HDTenEightyP/NetNews huggingface dataset:
From: elkies@ramanujan.harvard.edu (Noam Elkies)
Newsgroups: sci.math,rec.music.classical
Subject: P.Glass and math? [Re: famous non-mathematicians who majored in math]
Date: 14 Oct 92 02:30:42 GMT
Article-I.D.: husc3.1992Oct13.223043.16366
Organization: Harvard Math Department

In article <1992Oct13.202553.7542@aio.jsc.nasa.gov>
lawton%ecfa@jesnic.jsc.nasa.gov (Eric G. Lawton) writes:
>In article <1992Oct8.191230.16442@lehi3b15.CSEE.Lehigh.EDU> 
>buyskes@lafcol.lafayette.edu (Steve Buyske) writes:
>>         So the question is, do you know of any well-known people who 
>> majored in math but aren't known as mathematicians?
>
>I believe Phillip Glass (the American Composer) has a background in 
>mathematics.  Can someone verify this?

I can't (nor refute it), so I'm cross-posting to rec.music.classical
which as it happens has an ongoing Glass thread (fiber optics?).

Meanwhile I note that music theorist David Lewin and serial composer
Milton Babbitt got their undergraduate degrees in mathematics, and
math figures prominently in their work.

Oh, and Tom Lehrer does not have a Ph.D. in mathematics, though he was
a math graduate student at Harvard for one year.

--Noam D. Elkies (elkies@zariski.harvard.edu)
  Dept. of Mathematics, Harvard University
From: sec@otter.hpl.hp.com (Simon Crouch)
Newsgroups: sci.math
Subject: Re: Re: "The Universe of MOTION" (crackpot index)
Date: 16 Oct 92 13:42:01 GMT
Organization: Hewlett-Packard Laboratories, Bristol, UK.


WHAT we REALLY NEED is some NOTION of......

oops, sorry, I got carried away there. Let's try again:

What we really need is some notion of "crackpot density" (CPD). It's one
thing to demolish(TM) western science in a long tedious spouting but another
thing entirely to manage it in one page! So, let's have these indices
normalised.

Oh, BTW, I've noticed that the maximum possible crackpot density (using
JB's definitions and a TOP SECRET normalisation procedure) is

	   (Pi/Fine Structure Constant)^(Feigenbaum's number)

Can I have my Nobel Prize now?
Newsgroups: sci.math
From: shteingd@broxton.math.ucla.edu (Semion D. Shteingold)
Subject: Re: Topological Question
Reply-To: shteingd@broxton.math.ucla.edu (Semion D. Shteingold)
Organization: UCLA Mathematics Department
Date: Mon, 12 Oct 92 23:04:58 GMT

In article <1992Oct12.163249.1@vmsa.technion.ac.il>,
chr09tk@vmsa.technion.ac.il writes:
|> Hello!
|> 
|> Can anyone help me with the folowing topological question:
|> Is there a connected and locally connected topological space which is
not path
|> connected? 
|> Is there such a space which is also compact?
|> 
|> Thanks in advance,
|> Guy 

What about X={(x,sin(1/x)):x \in (0;1]}+{0}*[-1;1] ?
I think it's ctd, cpt, but not linear ctd.
Newsgroups: sci.math,sci.math.symbolic,sci.math.num-analysis,sci.stats
From: jmborwei@math.uwaterloo.ca (Jonathan Borwein)
Subject: New Centre
Summary: Experimental Mathematics
Organization: University of Waterloo
Date: Fri, 16 Oct 1992 14:15:07 GMT

Expires :
Followup-To:  jborwein@math.sfu.ca, jmborwei@orion.uwaterloo.ca
Organization: University of Waterloo
Keywords:  Fellowships, symbolic math, experimental math

documentstyle[12pt]{article}
\parskip=0.5ex

\begin{document}
\begin{center}{\Large \bf Simon Fraser Centre for Experimental and
Constructive Mathematics} \end{center}

This Centre
is intended to further research and graduate education in Computation in
the Mathematical Sciences. The Centre aims to provide a sophisticated
environment for Mathematical research on topics that require a substantial
mix of computation, experimentation and mathematics. Of interest are questions
on how one uses the computer: To build intuition?  To generate hypotheses?
To validate conjectures or prove theorems? To discover nontrivial examples
and counter-examples?

