HDTenEightyP/NetNews huggingface dataset:
From: ags@seaman.cc.purdue.edu (Dave Seaman)
Subject: Re: Function Terminology
Organization: Purdue University
Date: Fri, 11 Dec 1992 22:18:19 GMT

In article <1gaq3tINNg9q@uwm.edu> radcliff@csd4.csd.uwm.edu (David G  
Radcliffe) writes:
> Suppose I have a function f: A --> B, and C is a subset of B which
> contains the image set of f.  I define a function g: A --> C by
> setting g(a) = f(a) for all a in A.  Usually, f and g can be considered 
> as the same function, but sometimes the distinction is important.
> 
> Is there a standard term or notation for this?

The standard terminology is that f and g have the same image, but  
different ranges. B is the range of f, and C is the range of g. If the  
range of a function happens to coincide with its image, the function is  
said to be "onto", or is called a "surjection."

--
Dave Seaman
ags@seaman.cc.purdue.edu
Newsgroups: sci.math,misc.education
From: asimov@wk223.nas.nasa.gov (Daniel A. Asimov)
Subject: Re: The Continuum Hypothesis:  Must it be {True or False}, or Not?
Organization: NAS, NASA Ames Research Center, Moffett Field, California
Date: Mon, 14 Dec 92 20:00:24 GMT
Distribution: usa

In article <1992Dec11.162239.8548@cadkey.com> dennis@cadkey.com (Dennis Paul Himes) writes:
>In article <1992Dec9.183849.13004@nas.nasa.gov> asimov@wk223.nas.nasa.gov (Daniel A. Asimov) writes:
>>Among those of you who are familiar with the statement of the
>>Continuum Hypothesis, and the fact that it was proved to be
>>independent of ZF + AC, I would like to know:
>>
>>Do you see the Truth or Falsity of the Continuum Hypothesis as 
>>being exclusively dependent on a whether it can be proved or 
>>disproved in some specific axiom system?
>>
>>Or rather, do you see the Continuum Hypothesis as being 
>>{True or False}, in some sense independent of whether or 
>>not it is decidable in any given axiom system?
>>
>
>	Truth is a relative term, although it is usually treated as absolute,
>since when discussing the nature of reality it is relative to the universe.
	[...]
>whether CH is "true" in a very loose use of the term.  I personally have no
>idea how you would go about answering that question.
>
>               Dennis Paul Himes    <>    dennis@cadkey.com

I don't think I succeeded in conveying my question clearly in this case.

Let me ask a similar question in perhaps a simpler setting:

	ASSUME that Fermat's Last Theorem is undecidable from the 
	usual axioms of arithmetic. 

	Then there is a meta-argument which can now conclude that FLT is in fact
	true.  For if it were false, then there must exist a counterexample.
	Now simply doing the arithmetic to show that the counterexample
	really is one, constitutes a disproof of FLT, contradicting undecidability.  
	Therefore, undecidability implies that FLT cannot be false, so it is true.

	Do people buy this, that FLT must be {true or false}, regardless of
	whether it is provably true or false (i.e., decidable)?


Dan Asimov
Mail Stop T045-1
NASA Ames Research Center
Moffett Field, CA 94035-1000

asimov@nas.nasa.gov
(415) 604-4799

Newsgroups: sci.math
From: jhoste@kuju.claremont.edu (Jim Hoste)
Subject: looking for article on loaded dice
Keywords: probability, dice, loaded dice
Organization: Harvey Mudd College, Claremont, CA 91711
Date: Tue, 15 Dec 1992 23:34:07 GMT

Next semester I will be teaching an elementary probability class  
structured around the theme of games and gambling. I want to include some  
material on loaded dice. Surely someone has worked out the physics of  
rolling a die (in the shape of a cube) whose center of mass is not in the  
center of the die. What are the probablities of landing on the various  
faces as a function of the location of the center of mass? The same  
question can be asked for dice in the shape of other polyhedron,  
homogenious or not. 
	I am also interested in the following related question:
Can one create a die having n faces where the probability of landing on  
each of the faces is given in advance?  This is certainly true if *die* is  
interpreted fairly loosely. Somebody must have worked this out already.
	Can anyone recommend any good articles on these topics?
	I will summarize the replies that I receive.
	Thanks, Jim Hoste

