HDTenEightyP/NetNews huggingface dataset:
Newsgroups: sci.math


Hello sci.math

I've been doing some self assigned homework. I was investigating
the effect of a general 2nd order covariant metric on covariant
differentiation. Normally, the metric is considered symmetrical.
I'll post only the result and ask the net for it's wisdom concerning
it's correctness, etc.

                      2       i  j
Given the invariant ds = g  dx dy 
                          ij

for arbitrary dx and dy, one concludes the tensor character of g.

Write g in it's symmetric and asymmetric components

  g   = s   + t    , s   = s    , t   = -t
   ij    ij    ij     ij    ji     ij     ji

        ij        j
Define s   s   = d  , where d = 1 if j=k, else d = 0.
            ik    k

The result for the covariant derivative of a contravariant vector A is

   i     i  j    p ai     r
  A  = dA/dx  + A s  g  {pj}  , where d denotes partial differentiation
   ,j                 ar

and the {} term is the Christoffel symbol of the second kind. This reduces
to the expected equations if g is symmetric.

One place I can think of that an asymmetric metric makes a difference is
in the case of complex dx and dy. Here one gets for two dimensions with
the definitions
   
    2         i *  j
  ds  = g  (dx ) dy , dx = [a+jb,c+jd] = dy
         ij

  ds^2= g11(a^2 + b^2) +g22(c^2 + d^2) +(ac + bd)(2s12) +j(ad - bd)(2t12)
 
So an imaginary asymmetric part of g (t12) leads to a modified line element
for complex contravariant differentials which is still real. Any comments?

--------------------------------------------------------------------------
Ric Peregrino     c/o Hewlett Packard Co.        I represent only myself
ric@spd.hp.com    1501 Page Mill Rd. Bldg. 5M    I may be wrong, maybe not
415-857-7526      Palo Alto, CA 94304            Do DC photons exist?
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Newsgroups: sci.math
From: schwab@miranda.mathematik.uni-kl.de (Hartmut Schwab)
Subject: Combinatorial Problem 
Keywords: combinatorics
Reply-To: schwab@mathematik.uni-kl.de
Organization: UC Berkeley IC CAD Group
Date: Thu, 27 Aug 1992 13:55:18 GMT


I have a Problem, which I think is very easy.
But I don't know how to find the solution.

Given an Integer K.
Partition K into m Integers c[i], such that their sum is K.
Condition: For all i :  0 <= c[i] <= k[i].

How many different Solutions are there?

Two solutions c0 and c1 are different, if there is an i such that
c0[i] <> c1[i].

Therefore in the case K = 3, m = 2 , 0 <= c[1] <= 2, 0 <= c[2] <= 3
we get the solutions:  0+3, 1+2, 2+1. These are 3 different solutions.

You could think of K bowls which are put into m boxes.
The condition says, that box i is only able to take k[i] or less bowls.

Without the condition I am able to solve it. But I have problems with
the condition.

I am interested in an easy to calculate term.


Where can I get a solution to this problem?

Thanks in advance.


Hartmut Schwab
schwab@mathematik.uni-kl.de
Newsgroups: sci.math
From: music@erich.triumf.ca (FRED W. BACH)
Subject: PRIME NUMBER LIST
News-Software: VAX/VMS VNEWS 1.41    
Keywords: prime number
Organization: TRIUMF: Tri-University Meson Facility
Date: Sat, 29 Aug 1992 22:51:00 GMT

   Dear sci.math-ers

    With all the prime-number research going on into advanced
    computer algorithms and security, one would think that
    there would be a on-line list of prime numbers somewhere.

    Oh, I know I could write some code, but why re-invent the wheel?

    If you know where I can get a simple list of prime numbers to fairly
    large numbers, please reply via E-Mail to music@erich.triumf.ca     .  

    Thanks.

