HDTenEightyP/NetNews huggingface dataset:
Newsgroups: sci.math
Subject: Re: Warm and Fuzzy? Koalas vs. Math
From: a_rubin@dsg4.dse.beckman.com (Arthur Rubin)
Date: 15 Sep 92 23:01:58 GMT

In <1992Sep14.034933.26912@galois.mit.edu> jbaez@riesz.mit.edu (John C. Baez) writes:

>matmcinn@nuscc.nus.sg (Mcinnes B T (Dr)) inquires:

>>By the way, John, what IS the best flavour of ice cream?

>It should be easy to calculate once we work out the bugs in our Theory
>of Everything.

>In the meantime, I've been studying a little string theory.  I
>recommend Kaku's Introduction to Superstrings, in part because it is
>a good exposition, and in part because he is honest, even listing the
>pros and cons of string theory quite honestly.  Heck, I'll list 'em,
>just to prove I am not alone in my criticisms.  [Slightly abridged.]

>3)  It is presumputous to assume that there will be no surprises in
>the "desert" between 100 and 10^19 GeV.  New, totally unexpected
>phenomena have always cropped up when we have pushed the enrgy scale
>of our accelerators.  Superstring theory, however, makes predcitions
>over the next 17 orders of magnitude, which is unheard of in the
>history of science.

But does it predict no new "particle"s in that range?

>5)  The theory has an embarrassment of riches.  There are
>apparently *thousands* of ways to bread down the theory to low
>energies.  Which is the correct vacuum?  Although superstring theory
>can produce the minimal theory of SU(3) x SU(2) X U(1), it also
>predicts many other interactions that have not yet been seen.  

I guess it doesn't make predictions yet....

>6)  No one really knows how to break a 10-dimensional theory down to 4
>dimensions.   

If only it were 11-dimensional....


--
Arthur L. Rubin: a_rubin@dsg4.dse.beckman.com (work) Beckman Instruments/Brea
216-5888@mcimail.com 70707.453@compuserve.com arthur@pnet01.cts.com (personal)
My opinions are my own, and do not represent those of my employer.
My interaction with our news system is unstable; please mail anything important.
From: ara@zurich.ai.mit.edu (Allan Adler)
Newsgroups: sci.math
Subject: hyperflex?
Date: 8 Sep 92 05:04:24 GMT
Article-I.D.: camelot.ARA.92Sep8000424
Distribution: sci
Organization: M.I.T. Artificial Intelligence Lab.


Let C be an algebraic curve in n dimensional space over an algebraically
closed field. Let x be a point of C. We can describe a tangent to C
at x as a line going through x and a point of C infinitely near to x,
hence through 2 consecutive points of C. If the line actually goes through
3 consecutive points of C, we call it a point of inflection. I think that
if the line goes through 4 consecutive points, it is called a hyperflex,
but I don't have a reference for this terminology.

Can someone confirm or deny this and provide a reference?

Allan Adler
ara@altdorf.ai.mit.edu
Date: Monday, 14 Sep 1992 14:35:44 EST
From: <RVESTERM@vma.cc.nd.edu>
Newsgroups: sci.math
Subject: Re: Chess Problem

for the bishop problem, you say that (for example) there are 64-8=56 safe
places to put the second bishop.  however, this is not true.  consider the
case, for example, when the first bishop is placed in one of the four
center squares of the board.  the second bishop then is not safe in fifteen,
not eight, places.
From: kewe@bskewe.atr.bso.nl (Cornelis Wessels)
Newsgroups: sci.math
Subject: Fast Fourier Transform 
Date: Mon, 14 Sep 92 19:03:51 GMT
Organization: Me? Organized?


In article <1992Sep14.111815.12937@phillip.edu.au> t9014186@phillip.edu.au writes:

  > 
  > Does anybody know where I can find, or does anybody have, a source listing of
  > how to perform a Fast Fourier Transform ??
  > 
  > A listing in C would be preferable but not essential.
  > 
  > 
  > 
  > -- 
  > =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
  > =-= Steven Corral                                                       =-=
  > =-=                                                                     =-=
  > =-= T9014186@phillip.edu.au                                             =-=
  > =-= scorral@arcadia.mc.phillip.edu.au                                   =-=
  > =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
  > 
Cornelis Wessels
kewe@bskewe.atr.bso.nl
From: wsadjw@rw7.urc.tue.nl (Jan Willem Nienhuys)
Newsgroups: sci.math
Subject: Re: what are quadturnians?
Date: 9 Sep 92 15:31:05 GMT
Reply-To: wsadjw@urc.tue.nl
Organization: Eindhoven University of Technology, The Netherlands