ps I am also posting to:
	rec.gambling
	sci.math
	sci.physics
From: mnewman@comlab.ox.ac.uk (Matthew Newman)
Newsgroups: sci.math
Subject: Re: Would Pi repeat, were it expressed in a base other than 10?
Date: 14 Dec 92 09:33:20 GMT
Organization: Oxford University Computing Laboratory, UK
Originator: mnewman@client24.comlab


werdna@cco.caltech.edu (Andrew Tong) writes :
>G.Joly@cs.ucl.ac.uk (Gordon Joly) writes:
>> [see subject line ]
>>That is say non-decimal.
>
>Intuitively (not saying much, that is), I'd say yes, but that it would re-
>quire a transcendental base....

Try writing it in base 3.1415926--- :->
Newsgroups: sci.math,rec.puzzles
From: palais@binah.cc.brandeis.edu
Subject: Re: Densest Sphere Packings in 3D?
Reply-To: palais@binah.cc.brandeis.edu
Organization: Brandeis University
Date: Sat, 19 Dec 1992 16:23:53 GMT

Wu-Yi Hsiang will lecture on his proof that the face-centered cubic
lattice is densest at the AMS Annual meeting in San Antonio next 
month. There is a manuscript floating around. Yo can contact Hsiang
at the Berkeley Math Dept. I don't believe he does email
From: lady@uhunix.uhcc.Hawaii.Edu (Lee Lady)
Newsgroups: sci.math
Subject: Re: Difference between "show" and "prove"
Summary: Is a demonstration different from a proof?
Keywords: proof  demonstration
Date: 16 Dec 92 19:14:42 GMT
Followup-To: sci.math
Organization: University of Hawaii (Mathematics Dept)

In article <BzAIMI.Gt@news.cso.uiuc.edu> west@symcom.math.uiuc.edu 
       (Douglas West) writes:
>cdeloge@cs.ulowell.edu (Carolyn Deloge) writes:
>
>>Hi, I am a CS graduate student and I have a question for the math people.
>>What is the difference between "show" and "prove"?
>
>Technically both mean the same thing, which one might also word as 
>"demonstrate"

Many years ago when I was a computer programmer, one of my fellow workers
was complaining about a former professor and said, very emphatically,
"He didn't even know the difference between a proof and a demonstration."
Not wanting to reveal that I was equally ignorant, I never asked my
fellow worker exactly what the distinction was.  

Later on, after I became a graduate student in mathematics, I did ask
several mathematicians and none of them thought there was a difference
between the two terms.  But obviously somewhere, maybe in mathematical
logic, some people have attached different meanings to these two words
and I'm still curious about it.  

--
It is a poor sort of skepticism which merely delights in challenging
those claims which conflict with one's own belief system.  
                                                          --Bogus quote 
lady@uhunix.uhcc.hawaii.edu         lady@uhunix.bitnet
Newsgroups: sci.math
From: cet1@cus.cam.ac.uk (C.E. Thompson)
Subject: Re: Tiling problem
Organization: U of Cambridge, England
Date: Sun, 20 Dec 1992 00:06:25 GMT

In article <1992Dec18.111210.2852@odin.diku.dk>, torbenm@diku.dk
(Torben AEgidius Mogensen) writes:
|> cet1@cus.cam.ac.uk (C.E. Thompson) writes:
|> 
|> >It occured to me that one could put more constraints on the problem by using
|> >periodic boundary conditions. This brings the probabilisticly suggested largest
|> >square down from about 17 to about 11, and so it might be more ammenable to
|> >a brute-force-and-ignorance computational attack.
|> >
|> >This version could be stated as: colour the tiles of the infinite plane square
|> >lattice black and white, periodically with period N in both directions, such
|> >that the only (orthogonally oriented) squares with all four corners the same
|> >colour have both sides divisible by N.
|> 
|> Well, since someone already posted a 13x13 solution, an estimate of 11
|> is a bit on the low side. But the suggestion sounds interesting.