 Fred W. Bach ,    Operations Group        |  Internet: music@erich.triumf.ca
 TRIUMF (TRI-University Meson Facility)    |  Voice:  604-222-1047 loc 278/419
 4004 WESBROOK MALL, UBC CAMPUS            |  FAX:    604-222-1074
 University of British Columbia, Vancouver, B.C., CANADA   V6T 2A3

 These are my opinions, which should ONLY make you read, think, and question.
 They do NOT necessarily reflect the views of my employer or fellow workers.
From: jack@dcs.glasgow.ac.uk (Jack Campin)
Newsgroups: sci.math
Subject: Re: Proof of God's Existence
Date: 1 Sep 92 13:51:32 GMT
Reply-To: jack@dcs.glasgow.ac.uk (Jack Campin)
Organization: COMANDOS Project, Glesga Yoonie

bubai@matt.ksu.ksu.edu (P.Chatterjee) wrote:
> I was told by somebody that there is a mathematical proof of God's
> existence; was wondering if somebody could shed some light on the same.

What you might have in mind is Robert K. Meyer's "God Exists!", published
in the American philosophical journal "Nous" around 1980.  It uses Zorn's
lemma in a version of Aquinas's "first cause" argument.  Meyer is a serious
and reputable (if idiosyncratic) logician, and a Christian; the paper isn't
a leg-pull like the Ian Stewart item mentioned here before.

-- 
--  Jack Campin    room G092, Computing Science Department, Glasgow University,
17 Lilybank Gardens, Glasgow G12 8RZ, Scotland   TEL: 041 339 8855 x6854 (work)
INTERNET: jack@dcs.glasgow.ac.uk or via nsfnet-relay.ac.uk    FAX: 041 330 4913
BANG!net: via mcsun and uknet     BITNET: via UKACRL    UUCP: jack@glasgow.uucp
Newsgroups: sci.math
From: rsilver@world.std.com (Richard Silver)
Subject: Re: Proof of God's Existence
Organization: The World Public Access UNIX, Brookline, MA
Date: Tue, 1 Sep 1992 10:11:41 GMT

In article <17ui6kINNsft@matt.ksu.ksu.edu> bubai@matt.ksu.ksu.edu (P.Chatterjee) writes:
>I was told by somebody that there is a mathematical proof of God's existence;
>was wondering if somebody could shed some light on the same. 
>Thanks. Looking forward to the response.

You do not need proof. Just ask those who die in his name. 

And please find other newsgroups for such lame queries.
From: weemba@sagi.wistar.upenn.edu (Matthew P Wiener)
Newsgroups: sci.math
Subject: Re: Another induction problem
Date: 30 Aug 92 22:19:39 GMT
Reply-To: weemba@sagi.wistar.upenn.edu (Matthew P Wiener)
Organization: The Wistar Institute of Anatomy and Biology
In-reply-to: ara@zurich.ai.mit.edu (Allan Adler)

In article <ARA.92Aug30103547@camelot.ai.mit.edu>, ara@zurich (Allan Adler) writes:
>Hironaka's proof of resolution of singularities depends on a complicated
>induction scheme. I heard a rumor once that the scheme is so complicated
>that someone else published a paper proving that such a scheme could work.

>Is this rumor true and if so, what is a reference?

I couldn't say a thing about the above, but it has happened in other fields.
If you want complicated inductions, check out recursion theory.  Some of
them go by names like "infinite injury method" and the like.  To aid in
understanding such, a visual technique of describing these inductions was
developed called "pinball machines".  (I think it's in Soare's text.)

The ultimate was probably the set theoretic recursion work of Jensen.  He
came up with some megahairy complicated induction proofs, and repeatedly
abstracted them out.  The messiest is the "morass".  The last I heard,
only the details of the gap-1 morass have been published, and it's been
over 20 years now.

I never did get the courage to read Szemeredi's paper, proving the
(expensive) Erd"os conjecture that a set of positive density contains
arbitrarily long arithmetic progressions.  The diagram outlining the
induction looked too much like the Krebs cycle for my tastes.
-- 
-Matthew P Wiener (weemba@sagi.wistar.upenn.edu)
Newsgroups: sci.math
From: regeorge@magnus.acs.ohio-state.edu (Robert E George)
Subject: Re: Godel and the US constitution
Organization: The Ohio State University
Date: Tue, 1 Sep 1992 20:34:02 GMT

