HDTenEightyP/NetNews huggingface dataset:
From: sibley@math.psu.edu (David Sibley)
Newsgroups: sci.math
Subject: Re: An elementary, "naturally occurring" p
Date: 7 Apr 92 16:47:02 GMT
Reply-To: sibley@math.psu.edu
Organization: Dept. of Mathematics, Penn State University

In article 25777@linus.mitre.org, bs@gauss.mitre.org (Robert D. Silverman) writes:
>In article <1992Apr1.183035.14916@Princeton.EDU> carabalo@phoenix.Princeton.EDU (David G. Caraballo) writes:
>:Prove or disprove that there exists a bijection f:[0,1] -> [0,1] that is
>:not continuous at any point. 
> 
>Doesn't the following function do it?
>
>f(x) = 1-x  if x is irrational.
>f(x) = x if x is rational.
>

Nope. That function is continuous at x = 1/2.

David Sibley
sibley@math.psu.edu
Xref: sparky sci.math:5796 rec.humor:16052
From: tim@crash.canon.co.uk
Newsgroups: sci.math,rec.humor
Subject: A new constant has been discovered!
Date: 9 Apr 92 09:02:42 GMT
Organization: Canon Research Centre Europe Ltd

There is a constant K associated with cartons of orange juice. K is positive
and non-variant for all designs of cartons. It is defined as follows:

K = easy-to-open-factor * easy-to-pour-factor

Tx. [should this go in the sci.math FAQ?]
--
-- Tim [O'Donoghue] <tim@crash.canon.co.uk> <...!uunet!uknet!canon!tim>
Newsgroups: sci.math
From: palais@binah.cc.brandeis.edu
Subject: Re: Why should Trace be so easy to calculate?
Reply-To: palais@binah.cc.brandeis.edu
Organization: Brandeis University
Date: Wed, 8 Apr 1992 13:38:10 GMT

I'm not sure that this is the kind of answer you are looking for, but
one reason that the trace is special (in a way that makes it easy to 
calculate) is that it is the only symmetric function of the eigenvalues
that is LINEAR. This means that one only has to calculate it for a 
basis. Now for the basis element E(i,j) for the n by n matrices, having 
a 1 in the i,j spot and zero elsewhere it is easy to check that 0 is 
an eigenvalue of multiplicity n if i is not equal to j and that when 
i=j, 0 is an eigenvale of multiplicity n-1 and 1 is a simple eigenvalue.
Those two facts of course don't change when you want to compute the 
other symmetric functions of the eigenvalues of a matrix A (or what is the
same, compute trace(A^i)), but since these invariants are not linear in 
A it doesn't help to compute them.
From: william@phnom-penh.berkeley.edu (Mr. Grosso)
Newsgroups: sci.math
Subject: Information Theory
Date: 7 Apr 92 04:04:38 GMT
Article-I.D.: agate.rr70mINN85g
Organization: U.C. Berkeley Math. Department.
NNTP-Posting-Host: phnom-penh.berkeley.edu


I'm looking for a good introductory book on the above. The book can assume a 
lot of (general math) background, but none in the specific subject.

E-mail recommendations would be most welcome.

Bill Grosso
Newsgroups: sci.math
From: Dave Dodson <dodson@convex.COM>
Subject: Re: factoid about new prime
Originator: dodson@bach.convex.com
Reply-To: dodson@convex.COM (Dave Dodson)
Organization: Engineering, CONVEX Computer Corp., Richardson, Tx., USA
Date: Tue, 7 Apr 1992 15:04:55 GMT
X-Disclaimer: This message was written by a user at CONVEX Computer
              Corp. The opinions expressed are those of the user and
              not necessarily those of CONVEX.

In article <1992Apr1.201324.25572@linus.mitre.org> bs@gauss.mitre.org (Robert D. Silverman) writes:
>In article <3987@crl.LABS.TEK.COM> scott@ferrari.LABS.TEK.COM (Scott Huddleston) writes:
>:It was mentioned on CNN that the new prime number discovered
>:recently is four times bigger then the previous record.
> 
>This is a (slight) exaggeration. 756839/216091 = 3.5024 times as big.

I thought the original posting was supposed to be humor:  If the previous
largest known Mersenne prime was P, CNN was saying that the new one is 4P,
which obviously has 4 as a factor, and therefore is not prime.