My first reaction to this was to point out that the "periodic boundary
conditions" version is really more restrictive -- in term of the original
problem one is demanding that i x (N-i) rectangles ("wrap-round squares")
have their 4 corners not all the same, as well as the i x i squares, for
1 <= i <= N-1. Thus the N = 12 solution that Robert Israel posted:

         bb
         ||
        000011011111
        011010010101
        001100110011
        010110100110
        010100101010
        011001100101
        101101001100
        100101010110
        110011010010
    a-> 101010011001 <-a 
    a-> 110011001011 <-a
        100110100101
         ||
         bb

has several wrap-round squares (e.g. the 1x11 rectangles marked a and b)
which violate the stronger condition. 

But I then noticed, to my considerable astonishment, that Robert Israel's
later N = 13 solution:

        0001101010110
        0101011000011
        1100001101110
        0110101011000
        0101100001101
        0000110101011
        1011101100001
        0110000110111
        0011010101100
        1010110000110
        1000011011101
        1101110110000
        1011000011010

*does* satisfy the stronger condition, having no i x (13-i) rectangles with
four corners the same. Unless this is a consequence of his search strategy,
there is something very odd going on.

The probabilistic argument I had in mind, following Torben Morgensen's 
original one, involves assuming that the probability of each sub-square
violating the conditions is 7/8, independently of the others. For N=13 there 
are 650 regular sub-squares (giving Torben's estimate of 2^169*(7/8)^650 =
1.511e13 solutions) and another 364 wrap-round ones, giving an estimate of
2^169*(7/8)^1014 = 1.175e-8 solutions. So the undoubted existence of at 
least one solution suggests that the assumption of independence was not
a very good one!

Chris Thompson
JANET:    cet1@uk.ac.cam.phx
Internet: cet1@phx.cam.ac.uk
Newsgroups: sci.math,sci.physics,sci.bio,sci.chem,misc.education
From: knapp@spot.Colorado.EDU (David Knapp)
Subject: Help! was Re: Can we have sci.chem back? (was Re: TIME HAS INERTIA abian stuff)
Organization: University of Colorado, Boulder
Date: Tue, 15 Dec 1992 05:29:46 GMT

In article <1992Dec15.000110.1485@cs.wayne.edu> atems@igor.physics.wayne.edu (Dale Atems) writes:
>In article <1992Dec14.191434.20612@ucsu.Colorado.EDU> knapp@spot.Colorado.EDU (David Knapp) writes:
>>Can we please not consume so many net.resources to bashing ABIAN?
>>Will you all kindly look at how many groups you are crossposting to?
>>How about making an alt.abian group or taking this to email?
>
>The cross-posting was done either by Abian himself, or by someone who
>mistook his postings for real science. Your suggestion is an excellent
>one. Until this flood subsides, please use killfiles if your
>newsreader supports this feature.
>
>------
>Dale Atems
>Wayne State University, Detroit, MI
>Department of Physics and Astronomy
>atems@igor.physics.wayne.edu



Hey, all you'se guys. Why not let's form alt.abian and get that traffic


This ABIAN stuff has been happening in sci. groups for almost 6 months
now. Time for his own group!!

Will someone who knows how to create an alt group please do this?!
I've done it before but, by golly, I've forgotten how.




-- 
David Knapp                                      University of Colorado, Boulder
Perpetual Student                                   knapp@spot.colorado.edu
Newsgroups: sci.math
From: regeorge@magnus.acs.ohio-state.edu (Robert E George)
Subject: RE: Marilyn vos Savant and Pancakes??
Organization: The Ohio State University
Date: Tue, 15 Dec 1992 01:42:53 GMT


burchell@cse.unl.edu (David Burchell)  asks:

>I ask the net Gods: Can this be correct??

  The  net Gods are probably busy, so I will answer your question.



>From ``Ask Marilyn'' by Marilyn Vos Savant, Parade magazine, December
13, 1992.

>You have a hat in which there are three pancakes.  One is golden on
>both sides, one is brown on both sides, and one is golden on one side
>and brown on the other.  You withdraw one pancake and see that one side
>is brown.  What is the probability that the other side is brown?

>---Robert H. Batts, Acton, Mass.