In article <CHALCRAFT.92Sep9092653@laurel.uk.tele.nokia.fi> chalcraft@uk.tele.nokia.fi (Adam Chalcraft) writes:
#
#The extra information is that you represent (x,y,z) in the obvious way by
#xi+yj+zk, and then translations correspond to addition. This much is
#obvious, and gains you nothing so far. The clever bit is that if
#
#  (x1i+y1j+z1k)*(x2i+y2j+z2k)=-t3+x3i+y3j+z3k
#
#then t3 is (x1,y1,z1).(x2,y2,z2) [dot product] and (x3,y3,z3) is
#(x1,y1,z1)^(x2,y2,z2) [cross product] (check sign before use :-).
#

somewhat easier: quaternions are pairs (a,v) with a real and v vector (3D),
evident addition, and multiplication:
 
(a,v)(b,w)= (ab - v.w , aw + bv + v^w ).

(I emailed the original poster, but it bounced.)

JWN
Newsgroups: sci.math
From: rscott@csws17.ic.sunysb.edu (Robert Scott)
Subject: Re: Warm and Fuzzy?  Koalas vs. Math
Organization: State University of New York at Stony Brook
Date: Mon, 14 Sep 1992 15:21:27 GMT


In article <22218@galaxy.ucr.edu> baez@ucrmath.ucr.edu (john baez) writes:

>of any other human activity, but it is NOT warm and fuzzy.  It is cool and
>smooth.  If you want something warm and fuzzy, raise koala bears.


I THINK MATH IS WARM AND FUZZY AND COOL AND SMOOTH.  SORT OF LIKE A BABY
SHARK.



-JAMES DOLAN
From: gjm11@cus.cam.ac.uk (G.J. McCaughan)
Newsgroups: sci.math
Subject: Re: Proof of God's Existence
Date: 4 Sep 92 22:19:11 GMT
Organization: U of Cambridge, England

In article <ARA.92Sep3133928@camelot.ai.mit.edu>, ara@zurich.ai.mit.edu (Allan
Adler) writes:

> [long tirade against religion]

Tell me, how would you react if, say, a Christian or a Muslim had posted here a
similarly-long tract in favour of their particular creed?
Newsgroups: sci.math
From: eln122b@fawlty3.eng.monash.edu.au (Ivan Chin)
Subject: ITPACK for complex number ?
Keywords: ITPACK
Organization: Monash University, Melb., Australia.
Date: Wed, 16 Sep 1992 01:46:57 GMT

I am looking for some iterative package like itpack
that solves Ax=b where A is a sparse slightly non symmetrical
diagonal complex matrix. As itpack is based on A being real.
If anyone who has such information please inform me through email
In fact anyone who knows about the iterative method 'Orthomin',
please inform me of the source (books , periodicals anything ).
Thanks 
Ivan...
From: edgar@function.mps.ohio-state.edu (Gerald Edgar)
Newsgroups: sci.math
Subject: Re: measures of the `size' of infinite sets
Date: 10 Sep 1992 08:22:24 -0400
Organization: The Ohio State University, Dept. of Math.
NNTP-Posting-Host: function.mps.ohio-state.edu


Here is an old gem along these lines.  A positive integer, in its
decimal representation, begins with one of nine possible
digits.  What proportion of them begin with the digit '1'?

Here is an exercise (alleged to work, I haven't done it...):
Take the front page of the New York Times.  Write down in decimal form
all of the numbers mentioned.  Then about 30% of the numbers will
begin with the digit '1'.

Or, take an atlas, and look up the lengths of the rivers (in km).
About 30% of them begin with the digit '1'.  Repeat, using miles.
Still 30%.

In what sense can the answer 'about 30%' be made precise?