The Centre will commence full operation July 1, 1993 at Simon Fraser
University in Burnaby, British Columbia. Activities will include the following.

(i)  Provision for and sponsorship of Post-Doctoral Fellowships in areas
related to Experimental and Constructive Mathematics.

(ii)  Sponsorship of regular short-term and longer-term research visitors
to the Centre.

(iii) Organization of regular Colloquia and occasional Conferences on
advances in Experimental and Constructive and maintenance of accessible software
archives.

(vi) Collaboration with similar centres and appropriate individuals at
other Canadian and foreign Universities and Institutes.

The initial steering committee consists of J. Borwein (Director), P.
Borwein and R. Russell. Enquiries can be directed to jborwein@math.sfu.ca

\medskip

The Centre  is soliciting applications for {\bf two Post-Doctoral Fellows}
commencing after July 1, 1993, in any areas compatible with the interests
of the centre.  The stipend will be set on the NSERC PDF scale.  These are
primarily research positions though some teaching may be involved.
Potential Post-Doctoral Fellows should send a curriculum vitae and arrange
for three letters of reference to be sent to Dr. J.M. Borwein,
Department of Combinatorics and Optimization, University of Waterloo, N2L
3G1, Ontario preferably by January 15, 1993.


\end{document}
From: edgar@function.mps.ohio-state.edu (Gerald Edgar)
Newsgroups: sci.math
Subject: Re: Help needed
Date: 9 Oct 1992 08:26:19 -0400
Organization: The Ohio State University, Dept. of Math.
NNTP-Posting-Host: function.mps.ohio-state.edu

This answer (namely there is no closed-form solution, but it can
be computed iteratively) should be in the FAQ for sci.math:

In article <u67csB1w165w@quest.UUCP> srhqla!quest!kdq writes:

>If someone would be so kind as to solve for (i), or look up the
>equation, or whatever, and respond by email, I would be eternally
>grateful (well, a long time, anyway).  I ask for email since this site
>does not receive sci.math.  Thanks in advance.
>
>             i
>m = p * ------------
>                   -n
>        1 - (i + 1)
>
-- 
  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: zlsiida@fs1.mcc.ac.uk (dave budd)
Newsgroups: sci.math
Subject: Re: Mattel on women
Date: 8 Oct 92 13:46:36 GMT
Organization: Manchester Computing Centre

In article <1aut2kINNenu@usenet.INS.CWRU.Edu> cxm7@po.CWRU.Edu (Colin Mclarty) writes:

>       I did help a girl get through third through fifth grade
>math.  She told me that addition facts are hard when you have to
>carry.  Now, I could have said "no they aren't" and then she could
>could have chosen among three possiblities: she was stupid, I was
>lying, I didn't know what I was talking about.  What I did say was
>"yeah, but you can do hard things" and by the time we got to 

And if the doll said this there wouldn't be a problem.  The way the language 
works, if the statement 'math class is hard' stands alone with no other 
support either way, girls WILL take it to mean 'too hard for me'.  Maybe not 
all girls, but enough to make this doll a Bad Thing (TM).


              Have another day    [Armageddon, the musical] 
  Dave Budd, MCC, Oxford Rd, Manchester, England   (44|0)61-275-6033  
Newsgroups: sci.math
From: nichols@math.umn.edu (Preston Nichols)
Subject: Re: Mattel says "Math is tough."
Organization: University of Minnesota
Date: Thu, 8 Oct 1992 20:12:06 GMT

In article <1992Oct5.212115.3356@bnlux1.bnl.gov> kyee@bnlux1.bnl.gov (kenton  
yee) writes:
> In article <BvLyKC.LFH@rice.edu> iltiss@owlnet.rice.edu (Steven Patrick  
Iltis) writes:
> >        Mattel has just released a new product. A Barbie doll that says
> >"Math is tough".
> >        This thoughtless attack on mathematics education in general and
> >women in particular should not be allowed to happen without a significant
> >protest from the mathematics and scientific community.
> 
>   Why do you assume women will be turned off by math simply
                      ^^^^^
>  because it is tough?   I know lots of people who like math
                                         ^^^^^^
>   BECAUSE it is tough.  
> 
I hope this doesn't come off as a flame, but the change in nouns above really  
made me wonder what you intended.
From: elkies@ramanujan.harvard.edu (Noam Elkies)
Newsgroups: sci.math
Subject: Re: real exponential sums
Date: 13 Oct 92 15:37:04 GMT
Article-I.D.: husc3.1992Oct13.113705.16330
Distribution: world
Organization: Harvard Math Department