In article <1992Sep1.175844.16825@nas.nasa.gov> asimov@wk223.nas.nasa.gov (Dani
el A. Asimov) writes:
[deletions]
>
>Out of curiosity, does anyone know how Godel envisioned a
>consitutional dictatorship possibly arising in the U.S. ???
[deletions]

I have no idea how Godel envisioned a dictatorship, but it is not very
difficult to see how it could happen: any of the Bill of Rights can be
repealed, just as Prohibition was repealed; terms could be extended
indefinitely, the Supreme Court could be abolished, elections could be
abolished, the veto repealed, et cetera. All that
would be required would be a series of constitutional amendments, of which
we have already had many. Each would require a 2/3 majority in both the
Senate and the House, and control of 3/4 of the State legislatures. (Another
route could be via the state convention method, or even the constitutional
convention.) Gaining such majorities would not be easy, but it is not
impossible either: the only action prohibited by the Constitution appears
to be the abolition of equal representation in the Senate -- but note
that an amendment could strip the Senate of any and all powers.


So, have a nice day!

Robert George
(speaking only for myself)

"The very essence of individual freedom is equal justice under a rule of
law, a law to which every man shall be subject and which no executive
can modify."
    Senator Robert Taft , March 11, 1944
From: baez@ucrmath.ucr.edu (john baez)
Newsgroups: sci.math
Subject: Re: polynomial roots and zero divisors
Date: 28 Aug 92 18:55:33 GMT
Article-I.D.: galaxy.22038
Organization: University of California, Riverside

In article <640033@otter.hpl.hp.com> sec@otter.hpl.hp.com (Simon Crouch) writes:
>In sci.math, rcollins@cs.umass.edu (Bob Collins) writes:

>>   I would like to find the eigenvalues/vectors of a square 
>> matrix.  Unfortunately, the elements of the matrix are not 
>> members of a field.  In particular, they are "dual numbers",

>    I'm unfamiliar with Yaglom's definition, but you seem to be using
>    a very simple case of "superspace" (the definition of it that
>    is the algebra generated by 1 and anticommuting b_{1}....b_{n})
>    with one anticommuting generator.



It may come in handy when looking for references to know that "dual
numbers," "super-vector spaces," "Grassman algebras," and "exterior
algebras" are all the same thing.  Most of the modern math literature
uses the last terminology, and the symbol Lambda V where V is the vector
Newsgroups: sci.math
From: Madeleine Thomas
Subject: Re: HELP! Inscribed Circle...
Reply-To: Re:HELP! Inscribed Circle...
Organization: Bell-Northern Research
Date: Fri, 28 Aug 1992 12:10:42 GMT

To anyone who might have read the previous posting
where I requested assistance with a lat-long problem;
it was mentioned in a response that a comment I made 
was kind of derogatory. I regret that it was taken in that manner,
I assure you it was actually meant as a compliment. I 
am not very good at mathematics, and the discussions on
this thread are usually beyond my depth.  My apologies to
anyone I offended...

Bob - thanks for your assistance.

Madeleine Thomas
Newsgroups: sci.math
From: furuya@nu.uleth.ca (Ted Furuya)
Subject: Calculus Help!
Organization: University of Lethbridge
Date:  3 Sep 92 19:07:57 GMT

I was wondering if anyone out there knows of a program that actually teaches
calculus.  I need one that runs on an IBM PC.  

                                               -Ted
From: bubai@matt.ksu.ksu.edu (P.Chatterjee)
Newsgroups: sci.math
Subject: Proof of God's Existence
Date: 31 Aug 1992 20:49:08 -0500
Organization: Kansas State University
NNTP-Posting-Host: matt.ksu.ksu.edu

I was told by somebody that there is a mathematical proof of God's existence; was wondering if somebody could shed some light on the same.

Thanks. Looking forward to the response.
From: elkies@ramanujan.harvard.edu (Noam Elkies)
Newsgroups: sci.math
Subject: Re: Godel and the US constitution
Date: 1 Sep 92 20:00:44 GMT
Article-I.D.: husc3.1992Sep1.160045.15281
Organization: Harvard Math Department

In article <1992Sep1.175844.16825@nas.nasa.gov>
asimov@wk223.nas.nasa.gov (Daniel A. Asimov) writes:
>Out of curiosity, does anyone know how Godel envisioned a
>consitutional dictatorship possibly arising in the U.S. ???