If you have seen this before, wait a few days before posting answers,
so that others have some time to think about it...
-- 
  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: Looking for Computer Aid
Date: 13 Sep 92 22:59:27 GMT
Article-I.D.: clark.1992Sep13.225927.333
Organization: Clark College, Vancouver, Wa.  USA

In article <20284@plains.NoDak.edu> myhre@plains.NoDak.edu (Robert Myhre) writes:
>
>  HI all.  I was wondering if anyone knew of a program for tutoring in
>Calculus, mainly integrationg?  I could use some refresher/aid!
>
>Thanks
>
>Robert Myhre

Robert:  Broderbund has an interesting progam available in both
PC and MAC versions, called Calculus.  I haven't used it very
much but it seems to be a good one so far.

Dennis
watson@clark.edu
> 
Newsgroups: sci.math
From: orourke@sophia.smith.edu (Joseph O'Rourke)
Subject: Re: Minimizing waste when cutting fabric.
Keywords: Waste; Fabric
Organization: Smith College, Northampton, MA, US
Date: Sun, 6 Sep 1992 00:00:32 GMT

In article <8832@amsaa-cleo.brl.mil> matt@amsaa-cleo.brl.mil (Matt Rosenblatt) writes:
>Suppose I am an upholsterer who buys fabric in rolls.  [...]
>This must be a basic version of a much more general problem where
>the pieces to be cut can take all sorts of shapes.  Surely there
>have been algorithms designed for the more general case.  What kind
>of algorithms are they, and where can I find them?

Victor Milenkovic in the Computer Science Department at Harvard University
is working hard on this, and has published a series of papers on the
topic, the most recent at the 4th Canadian Conference on Computational
Geometry a few weeks ago.  Check with him.
From: maj@waikato.ac.nz
Newsgroups: sci.math
Subject: Re: measures of the `size' of infinite sets
Date: 16 Sep 92 09:25:42 +1200
Organization: University of Waikato, Hamilton, New Zealand

In article <1992Sep15.040424.13593@sq.sq.com>, msb@sq.sq.com (Mark Brader) writes:
>> Here is an exercise (alleged to work, I haven't done it...):
>> Take the front page of the New York Times.  Write down in decimal form
>> all of the numbers mentioned.  Then about 30% of the numbers will
>> begin with the digit '1'. ...
>> Or, take an atlas, and look up the lengths of the rivers (in km).
>> About 30% of them begin with the digit '1'.  Repeat, using miles.
>> Still 30%.
> 
> Just a side remark here.  It occurs to me that a larger fraction of
> students today will find this "30% effect" surprising or counter-
> intuitive than was the case when I was in school.  You see, in those
> days, we used *slide rules*...
> -- 
> Mark Brader             "True excitement lies in doing 'sdb /unix /dev/kmem'"
> utzoo!sq!msb, msb@sq.com                                -- Pontus Hedman
> 
> This article is in the public domain.

If numbers vary over several orders of magnitude, it may be 
reasonable to treat their fractional parts as uniformly distributed
on [0,1). 

MTB > let k1=logten(2)
MTB > print k1
K1       0.301030

-- 
Murray A. Jorgensen [ maj@waikato.ac.nz ]    University of Waikato
Department of Mathematics and Statistics     Hamilton, New Zealand      
__________________________________________________________________
'Tis the song of the Jubjub! the proof is complete,
if only I've stated it thrice.'
Newsgroups: sci.math
From: brock@NeXTwork.Rose-Hulman.Edu (Bradley W. Brock)
Subject: Re: Perfect numbers requested.
Organization: Rose-Hulman Institute of Technology
Date: Wed, 9 Sep 1992 17:22:51 GMT


In article <1992Sep9.095140.2009@drycas.club.cc.cmu.edu>  
perry@drycas.club.cc.cmu.edu writes:
> 	Could someone please direct me to an ftp site, or mail me 
> a list of perfect numbers?  I am currently running a program to find
> perfect numbers, and it is taking a terribly long time. 
> 
> BTW, a perfect number is a number in which the sum of the factors equals the
> number.
On p. 204 of Ken Rosen's Elementary Number Theory and its Applications, 2nd ed.  
is a list of the known Mersenne primes, except of course the most recently  
discovered 2^756839-1 (Focus 12:3 (June 1992),3).

(Recall that a perfect even number is of the form 2^(p-1)(2^p-1) where (2^p-1)  
is a Mersenne prime, and that no odd perfect numbers have been discovered.)