In article <1behulINNm4e@uwm.edu> litow@csd4.csd.uwm.edu
(bruce e litow) writes:
>Let a_k = exp(k/N) where 0 <= k < N and let S1 and S2 be two sums
>over two disjoint subsets of the a_k. By Lindemann's Thm, 
>S1 - S2 can never vanish but is there a decent lower bound on
>|S1 - S2| ? In particular, 1/N^O(1) ?

That's too much to hope for.  There are 2^N subsums in all, each of
absolute value <=N.  However you put 2^N points in a radius-N circle,
some pair must be at distance at most O(N/2^(N/2)), which decreases
faster than 1/N^O(1).  [If all distances had been >=2r, you'd have
a packing of 2^N circles of radius r in a circle of radius N+r, whence
2^N*r^2 >= (N+r)^2;  now solve for r.]  Now eliminate the roots of
unity occurring in both sums to get two disjoint subsums S1, S2 at
the same small distance.

This bound can be reduced a bit further (by a factor of sqrt(N)) by
noting that a positive proportion of the 2^N sums must have absolute
value O(sqrt(N)) [Central Limit Theorem and all that].  Actually
finding such S1 and S2 when N is at all large (say N=100) is of
course a much harder problem...

--Noam D. Elkies (elkies@zariski.harvard.edu)
  Dept. of Mathematics, Harvard University
From: Herman.Woltring@bbs.oit.unc.edu (Herman Woltring)
Subject: Re: Richard Fateman's e-mail address
Summary: finger user_id@stanford.edu
Keywords: finger command, unix
Organization: Extended Bulletin Board Service
Date: Fri, 16 Oct 1992 19:37:31 GMT

In article <92285.111410C44590@TRMETU.BITNET> <C44590@TRMETU.BITNET> writes:
>Hi,
>i am looking for e-mail adresses of either Prof.Kathy Yeklick or Mr.
>Richard Fateman of the department of Mathematics,Berkeley University.
>
>any help is highly appreciated.
>
>regards.
>reza
>METU; Ankara_ TUrkey
 
If you have access to a Unix machine, you can issue the command
 
   finger yeklick@stanford.edu
   finger fateman@stanford.edu
 
upon which the true email address, *if* published, is returned, together
with help information.  I've tried it, and scored negative on both counts.
From a BITNET machine like yours, you might send a query for help to
POSTMAST@STANFORD.BITNET.  For more specifics about STANFORD, send the
command SEND NODENTRY STANFORD to NETSERV@TREARN.BITNET.
 
Good luck -- Herman J. Woltring <woltring@hnykun53.bitnet>
--
   The opinions expressed are not necessarily those of the University of
     North Carolina at Chapel Hill, the Campus Office for Information
        Technology, or the Experimental Bulletin Board Service.
           internet:  bbs.oit.unc.edu or 152.2.22.80
Newsgroups: sci.math
From: mutation@dorsai.com (Florian Lengyel)
Subject: Re: too intuitive to prove
Organization: The Dorsai Embassy +1.718.729.5018
X-Newsreader: Tin 1.1 PL4
Date: Fri, 9 Oct 1992 13:59:34 GMT

menasian@milton.u.washington.edu (Gregor Menasian) writes:
: A group of us are working on a problem that is far too obvious for us to
: grasp.  We need to prove, either formally or informally, that a relaion R
: on a set A is symmetric if and only R=R^(-1)
: 
: We're looking for either ideas to start us off or a complete proof.  
: (a complete proof is, of course, perfered)
: 
: Our biggest problem is that the proof must be formal.  
: 
: Thanks, 
: We call our selves the mutants.
: 
R = R^{-1} implies R is contained in R^{-1}, which is equivalent to
\forall (a, b) \in R, (b, a) \in R. If R is contained in R^{-1},
then also R^{-1} is contained in (R^{-1})^{-1} = R, so that
R = R^{-1}. 

That will be $75/hour, please.

