids have prime and square valued> letters in their 'rst names adding together for 46.>> Vito was born on day 52, it's the number of chapters in Bible Book> 24, while his daughter gets a name that exceeds his by 24. Vito and I> were together born 530 days closer to the beginning of our years than> to the end of our years (Psalm 52). This 530 is a combination of the> 'rst three perfect numbers (6, 28 and 496), they have factors that> add to form themselves:>> Perfects> 6 - 1, 2, 3> 28 - 1, 2, 4, 7, 14> 496 - 1, 2, 4, 8, 16, 31, 62, 124, 248>> The males have 'rst names adding together for 218, and mom's name> adds to 218. Mom was born with 18 letters and took a last name that> begins with the 18th letter of the alphabet, it is a last name that> adds to 135 (Numbers 18). Vito and his sister have 'rst names adding> together for 108 (Leviticus 18).>> Rizzuto adds to 135 (the 103rd non-prime), the 11 different letters> utilized in the construction of the 'rst names for the kids add> together for 103.>> 3x3x3x3x3x3> 3x3x3> 103 <- the 3x3x3rd prime> -----------> 859 <- the number of verses in Bible Book 3>> The parents were born in 46 and 48, Bible Books 46 and 48 contain> 437 and 149 verses. These Books contain an average of 293 verses while> the 437 is 293.28% of the 149. The 437 and 149 are the 353rd non-prime> and 35th prime, and so it is pretty that there would be 35 letters in> the family 'rst names, and pretty that the last name would add to> 135. Mom and her sons have 'rst names adding together for 235. The> brothers have 'rst names adding together for 152 (Numbers 35).> Libertina Kabatoff adds to 152 (Numbers 35), prettier as 293 is the> 62nd prime while Kabatoff adds to 62.>> Rizzuto adds to 135, or 57 plus the 57th non-prime (78). The main> Books of end-times prophecy are Daniel with 357 verses and Revelation> with 404 verses, or 57 plus the 57th prime (269) plus the 57th> non-prime (78).>> Primes Non-Primes> 2 1> 3 4> 5 6> 7 8> 11 <-5th-> 9>> Vito and his sister Maria have 'rst names adding to 66 and 42,> together these Bible Books contain 1555 verses. Vito has 11 letters> and a 'rst name adding to a multiple of 11, his kids have 'rst names> adding together for 11x11+11x11 (11 is the 5th prime). Then Vito> marries Giovanna (83) Cammalleni (83), there are 83 verses in Bible> Book 55, and she soon 'nds herself in a family of 5. The 5th of 5> family members has a name adding to 225, prettier as 25 is not only> 5x5 but is 5 plus the 5th prime (11) plus the 5th non-prime (9),> keeping in mind that Bible Book 5 contains 959 verses. Perhaps mom was> 25 (5x5 or 5+5p+5np) years old when she gave birth to the 5th of 5> family members. Libertina's 'rst name adds to a multiple of 5 and> also a multiple of 9 (5th non-prime). Libertina's (the 5th of 5 family> members) 'rst 5 letters add together for dad's 46th year of birth. My> name adds to 187 (the terminating chapter of Bible Book 5), it is> 5x5x5 plus twice the 5th prime in prime position (31). If Libertina> took my 62 (twice the 5th prime in prime position) valued last name,> then her names would have an average value of 76 (55th non-prime).> Lamentations is Bible Book 25 with 154 verses, the 154th prime is 887> while Vito was born on the 19x887th day of the century, pretty because> if Libertina married me then he would be lamenting. Vito and his kids> already have 'rst names adding together for 308, or twice the 154> verses of Lamentations. Note that Bible Books 5 and 5x5 differ in> length by 805 verses (the 666th non-prime). And Old Testament Book 9> (the 5th non-prime) and New Testament Book 9 (the 5th non-prime)> together contain 959 verses (the number of verses of Book 5).