--
Bradley W. Brock, Department of Mathematics
Rose-Hulman Institute of Technology  | "Honor one another above yourselves."
brock@nextwork.rose-hulman.edu       | -Paul of Tarsus to the Romans
From: koiran@ens-lyon.fr (Pascal Koiran)
Newsgroups: sci.math
Subject: dynamical systems and (perhaps) algebraic geometry
Date: 8 Sep 92 11:06:04 GMT
Reply-To: koiran@ens-lyon.fr
Organization: Ecole Normale Superieure de Lyon

Hello,

Can someone provide a solution to the following problem, or give references
to related work in the litterature ?

Let f:[0,1]^n-->[0,1]^n (n>1) be a function of the form
f(x)=(P_1(x),P_2(x),...,P_n(x)) where the P_i's are polynomials.
Let's consider the iterates of f. Is the following situation possible ?

for all k, there exists an infinite number of k-cycles (by k-cycle, I mean
a cycle of length exactly k).

Generalize to rational functions instead of polynomials, and to analytic 
functions.

Thanks,

Pascal.
Newsgroups: sci.math
From: spworley@netcom.com (Steven)
Subject: 3 space terahedron-packing
Date: Thu, 10 Sep 92 03:20:41 GMT
Organization: Netcom - Online Communication Services  (408 241-9760 guest) 

I am trying to implement an interpolation algorthim over 3D space by
using a "grid" of tetrahedrons. What I need to compute is a complete
tiling of 3-space with unit length tetrahedrons: ie, given an XYZ
location, identify the four points of the tetrahedron that encloses
that location in this "packed" space. Obviously any offset or rotation
of this packing "solution" is also a solution, but I don't care which
particular tiling I compute as long as it is constant.

Where would I look to solve this problem? Computational geometry
books?  I've already sat down with pencil and paper, and have also
made about 10 oragami paper solids. This problem looked pretty simple
when I first started it, but it seems like an elegant solution is
eluding me. :-( 

If anyone can point me to any references for this kind of tiling, or
by sheer chance have an algorithm (hah!) I'd appreciate any help you
can give me. Thanks!

-steve
spworley@netcom.com
From: matt@amsaa-cleo.brl.mil (Matt Rosenblatt)
Newsgroups: sci.math
Subject: Re: Proof of God's Existence
Summary: Never heard of the Sailor Man?
Keywords: . . . and that's all what I am!
Date: 15 Sep 92 16:55:21 GMT
Organization: U.S. Army Material Systems Analysis Activity, APG MD

In article <1992Sep5.200902.1@tnclus.tele.nokia.fi> 
hporopudas@tnclus.tele.nokia.fi writes:

>In article <8815@amsaa-cleo.brl.mil>, matt@amsaa-cleo.brl.mil
>(Matt Rosenblatt) writes:

>> In article <1992Sep1.090011.1@tnclus.tele.nokia.fi>
>> hporopudas@tnclus.tele.nokia.fi writes:

>>>   I think that God's existence is an axiom. He says in the Holy Bible
>>> (Second book of Moses 3:14-15 in Old Testament and also in Johannes
>>> 8:28-29 in New Testament) that He is "Existence Himself".  [Hannu]

>> Er, not quite.  What He says in 2 Moses 3:14 is, "I AM WHAT I AM."
>> If "I AM WHAT I AM" amounts to an existence proof, then we have just
>> proved that Popeye The Sailor Man exists, too.   [Matt Rosenblatt]

>  Contents of your sentence is empty.  [Hannu]

This just goes to show you.  I have no doubt that Hannu and the rest
of the Finns have heard of "Mickey Mouse."  How is it that "Popeye"
does not have the same world-wide renown?

For those who have never heard of him, Popeye is a fictional American
cartoon and comic-strip character.  He is the one who gains superhuman
strengh whenever he eats a can of spinach.  In his own dialect, his
slogan is, 

           "I YAM WHAT I YAM, AND THAT'S ALL WHAT I YAM,
            I'M POPEYE, THE SAILOR MAN."

With all that, no matter how many times he asserts, "I AM WHAT I AM,"
he is still a fictional character.  Therefore, one may not prove the
existence of a being solely on the basis that he is quoted as having
said, "I AM WHAT I AM."  Let Popeye appear in thunder and lightning
and smoke to six hundred thousand men with their wives and children
and tell them, "I AM," and then I'll believe he exists.