It would seem that all you need is 2/3 of the Senators and
Representatives to agree on an Amendment that would make
(say) Madonna the absolute ruler of the United States...

--Noam D. Elkies (elkies@zariski.harvard.edu)
  Dept. of Mathematics, Harvard University
From: bubai@matt.ksu.ksu.edu (P.Chatterjee)
Newsgroups: sci.math
Subject: A set-theoretic proof:need help
Date: 1 Sep 1992 22:38:24 -0500
Organization: Kansas State University
NNTP-Posting-Host: matt.ksu.ksu.edu

Hi,

I have a 'homework' problem which I'd like some help on. It's a proof. It's awfully simple but the only problem is that I'm not sure how exactly one should approach it especially if one is looking to give a 'slick' proof.

It goes like this:

Prove that for subsets A, B c X:

A c B <=> A U B = B <=> A ^ B = A <=> B' c A'

where: c:= subset
       U:= union
       ^:= intersection

My request is for some help on how to go about using the logical equivalence symbol in proving the above equivalences. I have constructed a 'scrappy' and lengthy proof but would like to achieve brevity in expression.

Would really appreciate if somebody, without giving the actual proof, helped me with how to proceed.

Thanks for all the help.
From: clong@remus.rutgers.edu (Chris Long)
Newsgroups: sci.math
Subject: Re: Transcendence question (QUASI-SPOILER)
Date: 24 Aug 92 03:08:28 GMT
Organization: Rutgers Univ., New Brunswick, N.J.

In article <BtGFJv.2GJ@andy.bgsu.edu>, Ray Steiner writes:

> Is there an irrational number t such that 2^t and 3^t are
> both rational? Is this question still open? The answer is
> yes if we just consider 2^t (2^{log_2 3} being an example)
> but no if we look at 2^t, 3^t and 5^t.(This is a case
> of the famous "6 exponentials theorem.") The general case
> of a^t and b^t, a and b integers, is still open.

If ln(a) and ln(b) are Q-linearly independent, this follows from
the unproven Schanuel conjecture.  Let a^t = q and consider
degree( Q(ln(a), ln(b), ln(q), ln(q)*ln(b)/ln(a), a, b, q, b^t) )
= degree( Q(ln(a), ln(b), ln(q), ln(q)*ln(b)/ln(a)) ) if b^t is
rational, and this must be >= 4 by Schanuel, which is clearly
false.  It remains to be proven that ln(a), ln(b), ln(q), and
ln(q)*ln(b)/ln(a) are Q-linearly independent, but this would
follow if ln(a), ln(b), and ln(q) were algebraically independent,
which would follow from Schanuel if they were Q-linearly independent.
But assuming not, we obtain a contradiction.

This isn't a proof, but at least it shows that such t probably
do not exist.
-- 
Chris Long, 265 Old York Rd., Bridgewater, NJ  08807-2618

"In a study of schoolboys, an educator discovered a correlation between size
 of feet and quality of handwriting.  The boys with the larger feet were,
 on the average, older."        Wallis & Roberts, _The Nature of Statistics_
From: matt@amsaa-cleo.brl.mil (Matt Rosenblatt)
Newsgroups: sci.math
Subject: Re: Calendar (NEW) -- CORRECTION
Keywords: Vernal Equinox
Date: 28 Aug 92 13:16:53 GMT
Organization: U.S. ARMY MATERIEL SYSTEMS ANALYSIS ACTIVITY (AMSAA), APG, MD.