----------------------------------------------------------------------

Dave Dodson		                             dodson@convex.COM
Convex Computer Corporation      Richardson, Texas      (214) 497-4234
From: reid@durban.berkeley.edu (michael reid)
Newsgroups: sci.math
Subject: Re: Does Goedel's work apply to number theory?
Date: 14 Apr 1992 12:12:33 GMT
Organization: University of California, Berkeley
NNTP-Posting-Host: durban.berkeley.edu

In article <1992Apr9.224106.4243@wdl.loral.com> mab@wdl39.wdl.loral.com
(Mark A Biggar) writes:
>I believe that the following problem has been shown to be undecidable in first
>order logic + peano axioms (which should be sufficient for number threory):

>Call a finite set in positive integers LARGE if the smallest member
>of the set is greater then the number of elements in the set.

>Take the set of numbers 1..N and partition them as follows: randomly
>select a pair out of the set and color (label) one of the pair BLUE
>and the other RED.  Continue selecting pairs without replacement and coloring
>until the set is empty (if N is odd randomly color the left over element).

>Now for any given k, show that there exists a sufficiently large N such that
>it is guarenteed that the will exist a LARGE subset of the RED numbers
>containing k elements.

>It is possible (using higher order logic) to determine the function
>N=f(k) and determines the smallest N for a given k, but this function grows
>so fast (it's faster the ack(N,N)) that it is impossible to prove that it
>the the solution to the problem when limited to the above axiom system.

what am i missing here?  what's wrong with taking  N = 4k + 2 ?
that way, we have  2k + 1  red numbers, the  k  largest of which
are all greater than  k.

maybe your recipe for coloring the numbers needs some revision.
clarifications will be appreciated.
Newsgroups: sci.math
From: gerry@macadam.mpce.mq.edu.au (Gerry Myerson)
Subject: Re: Erdos (was Re: Fermat's Last Theorem)
Organization: ceNTRe for Number Theory Research
Date: Tue, 7 Apr 92 23:54:18 GMT

In article <1992Apr7.051902.4889@rata.vuw.ac.nz>, harper@kauri.vuw.ac.nz (John Harper) writes:
> 
> 
>  >Pardon my ignorance. Who is this Erdos dude?
> Several people have been abusing one another instead of answering the
> question. Paul Erdos is a very famous Hungarian mathematician (aged around
> 80 I'd guess) 

79; he'll be 80 next March. Does everyone know his story about being three 
billion years old? It seems that when he was a young man, the geologists 
said the world was a billion years old; now, they say it's four billion years 
old; ergo....

>who occasionally offers cash prizes of a few hundred dollars
> for solutions to problems that he hasn't solved himself and that interest him.
> The problems I have seen are HARD and are on combinatorics and number theory.
> 
> John Harper Mathematics Dept. Victoria University Wellington New Zealand

Gerry Myerson
Newsgroups: sci.math
From: gindrup@math.okstate.edu (Eric `'d'kidd' G..)
Subject: Re: Large primes; largest pi(n) known.
Organization: Oklahoma State University, Math Department
Date: Fri, 10 Apr 1992 20:44:14 GMT

In article <1992Apr7.103427.4558@csc.canterbury.ac.nz> wft@math.canterbury.ac.nz (Bill Taylor) writes:
>
>i.e. (I presume equivalently)
>
>what is the largest n for which pi(n) is known ?
>
These aren't exactly equivalent since there exists a way to compute pi(n)
using a complete table of pi(x) up to x=n/2.  The method is in Apostol's
First Big Book Of Number Theory, if someone has that handy and can post the
method...  So, the list of pi(n) is extendable indefinitely with an initial
table.  The problem is that the method is slow.  I remember from "The Book
of Prime Number Records" that pi(n) is known for something like 10^9 and
may be known for 10^12.  However, these numbers do not represent the ceiling
of known primes.

--Eric Gindrup ! gindrup@hardy.math.okstate.edu
Newsgroups: sci.math
From: kyee@bnlux1.bnl.gov (kenton yee)
Subject: Euler's Pentagonal Identity
Organization: Brookhaven National Laboratory, Upton, NY 11973
Date: Sun, 5 Apr 1992 22:30:13 GMT

prod_{n=1}^inf (1 - z^n )  =   sum_{n=-inf}^{+inf} (-1)^n z^{n(3n+1)/2}

Find the simplest proof.  