					-- Matt Rosenblatt
					(matt@amsaa-cleo.brl.mil)
From: dfr@usna.navy.mil (PROF D. Rogers (EAS FAC))
Newsgroups: sci.math
Subject: Re: Help: inscribed circle of three circles
Date: 9 Sep 92 16:35:56 GMT
Organization: U. S. Naval Academy

In article <Sep.8.09.46.26.1992.3259@yoko.rutgers.edu> czako@yoko.rutgers.edu (Gabor M. Czako) writes:
!In a computer program I am writing I need to find the inscribed
!circle(s) of three circles.  In detail, I have three circles with
!centers (x_1, y_1), (x_2, y_2), and (x_3, y_3) and radii r_1, r_2,
!r_3.  I need to find the inscribed circle(s) with center (x, y) and
!radius r which satisfies the following equations:
!
!	(x - x_1)^2 + (y - y_1)^2 = (r + r_1)^2
!	(x - x_2)^2 + (y - y_2)^2 = (r + r_2)^2
!	(x - x_3)^2 + (y - y_3)^2 = (r + r_3)^2
!
!I have not been able to analytically solve for the 0, 1, or 2
!solutions of x, y, and r.  

G'day Gabe,

Look at the following paper:

Rogers, David R., Interactive graphics and numerical control,
CAD Journal pp 253-261, Vol 12 No 5 Sept 1980.

This problem as well as many others of this type are solved
for and discussed.

Dave Rogers
From: carter@cmptrc.lonestar.org (Carter Bennett)
Newsgroups: sci.math
Subject: Re: Chess Problem
Summary: Odds are 1 in 2213082684!
Date: 12 Sep 92 05:36:28 GMT
Organization: CompuTrac Inc., Richardson TX

rairan@ecf.toronto.edu (RAI Ranjan) writes:
>Chess Problem:
> Eight rooks are placed at random on a chessboard.  
> What is the probability that no two rooks can attack one another?

Ahoy!

   Oooh!  I like these problems.  Glad you sent it along!
First, let's check the number of distributions of 8 rooks on the board.
This is the combination calculation of 64 squares taken 8 at a time:

   / 64 \  -  (64!) / ( (64 - 8)! 8! )  = 4426165368
   \  8 /  -

   So there are 4426165368 possible ways to place the 8 rooks on the 
board.  My understanding is that no two rooks can attack each other 
only when they are arranged such that they line up on one of the two 
diagonals of the board.  Meaning there are 2 ways out of 4426165368 
possible setups that meet the criteria.  Putting that in normalized odds:

    2 / 4426165368 -> 1 chance in 2213082684

Two REALLY NEAT THINGS about this problem - 

  I've seen chess boards many times.  We've seen all kinds of arrangements
of chess pieces.  Just knowing how many possible arrangements of eight
pieces is still fascinatingly mind-boggling to me.

  BUT THE REALLY NEAT THING ABOUT THIS PROBLEM is that I was able to give
you integer answers to this problem because I had a calculator (HP48SX)
on hand that could handle them.  dc(1) on Unix would do it, too.  But
just a few short years ago, we would have had to settle for approximations
in exponential notation unless we actually multiplied 64x63x62...x56 out
by hand, and then dividing the result by 40320, again by hand!!!  Too
many significant digits to keep track of on yesterday's calculators!

  FOLLOW-UP QUESTION FOR EXTRA CREDIT:

  Determine the odds for doing the same with eight bishops!  ;-)

Carter R. Bennett, Jr. - Scientist      No matter where you go...
carter@scilab.lonestar.org - home                 .../dev/tty!
carter@cmptrc.lonestar.org - work
KI5SR
From: ara@zurich.ai.mit.edu (Allan Adler)
Newsgroups: sci.math
Subject: Promise in EGA
Date: 12 Sep 92 18:03:27 GMT
Distribution: sci
Organization: M.I.T. Artificial Intelligence Lab.


In EGA IV.21.15.9, Grothendieck considers  the following situation:
one has a scheme S and a flat S-scheme f:X-->S. Under those conditions,
he defines the group Div(X/S) of divisors on X relative to S. He then
is able to define functors Div_{X/S}: Sch/S--> Ab and 
Div_{X/S}^+:Sch/S-->Ens by associating to any S-scheme S'-->S the group
Div(X'/S') and the set Div^+(X'/S') respectively, where X' is the product
of X and S' over S.