>It's two out of three.  The pancake you withdrew had to be one of only
>two of them: the brown/golden one or the brown/brown one.  And of the
>three brown sides you could be seeing, two of them also have brown on
>the other side.
   I will assume the following:
   
Prob(drawing pancake with both sides brown) = 1/3
Prob(drawing pancake with one side brown)   = 1/3
Prob(drawing pancake with no sides brown ) =  1/3
Prob(seeing a brown side | you drew pancake with one side brown) = 1/2  
Prob(seeing a brown side | you drew pancake with both sides brown) = 1
Prob(seeing a brown side|you drew pancake with no sides brown) = 0

Prob(you drew pancake with both sides brown|you see a brown side)

     Prob(you drew a pancake with 2 brown sides AND you saw a brown side)

=   ---------------------------------------------------------------------
                       Prob(you saw a brown side)


                (1/3) (1)                            2
      =   ----------------------------------     =   ---
         (1/3)(1) + (1/3) (1/2) + (1/3)(0)           3


Long Live the Reverend Mr. Bayes!

(whose theorem was applied above)

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: hrubin@pop.stat.purdue.edu (Herman Rubin)
Subject: Re: Difference between "show" and "prove"
Organization: Purdue University Statistics Department
Date: Mon, 14 Dec 1992 17:52:05 GMT

In article <Bz7KyK.297@ulowell.ulowell.edu> cdeloge@cs.ulowell.edu (Carolyn Deloge) writes:
>Hi, I am a CS graduate student and I have a question for the math people.

>What is the difference between "show" and "prove"?

>I had a homework problem that asked to "show" the solution.  I answered by
>giving an example and some reasoning.  The teaching assistant marked it 
>incorrect, saying that I needed to "prove" it inductively.

>Can someone give me his/her definitions on these two words?  I would really
>appreciate it.  Thanks.

In mathematics, there is no difference.  Now you might not have to prove
it inductively, but you have to prove it, unless you were specifically
asked to do it inductively.

-- 
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
Phone: (317)494-6054
hrubin@snap.stat.purdue.edu (Internet, bitnet)  
{purdue,pur-ee}!snap.stat!hrubin(UUCP)
Newsgroups: sci.math
From: kekamins@zeno30.math.UWaterloo.ca (kekaminsky)
Subject: Re: Would Pi repeat, were it expressed in a base other than 10?
Organization: University of Waterloo
Date: Sun, 13 Dec 1992 18:59:16 GMT

In article <3321@ucl-cs.uucp> G.Joly@cs.ucl.ac.uk (Gordon Joly) writes:
>
>That is say non-decimal.
>

No, it wouldn't, for application of the Euclidean algorithm would then allow
you to then express it in base 10 in a repeating decimal expansion. Since the
decimal expansion is irrational (and transcendental), so will all other bases.

For an interesting play on this concept, read Carl Sagan 'Contact'.

Kirk
Newsgroups: sci.math,rec.games.abstract
From: edgar@function.mps.ohio-state.edu (Gerald Edgar)
Newsgroups: sci.math
Subject: Re: Function Terminology
Date: 14 Dec 1992 08:34:42 -0500
Organization: The Ohio State University, Dept. of Math.
NNTP-Posting-Host: function.mps.ohio-state.edu

David G Radcliffe wrote:
>>Suppose I have a function f: A --> B, and C is a subset of B which
>>contains the image set of f.  I define a function g: A --> C by
>>setting g(a) = f(a) for all a in A.  Usually, f and g can be considered 
>>as the same function, but sometimes the distinction is important.
>>
>>Is there a standard term or notation for this?
>>

I wrote:
>g is the astriction of f to C .

I have been asked for the source of this word.  The distinction between
codomains comes up in the theory of operator ideals.  The term "astriction"
was used frequently in lectures on that subject that I attended, given by
Daniel Lewis of Texas A&M.  Perhaps it also appears in the standard references
in the theory of operator ideals.  [I looked at Pietsch's book, but its
index does not list "astriction"; but the index was so skimpy that I am
not convinced that the word is not there.]  So if it is essential to track
down the origins of this word, consult Professor Lewis.
-- 
  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)
Xref: sparky sci.math:16924 sci.physics:21177 sci.bio:4581 sci.chem:5409 misc.education:5269
From: murphy@npri6.npri.com (David P. Murphy)
Newsgroups: sci.math,sci.physics,sci.bio,sci.chem,misc.education
Subject: Re: TIME HAS INERTIA - BASS JEALOUS AND INSECURE-ABIAN VALIDATED
Date: 14 Dec 92 17:05:35 GMT
Distribution: world
Organization: NPRI, Alexandria VA