(Yes, yes, I know this is a special case of Jacobi's triple product
 formula...)  

  kyee@bnlux1.bnl.gov
Newsgroups: sci.math
Subject: Large primes; largest pi(n) known.
From: wft@math.canterbury.ac.nz (Bill Taylor)
Date: 7 Apr 92 10:34:26 +1200
Distribution: world
Organization: Department of Mathematics, University of Canterbury

It doesn't seem to be on the FAQ, so can someone tell us...

what is the largest known prime for which all smaller primes are known;

i.e.

how far does the list of known primes extend, without gaps;

i.e. (I presume equivalently)

what is the largest n for which pi(n) is known ?


Bill Taylor             wft@math.canterbury.ac.nz
From: djoyce@black.clarku.edu (Dave Joyce)
Newsgroups: sci.math
Subject: Re: Zero, "Arabic" numerals, etc.
Date: 10 Apr 92 03:19:23 GMT
Organization: Clark University (Worcester, MA)

In <1992Apr10.014241.14414@midway.uchicago.edu> trivedi@rabi.uchicago.edu (Anil Trivedi) writes:

>In article <44588@mentor.cc.purdue.edu> hrubin@pop.stat.purdue.edu (Herman Rubin) writes:
>>What is being discussed is not the notion of zero, but a SYMBOL for zero.  
>
>Well, you are half way there but not quite. This is one of the deepest
>misunderstandings. The key intellectual and practical leap was in
>USING ZERO TO OBTAIN A PLACE VALUE REPRESENTATION OF THE NUMBERS.
> ...

I believe the Babylonians and Chinese both had a place value representation
before they had a written symbol for 0; the unwritten symbol for 0 seemed to
be enough.  And what better symbol for 0 than   ?
		     :)

Ifrah's book _From One to Zero_, the translation of his _Histoire Universelle
des Chiffres_, was mentioned earlier in this thread and really is an excellent
source for this stuff.


-- 
David E. Joyce				Dept. Math. & Comp. Sci.
Internet:  djoyce@black.clarku.edu	Clark University
BITnet:    djoyce@clarku		Worcester, MA 01610-1477
Newsgroups: sci.math
From: gindrup@math.okstate.edu (Eric `'d'kidd' G..)
Subject: Re: A simple question about R2 - Q2 (irrational points of the plane)
Organization: Oklahoma State University, Math Department
Date: Sat, 11 Apr 1992 18:04:50 GMT

In article <1992Apr11.175123.360@math.okstate.edu> gindrup@math.okstate.edu (Eric `'d'kidd' G..) writes:
>In article <1992Apr7.233720.12411@newshost.anu.edu.au> gerry@macadam.mpce.mq.edu.au (Gerry Myerson) writes:
>>In article <1992Apr7.174510@masg1.epfl.ch>, baumgart@masg1.epfl.ch (Marcel Baumgartner) writes:
>>> 
>>> Keywords: In R2 - Q2, does there exist an oblique straight line ?
>>
>>Sure; x+y=pi. 
>
>Can you PROVE that the sum of any two irrational numbers is irrational?
>From my humble memories comes a rumbling that that is still an open idea...
>
>-- Eric Gindrup ! gindrup@hardy.math.okstate.edu

Mayhaps I mean "... that the sum of any two transcendental numbers is transcendental..."

--Eric Gindrup
From: reus@klein.euromath.dk (Jens Peter Reus Christensen)
Newsgroups: sci.math
Subject: Re: Differentiable everywhere, f' continuous nowhere (was: An elementary, "naturally occurring" problem
Date: 10 Apr 92 11:16:02 GMT
	<3767@wet.UUCP> <COLUMBUS.92Apr7091624@strident.think.com>
Organization: University of Copenhagen, Dept. of Math.


 (Michael Weiss) 

   Along the same lines, prove that there does not exist a function
   f: [0,1] --> [0,1] which is differentiable everywhere, but whose derivative f' is
   continuous nowhere.

***

As a pointwise limit of a sequence of continuous functions the
derivative is continuous in a dense set, which are of second category
topologically.