Grothendieck then writes: "On verra plus loin (chap. VI) des cas importants 
o\`u le functeur $Div^+_{X/S}$ est repr\'esentable ($\bf0_{III}$,8.1.8)."

As we all know, Chapter 6 never got written. Did the theorem that Grothendieck
refers to ever get proved anywhere else and if so where?

Allan Adler
ara@altdorf.ai.mit.edu
Newsgroups: sci.math
From: gjm11@cus.cam.ac.uk (G.J. McCaughan)
Subject: Re: n doesnt divide 2^n-1
Organization: U of Cambridge, England
Date: Mon, 7 Sep 1992 22:45:54 GMT

It was conjectured that if we write 2^n=an+b with 0<=b<n then
a is always even and b is always a power of 2, or at least always even.
For n=25 we get b=7.
For n=12 we get a=341.
So, I'm afraid none of the conjectures is true.
Powers of 2 do seem to come up an awful lot for b, though.
--
From: bubai@matt.ksu.ksu.edu (P.Chatterjee)
Newsgroups: sci.math
Subject: Re: Set-Theory Doubts: Got some conceptual glitches
Date: 12 Sep 1992 19:41:50 -0500
Organization: Kansas State University
NNTP-Posting-Host: matt.ksu.ksu.edu

bubai@matt.ksu.ksu.edu (P.Chatterjee) writes:

>Hello there,

>I was just wondering if somebody on the net could help clarify a few conceptual glitches I have regarding very elementary concepts of set-theory.

>a) According to my textbook, the ORDERED PAIR of two objects x and y is the set <x,y> = {{x}, {x,y}}. It also goes on to state that by this definition, the ordered pair is determined by x and y; and the order, x first and y second, is important unless x=y.

>What throws me off is the definition; what is the motivation behind it?                      
>b) Let f: X --> Y be an injective mapping. By definition, this means:
>  for all x, x' in X: f(x) = f(x') ==> x=x'.

>Equivalently, x not equal to x' ==> f(x) not equal to f(x').

>My question here is: for the firstmentioned implication why is the CONVERSE not true? (I know it's not but am having trouble finding an intuitive/logical answerfor it).



>>I'm sorry for the STUPID statement about the CONVERSE being untrue; of course, by the definition of a function, as some people pointed out, the converse is   true. Obviously, I got caught up in the 'logical' bind of 'if P, then Q' propositions and made the error of thoughtlessly discounting the reverse implication.
Anyway, thanks to all concerned who pointed it out.
>Would really appreciate if somebody helped clarify these concepts.

>Thanks.
Newsgroups: sci.math,comp.lang.misc,comp.lang.fortran,comp.std.c,comp.lang.c
From: karl@ima.isc.com (Karl Heuer)
Subject: Re: Scientists as Programmers (was Re: Small Language Wanted)
Followup-To: comp.std.c
Organization: Interactive Systems, Cambridge, MA 02138-5302
Date: Sat, 12 Sep 1992 05:01:57 GMT

In article <1992Sep11.174618.6049@umbc3.umbc.edu> hybl@umbc4.umbc.edu (Dr. Albert Hybl (UMAB-BIOPHYS)) writes:
>>when the standard doesn't define the result, the implementations can do
>>whatever they want.
>
>Well the suicide gene has been spliced into ANSI C, has it.  This suggests
>that the lawyers and business administration types have legally colluded []
>to produce an inadequate language standard thus allowing each vendor to write
>compilers that contain proprietary extensions.

I don't understand what you find inadequate here.  Is it the fact that
undefined behavior exists?  That it's possible for a compiler to conform to
the standard and also support extensions?  Or are you talking about this
particular issue (integer overflow)?  What change would you like to have
seen in the Standard?

Karl W. Z. Heuer (karl@ima.isc.com or uunet!ima!karl), The Walking Lint
(Followups to comp.std.c)
From: matmcinn@nuscc.nus.sg (Mcinnes B T (Dr))
Newsgroups: sci.math
Subject: Re: Warm and Fuzzy?  Koalas vs. Math
Date: 14 Sep 92 01:28:50 GMT
Organization: National University of Singapore

By the way, John, what IS the best flavour of ice cream?
Newsgroups: sci.math