>> Primes> In Prime> Primes Positions> 1 2> 2 3 <- 3> 3 5 <- 5> 4 7> 5 11 <- 11> 6 13> 7 17 <- 17> 8 19> 9 23> 10 29> 11 31 <- 31> 12 37> 13 41 <- 41> 14 43> 15 47> 16 53> 17 59 <- 59> ---> 167> Esther> Book 17>> Vito (66) was born on day 52, it is an average of 59 (the 17th> prime). His sister's name adds to 177 (3 times the 17th prime). Vito> and his sister have names averaging 189 (the 'rst 17 primes minus the> 'rst 17 non-primes). Vito and Giovanna have names differing in value> by 17 (7th prime, the primes up to 7 add to 17). Giovanna's name adds> to 218 (Book 7 chapter 7). Vito and Giovanna were born with last names> adding together for 218 (Book 7 chapter 7). The 'rst of the kids gets> a 'rst name adding to a multiple of 17 and he was born in 67 (Exodus> 17). The second gets a 'rst name adding to 7 times the 7th non-prime> (12). The brothers have 'rst names adding to 68 and 84 (a span of> 17). The daughter gets a name adding to 225 (Book 7 chapter 7+7). The> kids were born in 67, 69 and 73, corresponding to Exodus 17, 19 and> 23, together for 59 (the 17th prime). Libertina's names differ in> value by 45 (45 chapters contain the length of 17 verses), she might> take my name and end up with 17 letters.>> Primes Non-Primes> 2 1> 3 4> 5 6> 7 8> 11 9> 13 10> 17 12> 19 14> 23 15> 29 16> 31 18> 37 20> 41 21> 43 22> 47 24> 53 25> 59 <-17th-> 26> --- ---> 440 251>> I wanted 17 French fry girls at my weddink, they would throw french> fries high up into the air, the french fries would fall to the ground> and get dirty, and nobody would ever eat french fries again. And I> wanted 59 big nosed Greeks with their big noses throwing hamburglers> at us from across the street. And I wanted American Noel Nibblett> blowing his bugle and leading a marching regiment of cadets up and> down the street while American Don Ocean and his Shriner friends ride> circles around them on their little motorscooters. Scientists have> recently discovered that tomatoes contain properties that help to> prevent prostate cancer, in men, and since A&W allows one to take as> much ketchup as they wanted, the Great A&W Rootbear was on the fast> track to becoming an international symbol of health and fertility...> so of course I wanted the Great A&W Rootbear to be the best man at my> weddink. My weddink was soon approaching and it was goink to be a> glorious affair, probababbly.>> 187 Dar 17 2 57 48/317 00> Daryl 60 Shawn 65 Kabatoff 62>> 187 Marcia 6 8 80 219/147 8571> Marcia 45 Veronica 87 Acevedo 55>> 207 Libertina 73> Libertina 90 Acevedo-Kabatoff 55-62>> Anyway, if you people think that you have the right to use my> abusive parents as tools and arrest and torture me, then I think that> I should have the right to ask women to marry me, or to marry Marcia> and me, our last names add together for the 117 verses of Song of> Solomon, it's the Bible's Book of Love. The nubile sweety was born on> the 6th and has a 6 lettered 'rst name). Isaiah is the Book with 66> chapters, pretty as it is Book 23, or the 6th prime plus the 6th> non-prime (13+10=23). Isaiah 4, 12 and 20 (adds to 6x6) each contains> 6 verses. Isaiah 4:1 is about Marcia (and me), and 6 other women who> are capable of feeling shame rather than pride, greed or lust, or who> limit their love for traditions and for people who abide by their> traditions. You people have Egyptian penises on the roofs of your> churches and lined city streets with representations of penises, and> had me tortured for years for saying so, others just sat back in> silence while they were doing this to me, and similarly you remain> silent and compassionless now that the arrests and torture have> ceased. You people spent millions of dollars having me tortured, and> then annually you spend billions on your decorated trees, I begged and> begged for assistance to 呈e the country (they tortured me for years> at the U of S) and you people are so cheap that you can't even offer> to buy me a cookie when I bust my ass to show you evidence that your> very name is a gift from God!!! Should Libertina marry me, great, but> if Marcia marries me and then Libertina marries Marcia and me, then> Nicolo and Leonardo are both goink to win themselves a shiny new> Cadillac!!! And if Libertina turns out to be some sort of sexual> acrobat then Vito and Giovanna are both goink to win themselves a> shiny new Cadillac too. Good luck and may God bless you!!!>> Daryl Shawn Kabatoff> Box 7134> Saskatoon Saskatchewan> Canada> S7K 4J1>> Isaiah 45:4, Ephesians 3:15 - God gives you your name!!!>> What a wonderful weddink there will be> What a wonderful day for you and me> Church bells will chime> You will be mine> In apple blossom time...