-- 
MUTATION@DORSAI.COM
FLORIAN@NEOTERIC.COM
From: cet1@cus.cam.ac.uk (C.E. Thompson)
Newsgroups: sci.math
Subject: Re: The problem of Irish men
Date: 15 Oct 92 21:52:10 GMT
Organization: U of Cambridge, England

In article <israel.719166972@unixg.ubc.ca>, israel@unixg.ubc.ca 
(Robert B. Israel) writes:
|>
|> Perhaps what Surya meant was:
|>   there are at least two Irish men who shook hands with the same
|>   number of other Irish men.
|> (i.e. multiple shakes with the same man don't count).

You must exclude loops as well as multiple edges: it doesn't count to shake
hands with yourself. (We would have had less quibbling if the problem had 
been about the Belgians rather than the Irish, wouldn't we?)

|> Actually you have to add another clarification 
|> [...]
|> 
|> Once you do this, it's an easy application of the Pigeonhole Principle.

Easy, but not absolutely trivial. You have to observe that orders 0 and N-1
cannot coexist.

Chris Thompson
JANET:    cet1@uk.ac.cam.phx
Internet: cet1@phx.cam.ac.uk
Newsgroups: sci.math
From: gokhman@ringer.cs.utsa.edu (Dmitry Gokhman)
Subject: Re: electronic math notation
Organization: University of Texas at San Antonio
Date: Sun, 11 Oct 1992 21:07:42 GMT

In article <1b58o7INN3ps@hilbert.math.ksu.edu> jxh@math.ksu.edu (James C. Hu) writes:
>but clarity more so.  Someday, we will be reading Usenet with WYSIWIG
>screens, transmitted via some sort of standard way, and we won't have
>to worry about it anymore :-).

Nexts already have mail facilities that do this (by using attached
uuencoded chunks).  phsssssss.... (I am holding my breath).  :) 
/////////////////////////////////////////////////////////////////////
- Mr. Gumby    * \oo7    Dmitry Gokhman -> gokhman@ringer.cs.utsa.edu
   says:        `/v/-*   
MY BRAIN HURTS  J  L             YOUR AD HERE!
/////////////////////////////////////////////////////////////////////
Newsgroups: sci.math
From: pamws@sunvis1.vislab.olemiss.edu (Mark Sprague)
Subject: Re: Question on numerical integration
Organization: Mississippi State University
Date: Fri, 9 Oct 1992 22:31:23 GMT

>In article <1992Oct7.113401.1322@rz.uni-karlsruhe.de> vhansen@ipfs.bau-verm.uni-karlsruhe.de (Wolfgang von Hansen) writes:
>>How can one calculate things like
>>
>> a                oo
>>Int f(x) dx  or  Int f(x) dx
>>-oo               a
>>
>>numerically. I know how to do such things with finite limits,
>>but I've got no idea how to deal with infinite limits.
>>
>>Thanks in advance, Wolfgang

With some functions there is an upper (or lower) limit beyond which there
is no significant contribution to the integral.  Once you determine that
limit, you have reduced the problem to an integral over finite limits.

-Mark Sprague
pamws@sunvis1.vislab.olemiss.edu
Newsgroups: sci.math
From: se_karne@rcvie.co.at (Georg Karner)
Subject: Re: Electronic math notation
Organization: Alcatel Austria - Elin Research Center, Vienna
Date: Fri, 9 Oct 1992 09:43:53 GMT

If you use TeX notation, probably most people on the net will understand
you. A complete list is given in

   Donald E. Knuth, The TeXbook, Addison Wesley

Just some of the most important rules

 _  preceeds a subscript
 ^  preceeds a superscript
 greek letters are written \alpha, \beta, ... and \Alpha, \Beta, ...
 quantifiers are \forall and \exists
 most standard functions (like the trigonometric ones) are preceeded by
 a \
 Curly braces {,} are used for grouping

For example, you may write

  \int_0^{2\pi} \sin x dx  = 0
  \forall x \sin^2 + \cos^2 = 1

  For nxn matrices A, B, C, we have C = AB if
 
     C_{ij} = \sum_{k=1}^n a_{ik} b_{kj}


etc.

Hope this helps.