--
|--------------------------------------------------------------------------|
|  Jens Peter Reus Christensen   |                                         |
|  Associate professor, Dr. Phil.|                                         |
|  Department of mathematics     | e-mail:          reus@euromath.dk       |
|  University of Copenhagen      |                  reus@danmat.euromath.dk|
|  Universitetsparken 5          | phone:           +45 3135 3133 ext. 458 |
|  DK-2100 Copenhagen            | fax:                      +45 3135 4254 |
|--------------------------------------------------------------------------|
|  Disclaimer: Except when explicitly stated otherwise any message         |
|  with this signature is the authors purely private responsibility.       | 
|--------------------------------------------------------------------------|
|  Motto : The first to present his case seems right, till another comes   |
|  forward and questions him. PROVERBS Chapter 18,v 17 .                   |
|--------------------------------------------------------------------------|
Xref: sparky sci.math:5976 sci.math.num-analysis:1438
From: nps1@ukc.ac.uk (N.P.Smart)
Newsgroups: sci.math,sci.math.num-analysis
Subject: Computational Problem
Keywords: Linear Algebra, S-unit Equation, Number Theory, Diophantine Equations
Date: 12 Apr 92 13:26:06 GMT
Organization: Computing Lab, University of Kent at Canterbury, UK.

Can anyone help with the following problem ?

Let A_{1},...,A_{r} be n by n matrices, with non-zero determinants and entries
which are integers which are given.

Let n_{i,j}  (1<=i<=3 , 1<=j<=r) be integer variables for which we know

	| n_{i,j} | <= H

where H is given.

The problem is to determin all such n_{i,j} such that the following
equation is satisfied....

    n_{1,1}       n_{1,r}        n_{2,1}       n_{2,r}        n_{3,1}       n_{3,r}     
A_{1}    ...  A_{r}       +  A_{1}    ...  A_{r}       +  A_{1}    ...  A_{r}       = 0

For those in the know this is just an S-unit equation, used in the solution
of Diophantine Equations, put into matrix form.

In the problems I am interrested in we have that

		r  approx  4
		H  approx 10000

Any help/ideas would be most helpfull. 
My own idea is to take larger and larger prime numbers are solve the equation
modulo these primes. One then has congruence conditions on the n_{i,j}'s which
drastically reduce the problem to a simple search. By choosing the primes
nicely one can simplify this method a great deal. But it still takes about 10 
days continuous CPU-time to run.

I will post a summary of the replies if anyone is interrested.


Nigel Smart
From: gindrup@math.okstate.edu (Eric `'d'kidd' G..)
Newsgroups: sci.math
Subject: Re: distribution of wealth
Date: 8 Apr 92 16:18:57 GMT
Organization: Oklahoma State University, Math Department

In article <1992Apr6.061033.11933@augean.eleceng.adelaide.edu.AU> dabbott@augean.eleceng.adelaide.edu.AU (Derek Abbott) writes:
>
>If you added up everbody's bank balances, in the world, and then
>divided by the world population, what would we all get??
>
>A lot or a little?

You would probably intend to convert to some common currency.  Say the Mexican
peso, since its value on the world market is probably smaller than anyhting
else.  So, 3500pesos = 1dollar.  The contributions from Africa and Asia
probably average out to less than a peso per person, if we consider Japan and
India separately.  Let the contribution from Central America be inconsequential
since most such people are more concerned with the day-to-day details of living
than with a bank balance.  That leaves India, Japan, Europe, North and South
America.  The U.S. owes itself a few trillion (10^12) dollars and it strikes me
as unlikely that there is really this much money in the world at once, even
including corporate bank balances, which I assume we AREN'T, from the statement
of the problem.  Then, 3.5*10^15 pesos / 5.3*10^9 people makes ~600000 pesos
each.  And that's about 200 dollars (American) to each person on the globe.