>> Note that every day Freemason Don Ocean libels me and calls me a> pedophile (or such) on the usenet, then I will repost the stats for> the following people: Daniel Bruner, Angel Cadwell, Brittanie Cecil,> Carl Koopang, Jay Larson, Brian Lott, Adam Millikan, Cody Milliken,> Christopher Ridsdale, Vito Rizzuto, Melissa Schultz, Erin Sorenson,> Ann Wigdahl, Michael Winkler, or maybe more (more or less). === Subject: Re: pls help arith prob!>Subject: pls help arith prob!>>please help me with the following simple problem that is frustrating me>immensely!:>>An old car has to travel a 2-mile route, uphill and down. Because it is so>old, the car can climb the 'rst mile-the ascent-no faster than an average>speed of 15mph. How fast does the car have to travel the 2nd mile (the>descent-where it can go faster) in order to achieve an average speed of 30>mph for the entire trip?>>thank you very very much!>Or, is it even possible??? Here's a similar problem:If I can only eat one donut per hour, can I eat two donuts in an hour?adam === Subject: Applying ergodic theorem to Brownian MotionI am reading a paper that applies the ergodic theorem where themeasure in question is the Wiener measure, and the transformation inquestion is w(t) --> (1/sqrt(a))w(at), where w refers to a continuouspath in Wiener space. Now, I can see that this transformation ismeasure preserving, but why is it ergodic? Intuitively it's verybelievable somehow, but I don't see the proof. Anyone know?Greg === Subject: Re: Applying ergodic theorem to Brownian Motion %-nbwyHlYn=yh4r^* v|!,o}OFN$97k ?cjI1!x?l>5*VZ)c/:of{IPQt legomir2000@yahoo.com (GregM) where the> measure in question is the Wiener measure, and the transformation in> question is w(t) --> (1/sqrt(a))w(at), where w refers to a continuous> path in Wiener space. Now, I can see that this transformation is> measure preserving, but why is it ergodic? Intuitively it's very> believable somehow, but I don't see the proof. Anyone know?Call the above transformation T_a, a>0.Let F be a bounded non-negative measurable function on the Wiener path space that is T_a invariant for all positive a.Let F_t be path-continuous version of the martingale E_t[F], where E_t is the conditional expectation with respect to the history of the Wiener process up to time t.Using the T_a-invariance of Wiener measure it is easy to check thatF_t(T_a) = F_{at} for all positive a and t.Therefore, for z>0,E[exp(-z*F_t)]= E[exp(-z*F_t(T_a))]= E[exp(-z*F_{at})],and the latter converges to E[exp(-z*F_{0})]=exp(-z*E[F])as a --> 0+, by the continuity of t--> F_t and the fact that F_0=E[F].That is, for z>0,t>0E[exp(-z*F_t)]=exp(-z*E[F}).This means that F_t is almost surely equal to its mean value E[F]. Since $F_t converges to F almost surely as t-->in'nity, we conclude that F=E[F] almost surely. So invariant functions are constant, so the group of transformations {T_a, a>0} is ergodic.It seems to me that the same argument, with a con'ned to the multiplicatice subgroup {b^n: n in Z} of positive real numbers generatedby a 'xed b>0, shows that each T_b is ergodic.-- A. === Subject: Re: Applying ergodic theorem to Brownian that applies the ergodic theorem where the> measure in question is the Wiener measure, and the transformation in> question is w(t) --> (1/sqrt(a))w(at), where w refers to a continuous> path in Wiener space. Now, I can see that this transformation is> measure preserving, but why is it ergodic? Intuitively it's very> believable somehow, but I don't see the proof. Anyone know?GregParadoxically named, the ergodic theorem applies to transformationsthat are not necessarily ergodic. === Subject: Re: Applying ergodic theorem to Brownian MotionThis reminds me of something that happened when I was an undergraduate. My adviser, Ethan Coven, taught a graduate course entitled Ergodic Theory. Coven had an evaluation of that course posted inside his of'ce. In response to the instruction to evaluate the course content (as opposed to the quality of teaching), one student had written something like, The course content was interesting but somewhat disappointing. Then again, I did misread the course catalogue entry. I was expecting a course on Erotic Theory.BTW, while I was still an undergraduate, someone swiped this evalution from Coven's bulletin board.-- Stephen J. Herschkorn herschko@rutcor.rutgers.edu === Subject: Re: Convergence of in'nite sum; can anyone solve this?