In article <8708@amsaa-cleo.brl.mil> I wrote:

>In article <1992Aug24.191238.20599@linus.mitre.org> 
>chaloux@accordion.mitre.org (Dave Chaloux) writes:

->The celebration of the 
->resurrection is commonly linked to the celebration of the Passover.  
->It should also be noted that not all sects of Christianity make 
->this connection at the same time.  [Dave Chaloux] 

>This, too, is right, which is why they have "Russian Easter" in the
>Orthodox Church.  In the West, Easter Sunday usually does indeed
>fall close to the Passover.  But not *too* close: the "Easter Rule"
>ensures that if the 15th day of Nisan -- the first Full Moon after
>the Vernal Equinox -- occurs on a Sunday, Easter itself will be 
>relocated to another Sunday.  In this way, the rule keeps the 
>celebration of the resurrection from coinciding with the beginning 
>of the Jewish Passover feast.  [Matt Rosenblatt]

When I heard this, it sounded plausible, so I believed it.  But it
turns out to be incorrect.  Mr. John Harper of New Zealand was kind
enough to notify me that Easter Sunday can indeed coincide with the
first day of the Passover.  Indeed, this has happened as recently as
April 19, 1981.

					-- Matt Rosenblatt
					(matt@amsaa.brl.mil)
Newsgroups: sci.math
Subject: Re: Proof of God's Existence
From: news@massey.ac.nz (USENET News System)
Date: Tue, 1 Sep 92 23:52:30 GMT
Organization: Massey University

> 
> In article <Btw9nH.BIE@world.std.com> rsilver@world.std.com (Richard Silver) writes:
> >In article <17ui6kINNsft@matt.ksu.ksu.edu> bubai@matt.ksu.ksu.edu (P.Chatterjee) writes:
> >>I was told by somebody that there is a mathematical proof of God's existence;
> >>was wondering if somebody could shed some light on the same. 
> >>Thanks. Looking forward to the response.
> >
I sent an e-mail reply, but since no-one else has brought this up, it might
be of interest here.

I forget the details, but a philospher who had quite a reputation at the Russian
court offered to debate the existence of God. It happened that a well known
French mathematician was visiting at the time (possibly Laplace - I'm not
sure). He claimed to have a mathematical proof.
He said something like "3x+2 = 7 donc Dieu exist".
Unfortunately the philosopher did not know enough maths to understand
that he was being had and left discomfitted.

BTW, the original question surely belong in sci.math, but not
some of the pretentious boring flames. I particularly enjoyed
the connection with Zorn's lemma etc.

Terry Moore
Newsgroups: sci.math
From: khill@vax1.umkc.edu
Newsgroups: sci.math
Subject: Looking for faulty proof that 0=1.
Date: 2 Sep 92 17:11:26 GMT
Article-I.D.: vax1.1992Sep2.111126.1
Organization: University of Missouri - Kansas City

I am looking for the falacious "proof" that 0=1.
it starts with something like:

	a	=	b
	a*a	=	a*b
		.
		.
		.
	 0	=	1

I can not remember how the interim steps go, but I
do remember that the error in the proof is that
there is a step where both sides are divided by (a-b).
Since (a-b)=0 this is an impossible step.

I am want to use this "proof" to show my little brother,
who is taking a first year algebra course, that you must
ALWAYS check your results after working a problem.
-- 
===============================================================================
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From: edgar@function.mps.ohio-state.edu (Gerald Edgar)
Newsgroups: sci.math
Subject: Re: Elementary solution needed: harmonic bi-sequences
Date: 27 Aug 1992 14:29:13 -0400
Organization: The Ohio State University, Dept. of Math.
NNTP-Posting-Host: function.mps.ohio-state.edu

In article <1992Aug27.170048.26459@ugle.unit.no> ap@levangerhs.no (Andrei Prasolov) writes:
>   There is a problem which seems to have a very simple solution.
>I remember that I heard one in my youth. That solution used
>the epsilon-delta language only. However, I cannot recall that.
>
>DEF. Let`s call a bi-sequence (a(i,j), i,j from Z) HARMONIC if for all i,j
>
>(*)       a(i,j) = 1/4 (a(i,j+1) + a(i,j-1) + a(i+1,j) + a(i-1,j)).
>
>PROBLEM. Prove that any bounded (|a(i,j)| < C) harmonic bi-sequence is constant.
>

Here is a proof that I like.  Whether you consider it "elementary" depends
on your background.

The symmetric random walk on the two-dimensional integer lattice Z^2
is recurrent: it visits each node repeatedly (with probability one).
Apply the function a to that random walk.  The result is (by (*)) a
martingale.  But a bounded martingale converges (almost surely),
while _this_ bounded martingale runs repeatedly through all the values of
the function a.  Therefore a is constant.