-- 
+-- Georg.Karner@rcvie.co.at ---------------------------------------+
|   Georg Karner, Alcatel Austria-ELIN Research Centre,             |
|   A-1210 Vienna, Austria                                          |
+-- fax +43 1 391452 --------------------- voice +43 1 391621 263 --+

Newsgroups: sci.math
From: jbaez@riesz.mit.edu (John C. Baez)
Subject: Re: Area of five sided polygon needed
Organization: MIT Department of Mathematics, Cambridge, MA
Date: Tue, 13 Oct 92 03:05:26 GMT

In article <1992Oct12.200125.826@altair.selu.edu> fcs$1224@altair.selu.edu writes:
>Given a five sided polygon, is there a formula, in terms
>of its sides, for the area?

Clearly not, because the lengths of the sides don't determine the
area.  Pentagons are "floppy."  So are quadrilaterals, for that matter.
From: lusardi@acsu.buffalo.edu (Christopher Lusardi)
Newsgroups: sci.math
Subject: Re: STRUCTURE OF TIME and God
Date: 8 Oct 92 16:55:03 GMT
Organization: State University of New York at Buffalo/Comp Sci

I lost my faith at BYU in Provo. The Mormons believe that black people are
cursed thats why there black. I've read this in their Sunday school books. 
In the book of Mormon, it has to do with a younger brother becoming more 
powerful in the family, so the younger brother kind of turned the older one
black. The older brothers children became known as the Laminites. These are
the Indians of early America etc. The Mormons believe 3 groups of people
came to the Americas before Columbus in submarines etc. These early 
civilizations died out after battles on the hill Cumorah. The Mormons don't
believe in hell, but a hierarchy of heavens ruled over by god the father,
god the sun, ant the holy spirit. Most male 19 year olds go on missions
throughout the world. They say all the other religions fail because they 
don't compare to this. The Mormons believe in a 10% tithe of their income 
to the church etc.

Every year during home coming at BYU the school burns a hugh "Y" on a mountain
overlooking the university. (The university of Utah has a "V" or "U".)
BYU is the largest private religious school that I know. I say I'm an 
Catholic but I'm really agnostic.

My brothers are still religious. I'v had myself excommunicated from this 
church.

					Thats my 2 cents,
-- 
Christopher M. Lusardi     University At Buffalo  lusardi@sybil.cs.buffalo.edu
Newsgroups: sci.math
From: dagjo@ifi.uio.no (Dag Espolin Johnson)
Subject: 'Perfect' numbers
Organization: Dept. of Informatics, University of Oslo, Norway
Date: Thu, 8 Oct 1992 13:20:01 GMT
Originator: dagjo@sognsvann.ifi.uio.no


Does someone have a list of the first numbers (as many as possible) that are
'perfect'?

With 'Perfect number' I mean those numbers such that if you add together all
the numbers that is divideable with the numer, you get the number.

The first one is 6     (1+2+3 = 6)
The next one is 28     (1+2+4+7+14 = 28)


If this is a FAQ, please tell me where I can find the answer.


Dag Espolin Johnson  -  dagjo@ifi.uio.no
From: conrad@germain.harvard.edu (Keith Conrad)
Newsgroups: sci.math
Subject: p-adic gamma
Date: 15 Oct 92 03:49:13 GMT
Article-I.D.: husc3.1992Oct14.234914.16403
Distribution: world
Organization: Dept. of Math, Harvard Univ.

p = 3, 0 <= n <= 1082, n = 9k + r with 0 <= r <= 8
A_3(9k) = 2k
A_3(9k + 1) = 2k
A_3(9k + 2) = 2k
A_3(9k + 3) = 2k + 2
A_3(9k + 4) = 2k + 1
A_3(9k + 5) = 2k + 3 + ord_3(2k + 1)
A_3(9k + 6) = 2k + 2
A_3(9k + 7) = 2k + 2
A_3(9k + 8) = 2k + 3