> I am trying to prove the convergence of the following series;The limit as N approaches in'nity of;(1/(ln(N)) times (sum from 1 to N) of |mu(N)|/N,[as noted, the sum here should be sum(|mu(n)|/n, n= 1..N). I e-mailedyou this reply earlier, but as I received no acknowledgement and asyou have posted since then in this thread, I assume there's a goodchance you never saw it.]As Robin Chapman pointed out, if we set F(s) = sum(|mu(n)|/n^s), thenF(s) = zeta(s)/zeta(2s) for Re(s) > 1.Now F is a Dirichlet series with nonnegative coef'cients. Itconverges for Re(s) > 1, and (as follows from the above expression interms of zeta) is analytic for Re(s) > 1/2 except for a simple pole ats=1 with residue 1/zeta(2) = 6/pi^2. So by the Wiener-IkeharaTauberian theorem (see, e.g., Murty's problem book on analytic numbertheory) we have S(x):= sum(|mu(n)|, n <= x) = 6x/pi^2 + R(x), where R(x)/x -> 0 as x -> oo.Partial summation says that the sum you want is S(N)/N + int_1^N{S(t)/t^2 dt}.The term S(N)/N is bounded as N -> oo. In estimating the integral,6/pi^2 * log N pops out as the contribution from the main term in theestimate for S(x). The fact that R(x)/x -> 0 implies int_1^N{R(t)/t^2dt} = o(log N), so the limit you are after is 6/pi^2.One can also attack this problem elementarily. The key observation isthat |mu(n)| = sum(mu(d), d^2 | n). Then reverse the order ofsummation to obtain sum(|mu(n)|/n, n=1 .. N) = sum(mu(d)/d^2 * sum(1/k, k<= N/d^2), d <= sqrt(N)).The inner sum can be estimated as log(N/d^2) + gamma + O(d^2/N). Aftera little manipulation, one 'nds sum(|mu(n)|/n, n=1..N) = log N * sum(mu(d)/d^2, d<= sqrt(N)) + O(1).The sum here is almost 1/zeta(2); we have omitted the tail consistingof the terms with d> sqrt(N), which incurs an error which isO(sum(1/t^2, t > sqrt(N))) = O(1/sqrt(N)). This implies the 'rst termon the right hand side above is 6 log N/pi^2 + O(log(N)/sqrt(N)).Hence the entire sum is 6 log N/pi^2 + O(1), which again shows thelimit you're after is 6/pi^2.With a little more care about the error terms, the same method implies sum(|mu(n)|/n, n= 1..N) - 6 log N/pi^2in fact tends to a limit.Hope this helps,Paul === Subject: Re: Convergence of in'nite sum; can anyone solve this?> Larry Hammick convergence of the following series;>> The limit as N approaches in'nity of;>> (1/(ln(N)) times (sum from 1 to N) of |mu(N)|/N,Presumably meaning 1/ln(N) sum_{n=1}^N |mu(n)|/n> >> where |mu(N)| is the absolute value of the Mobius function, and ln(N)>> is the natural log of N.>> |mu(N)| is 1 whenever N is square-free, and 0 otherwise.>We know that>(1/(ln(N)) times (sum from 1 to N) of 1/N>has a limit at in'nity, from the def'n of Euler's constant. So, we are down>to showing that this has a limit:>(1/(ln(N)) times (sum from 1 to N) of k(N)/N>where k(N)=1 if N is divisible by a square, else k(N)=0.>But that expression must go to zero, because sum(1/N^2) is 'nite.No, that expression doesn't go to 0. For example, k(4 j) = 1 for any > positive integer j, so> 1/ln(N) sum_{n=1}^N k(n)/n >= 1/ln(N) sum_{j=1}^吶or(N/4) 1/(4j)> ~= ln(N/4)/(4 ln(N)) -> 1/4Robert Israel israel@math.ubc.ca> Department of Mathematics http://www.math.ubc.ca/~israel > University of British Columbia > Vancouver, BC, Canada V6T 1Z26/pi^2 does seem to be where the series is heading; see Matlab code below.sum = 0;jj = 1;mag(1) = 0;narray = 1:1:100000; for n=1:1:100000, f = factor(n); a = length(f); ff = unique(f); b re both algebraic integers.But don't you have the same problem in your object ring?Let x=1. Then x is an object. Let a = 1/2. Then a is not an object[1],but a number in a more inclusive ring. Then x = 2a, where x and 2are both objects.How does this differ from the 吧w in the algebraic integers?[1] According to what you've written, at least. Of course, sincelately you've been claiming that Goedel's work shows that human beingsare objects, too, who can tell? By the way, what is sqrt(2) times James Harris? Also, what is JamesHarris + George W. Bush + 4? I'm a little perplexed about how theobject ring's operations extend to humans.-- [I]t's good for the economy to charge for intellectual property, soopen source software cannot be good, while Microsoft is the mostfar-thinking company around and is doing it all for the good of thepublic. -- Linus Torvalds paraphrases Microsoft VP Craig Mundie === Subject: Re: Magidin is too many> --les ducs 031022webcast.htm