So maybe it's not elementary, but it is short and cute.

-- 
  Gerald A. Edgar                Internet:  edgar@mps.ohio-state.edu
  Department of Mathematics      Bitnet:    EDGAR@OHSTPY
  The Ohio State University      telephone: 614-292-0395 (Office)
  Columbus, OH 43210             -292-4975 (Math. Dept.) -292-1479 (Dept. Fax)
From: watson@clark.edu (Dennis Watson)
Newsgroups: sci.math
Subject: Re: Problematic smurfs!
Keywords: smurfs
Date: 31 Aug 92 22:39:19 GMT
Article-I.D.: clark.1992Aug31.223919.10029
Organization: Clark College, Vancouver, Wa.  USA

With regard to the three guys standing in line with 5 hats available: 3 brown
and 2 black.  The first guy in line has a brown hat.  Because:

The last guy does not see 2 black hats or he would leave knowing he has a
brown hat.

The middle guy does not see a black hat or he would leave knowing he has a
brown hat.

So the first guy knows he has a brown hat.

Dennis
watson@clark.edu
Newsgroups: sci.math
From: carle@molest.ugcs.caltech.edu (Matthew Thomas Carle)
Subject: Re: POLLY NOMIAL, Humor
Organization: California Institute of Technology, Pasadena
Date: Mon, 24 Aug 1992 02:01:17 GMT

chisnall@cosc.canterbury.ac.nz (The Technicolour Throw-up) writes:

>From article <1992Aug10.035041.16514@odin.corp.sgi.com>, by shreiner@arioch.csd.sgi.com (Dave Shreiner):
>> 	"Exchlf!" he swore, using the vilest oath he knew.  His patience was

>I've never understood this part of the story.  What exactly is the
>significance of "exchlf"?  I've always assumed that its an acronym or
>mnemonic from some branch of maths.  Does anybody know?

I've seen another version of the same story in which the exclamation is 
"Arcsinh!"  This makes a little more sense to me as an `oath.' (especially
when said out loud instead of read).  I've never seen "exchlf" used, though.

--

"This .sig intentionally left blank."
Newsgroups: sci.math
From: regeorge@magnus.acs.ohio-state.edu (Robert E George)
Subject: Re: Proof of God's Existence
Organization: The Ohio State University
Date: Thu, 3 Sep 1992 16:23:14 GMT

In article <1992Sep1.224045.8620@vax.oxford.ac.uk> loader@vax.oxford.ac.uk writ
es:
>In article <1992Sep1.215331.89956@vaxc.cc.monash.edu.au>, kevin@vaxc.cc.monash
.edu.au writes:
[deletions]
>> 1. It is possible to imagine a world, completely agreeing with the current o
ne
>> on all sensory data, in which God exists.
>> 2. It is possible to imagine a world, completely agreeing with the current o
ne
>> on all sensory data, in which God doesn't exists.
>> Call a world satisfying condition 1 M, and a world satisfying 2 M'.
>> Then the existence of these epistemically indistinguishable worlds proves th
at
>> any ontological statement about God is INDEPENDENT of any epistemically
>
>It is possible to imagine a world completely agreeing with the current
>one on all sensory data, in which Fermat's last theorem is false.
>It is possible to imagine a world completely agreeing with the current
>one on all sensory data, in which Fermat's last theorem is true.
>Then by the fact that mathematical truths are necessary truths and true
>in all possible worlds, FLT is true and false.
>
>Kabloom
>(The world disappears in a puff of logic.)
[deletions]
I think there is a need to use "imagine" very carefully. "Imagine" in the
original posting seems to mean more than a pipe-dream sort of fantasy.
The independence of the Parallel Postulate from the other axioms is shown
by defining ("imagining" if you like, but in *very concrete terms*) systems
for which the axioms of so-called neutral geometry and the PP hold; and by
defining a syustem for which the NG axioms hold and the PP does not.
Endulging in nebulous speculation ("Say, buddy, suppose the Parallel Postulate
doesn't hold out in the next galaxy") doesn't count as imagining in this
context.

Robert George
(speaking only for myself)
Newsgroups: sci.math