How I love C! The only language where

  main(){ puts("Hello, world!\nWhat's new?\n"); }

is equivalent to

  int j,i,p;main(){for(;i["]<i;++i){--i;j=j++/(---p)}"];read('-'-'-',writeln(
i+++"Hello, world!\nWhat's new?\n",&p),p));}read(j,i,p){write(j/p+p,i---j,i/i);}
writeln(i,p){int j;*(int *)p=1;j=i+5*((2*(i++)+14)/2);i=p=4;return(ijp(ijp(j,i),
p)/6);}ijp(j,p){if(p>0){ji(&j,p-1);ij(&j,p-1);};j--;return(j);}ji(j,p){if(p>0)
{ji(j,p-1);ij(j,p-1);};*(int *)j=*(int *)j-1;}ij(j,p){if(p>0){/*ji(j,p-1);*/ij
(j,p-1);};*(int *)j=*(int *)j-1;}

-'d' Kidd / Eric Idle / ESG / Eric Gindrup
`````````````````````````````````````````````````````````````````````````````
`gindrup@hardy.math.okstate.edu     (preferred)	      If at first you don't `
`						succeed, deficit spend.  It `
`uucp 'a.cs.okstate.edu!/dev/null'  (flames)	works for the Federal Gov't.`
`````````````````````````````````````````````````````````````````````````````
From: dodson@convex.COM (Dave Dodson)
Newsgroups: sci.math
Subject: Re: factoid about new prime
Date: 15 Apr 92 17:28:27 GMT
Article-I.D.: news.1992Apr15.172827.20350
Reply-To: dodson@convex.COM (Dave Dodson)
Organization: Engineering, CONVEX Computer Corp., Richardson, Tx., USA
Originator: dodson@bach.convex.com
X-Disclaimer: This message was written by a user at CONVEX Computer
              Corp. The opinions expressed are those of the user and
              not necessarily those of CONVEX.

In article <1992Apr10.164647.139@linus.mitre.org> bs@gauss.mitre.org (Robert D. Silverman) writes:
>In article <michaelg.702922014@Xenon.Stanford.EDU> michaelg@Xenon.Stanford.EDU (Michael Greenwald) writes:
>:Well, I was surprised that Monty Hall apparently understood why the
>:solution to the Monty Hall problem was right.  Sometimes people aren't
>:as dumb as they seem.  I won't be surprised again, even if the
>:newscaster in question is offering to trade a live goat for the prime
>:number behind curtain number 2^(2^32) + 1.
> 
>Uh, 1479*2^34 + 1 divides your "prime" number.

Uh, read again, Bob.  The number _behind_ the curtain, not the number
_of_ the curtain, is what was prime.

----------------------------------------------------------------------

Dave Dodson		                             dodson@convex.COM
Convex Computer Corporation      Richardson, Texas      (214) 497-4234
From: columbus@strident.think.com (Michael Weiss)
Newsgroups: sci.math
Subject: Archimedes tomb (was: Did Archimedes prove radial-projection measure-preserving?)
Date: 14 Apr 92 13:37:49
Organization: Thinking Machines Corporation, Cambridge MA, USA
	<1992Apr14.150526.15518@cl.cam.ac.uk>
NNTP-Posting-Host: strident.think.com
In-reply-to: cet1@cl.cam.ac.uk's message of 14 Apr 92 15:05:26 GMT


Has Archimedes' tomb been found?  I have a vague recollection of reading a
review of a book by Howard Eves (ambiguity deliberate, I'm not sure which)
where the reviewer said, approximately, "the book incorrectly refers
to Archimedes' tomb as still missing".  Is my recollection even
approximately correct?
From: bs@gauss.mitre.org (Robert D. Silverman)
Newsgroups: sci.math
Subject: Re: New Mersenne Prime
Date: 1 Apr 92 15:57:05 GMT
Organization: Research Computer Facility, MITRE Corporation, Bedford, MA

In article <1992Apr1.134653.18530@cl.cam.ac.uk> cet1@cl.cam.ac.uk (C.E. Thompson) writes:
:In article <1992Mar31.002011.4139@linus.mitre.org>, bs@faron.mitre.org 
: (Robert D. Silverman) writes:
:|> :The answer to your question is that the number discovered is the next
:|> :Mersenne Prime in the sequence, not just yet-another-one-discovered.
:|>  
:|> Where did you get your information???
:|> 
:|>  
:|> This is false. I have checked with the people who did the work.
:|> The range from 430K to 520K (approx) has been completely checked.
:|> The range from 360K to 430K has only been partially checked.
:|> The range from 520K to 750K has been checked only very sparsely.
:|> 
:|> They were very lucky to find the number.
:|> 
:|> BTW, the range from 170K to 216091 still has not yet been checked 
:|> completely either, so for all we know there may be unfound primes
:|> SMALLER than the previous largest.
:
:I don't understand why one would skip about in this way, unless it is
:to avoid duplication of other work in progress. Is there some unofficial
:carving-up of the search space?
 