I have looked at A_p(n) as well for p = 5, 7, 11, 13, and 17 for
n running up to at least 400 (in the case of 5 and 7 for n up to 1400),
and what seems to be happening is 
         A_p(n) = (p - 1)[n/p^2] + r_n,   ( [ ] = greatest integer)
where r_n >= 0 and for "most" residue classes n(mod p^2) it turns out that
if m = n (mod p^2) then r_m = r_n.  For example, when p = 2 this "mod p^2 
periodicity of r_n" occurs for all classes mod 4.  When p = 3 there is 
one exception, namely the class of 5 mod 9.  When p = 5 there seem to be 
(at least) four exceptions: the classes of 4, 7, 16, and 22 mod 25.  When 
p = 7 I have so far found only one class mod 49 for which the n in that
class don't have the same r_n value - it's 19 mod 49.  Due to the slower
growth of A_p(n) as p increases, there are probably some more exceptions to
this when p = 7 which I have not located.
Even in the (seemingly) few exceptional classes mod p^2 not admitting a
constant r_n value, it seems that r_n = const. + s_n where the const. only 
depends on the residue class and s_n increases very slowly with n (see the data
for p = 3 and the class of 5 mod 9).  
So what I'd like to know is if anyone can explain this behavior of
A_p(n), ESPECIALLY the periodicity of the r_n's mod p^2.  The fact that
A_p(n) grows like (p - 1)n/p^2 seems to be due to Gamma_p(n) being locally
analytic on cosets of pZ_p (well, for p > 2), although I haven't worked out
the details on this.

Responses can be given on this newsgroup, although I'd also appreciate it 
if they could be sent to me as well.  Thanks.
Newsgroups: sci.math
From: stevesa@microsoft.com (Steve Salisbury)
Subject: Re: Calculating pi: help!
Date: 16 Oct 92 20:01:12 GMT
Organization: Microsoft Corporation

In article <1992Oct15.103812.7219@kth.se> TordM@VanA.PhySto.SE writes:
>In article <7567@charon.cwi.nl>, dik@cwi.nl (Dik T. Winter) writes:
>
>>Compiler bug?  Try main(){printf("%.4d\n",0);} if this program does not
>>print 0000 your compiling system has a bug.
>
> compiler bug indeed; yet another reason not to use "c" :-)

Pardon me, but the compiler does NOT handle printf() format strings --
that's a C run-time library function.  This is in important distinction.
C run-time libraries are usually closely coupled with a given compiler,
but that's not the same thing as being "part of" the compiler.

According to the ANSI C standard, %.4d should emit at least four digits
(using leading zeroes), but this functionality was NOT in the older,
de facto C standard, the C book by Kernighan & Ritchie.

The more portable and dependable solution would be: printf ("%04d\n",...

Steve Salisbury

*  Obligatory  *|-------------------------------------------------------|
*  disclaimer  *| The views expressed in this message are my own and in |
* required  by *|   no way reflect the views of Microsoft Corporation.  |
* my employer: *|-------------------------------------------------------|
From: mlevin@husc8.harvard.edu (Michael Levin)
Newsgroups: sci.math
Subject: looking for epigenetic algorithm (like fractals, etc.)
Date: 14 Oct 92 22:40:13 GMT
Article-I.D.: husc3.1992Oct14.184014.16391
Distribution: usa
Organization: Harvard University Science Center


     The Mandelbrot and Julia set algorithms are epigenetic in the
sense that they map a small seed into a complex image. I.e., you put in
a polynomial (coded as a a couple of dozen characters, such as
"c^2 + 3*c + 10") and it creates an interesting image. Are there any
other algorithms which have that property? In other words, are there
any systems such that their implementation on the computer takes
relatively short inputs (strings with some interpretation) and
produces interesting and varied images? If anyione has any ideas,
please email to mlevin@husc8.harvard.edu.

Mike Levin
Newsgroups: sci.math
From: jbaez@riesz.mit.edu (John C. Baez)
Subject: Re: What a weird group!!!
Organization: MIT Department of Mathematics, Cambridge, MA
Date: Thu, 15 Oct 92 18:53:24 GMT

In article <1bjnc4INN7hp@function.mps.ohio-state.edu> edgar@function.mps.ohio-state.edu (Gerald Edgar) writes:
>
>>[the Bohr compactification of the real numbers]
>
>>But what does this group *look like*??  That's what I'd like to know!!
>
>The construction uses the Axiom of Choice, so no one knows...

Well, aren't there at least some theorems about it, so I can get some
idea of what it's like?  I wasn't asking for an explicit construction of
every element.  :-)

>For a (perhaps) simpler warm-up, try the Bohr compactification of the
>integers.

>Or, before you tackle visualizing that, how about visualizing the
>Stone-Cech compactification of the integers?

Is that a group too?  I'm just looking for some interesting tidbits of
knowledge.  
Newsgroups: sci.math