No. People skipped around in the past simply because they were trying to 
set a record. So they poked around various ranges. It is only the
dedicated work of Walter Colquitt and Gary Gostin that has systematically
filled in much of the gaps above p = 100000. Colquitt tested the entire
range from 216091 to 350K. Gostin tested everything from 100K to 170K.
I believe he is working on finishing up from 170K to 216091.

:Does anyone believe that there are heuristics that make some values of
:the exponent better bets to try, once has eliminated those for which
:2^p-1 has a factor 2kp+1 with small(ish) k?
 
No.

--
Bob Silverman
These are my opinions and not MITRE's.
Mitre Corporation, Bedford, MA 01730
"You can lead a horse's ass to knowledge, but you can't make him think"
From: dabbott@augean.eleceng.adelaide.edu.AU (Derek Abbott)
Newsgroups: sci.math
Subject: Re: Fermat's Last Theorem
Date: 10 Apr 92 01:32:58 GMT
Organization: Electrical and Electronic Eng., University of Adelaide

In article <1992Apr9.133316.24615@linus.mitre.org> bs@gauss.mitre.org (Robert D. Silverman) writes:
>You are probably not a professional sports player, yet I'm sure you
>know who the greatest pros are. Why do you know? Because you are
>interested in sports and follow them! Why should not the same thing
>apply in mathematics???
>--
>Bob Silverman

OK Bob here's a little general knowledge quiz for you. Who are the greatest
pros of the 20th century in the following sports:

a) Cricket
b) Baseball
c) Golf
d) Atheletics
e) Gymnastics
f) Ice skating
h) Bungee jumping
i) Tiddly Winks
j) Female mud wrestling
k) Barefoot boxing
l) Fartlek

?????
Newsgroups: sci.math
From: cyeomans@ms.uky.edu (Charles Yeomans)
Subject: Re: Fermat's Last Theorem
    <sundquis.702591357@s6.math.umn.edu> <1992Apr7.051902.4889@rata.vuw.ac.nz>
Date: Tue, 7 Apr 1992 14:24:42 GMT
Organization: University Of Kentucky, Dept. of Math Sciences
X-Bytes: 

In article <1992Apr7.051902.4889@rata.vuw.ac.nz> harper@kauri.vuw.ac.nz (John Harper) writes:
> >Pardon my ignorance. Who is this Erdos dude?
>Several people have been abusing one another instead of answering the
>question. Paul Erdos is a very famous Hungarian mathematician (aged around
>80 I'd guess) who occasionally offers cash prizes of a few hundred dollars
>for solutions to problems that he hasn't solved himself and that interest him.
>The problems I have seen are HARD and are on combinatorics and number theory.
>
>John Harper Mathematics Dept. Victoria University Wellington New Zealand

I understand that Erdos offered $3000 for a solution to the following
problem:  let {n_i} be a sequence of positive integers such that
SUM(1/n_i) diverges.  Then the sequence contains arithmetic progressions
of arbitrary length.  Try this one in your spare time.

Charles Yeomans
cyeomans@ms.uky.edu
yeomans@austin.onu.edu

Newsgroups: sci.math
From: marty@amaterasu.physics.uiuc.edu (Marty Gelfand)
Subject: Re: polyominoes, anyone?
Organization: Dept. of Physics, Univ. of Illinois at Urbana-Champaign
Date: Sat, 11 Apr 1992 03:37:00 GMT

In article <1992Apr10.175434.21073@Princeton.EDU> holerbch@phoenix.Princeton.EDU (Uwe Hollerbach) writes:
>G'day, folks!
>	Since pentominoes have come up recently in one or two threads
>in this newsgroup, I thought I'd ask a question which I have been
>wondering about for some time. Is there a formula for the number of
>n-ominoes, for general n, other than enumerating all possible n-ominoes,
>then counting how many you have? [...]

If I'm not mistaken polyominoes also go by the name "lattice animals" in
the physics literature...and that might be a place to look for the current
status of the asymptotics at large n.  I don't think exact results are
available unless the shape is restricted in various ways.  --Marty G.