 >    TIME HAS INERTIA is validated - C.R. Bass is discredited as a
 >jealous, putting down envious person who gets his feeling of security
 >by most pathetic means of eminating arrows of hate, sarcasm, enmity,
 >hostility and antipathy.  
 >
 >abian@iastate.edu (Alexander Abian)

nice thesaurus you've got there, alex.

ok
dpm
-- 
murphy@npri6.npri.com 602 Cameron St. Alexandria, VA 22314 (703) 683-9090

              When every one is dead the Great Game is finished.  Not before.
                              --- Hurree Babu, "Kim"
From: koc@rize.ECE.ORST.EDU (Cetin Kaya Koc)
Newsgroups: sci.math
Subject: Re: What is the number
Date: 17 Dec 92 19:45:06 GMT
Article-I.D.: flop.1gqlc2INN34g
Organization: College of Engineering, Oregon State University
NNTP-Posting-Host: rize.ece.orst.edu

>    Whose sum of the factorials of the digits is the number itself
> Two examples come immediately to mind:  1
> 								145

145 is correct: 1! + 4! + 5! = 1 + 24 + 120 = 145.
Also 40585 = 4! + 0! + 5! + 8! + 5! = 24 + 1 + 120 + 40320 + 120
                                    = 40585
Newsgroups: sci.math
From: dbriggs@zia.aoc.nrao.edu (Daniel Briggs)
Subject: Re: Would Pi repeat, were it expressed in a base other than 10?
Organization: National Radio Astronomy Observatory, Socorro NM
Date: Mon, 14 Dec 92 18:47:22 GMT

In article <1992Dec14.160421.26301@ulrik.uio.no>
  solan@smauguio.no (Svein Olav G. Nyberg) writes:
>Base pi? No joking?
>
>Well, what are the first 5 digits of what we normally
>call "5" in this base?

Well, with just grade school arithmetic I make the first six digits to be
11.22012.  (Hope I did it right!)  The usual algorithm of divide,
difference and remainder seems to work OK for transcendental bases.  You
can check it by expanding it out in the usual way.  1*pi^1 + 1*pi^0 +
2*pi^-1 + ...  The error is indeed less than pi^-5.  I'd be interested to
hear what the math gurus have to say about representation in such bases --
it's an interesting topic.

-- 
| Daniel Briggs  (dbriggs@nrao.edu)                      |  USPA B-14993
| New Mexico Tech / National Radio Astronomy Observatory |      DoD #387
| P.O. Box O / Socorro, NM 87801   (505) 835-7391        | 
Support the League for Programming Freedom   (info from lpf@uunet.uu.net)
Xref: sparky sci.math:16796 soc.history:10107 talk.politics.misc:64049
From: J.Theodore.Schuerzinger@dartmouth.edu (J. Theodore Schuerzinger)
Newsgroups: sci.math,soc.history,talk.politics.misc
Subject: Re: Math trivia puzzles
Date: 13 Dec 92 15:04:28 GMT
 <SMITH.92Dec9125601@michael.harvard.edu> 
 <1992Dec9.211607.2717@galois.mit.edu>  
 <SMITH.92Dec10112715@metatron.harvard.edu>
Organization: Dartmouth College, Hanover, NH
X-Posted-From: InterNews1.0a5@newshost.dartmouth.edu

In article <SMITH.92Dec10112715@metatron.harvard.edu>
smith@metatron.harvard.edu (Steven Smith) writes:

> I found my quotation in _The Mathematical Manuscripts of Karl Marx_
> (New Park Publications, 1983), which I stumbled upon in the QA300's in
> Cabot.  Certainly, a book titled _Marx Demystifies Calculus_ should
> contain far more entertaining passages than those you provide above.
> Please, please, indulge us with some of them.

Then there's a book called 'Karl Marx Plays Chess' by Andy Soltis. 
It's an anthology of his columns in the magazine 'Chess Life'.  His
columns are quite interesting, especially if you like to play chess.


--Ted Schuerzinger
email: .zed@Dartmouth.EDU
"I should have realized it would be bad vodka when all the label said
was 'Russian Vodka'."
Xref: sparky sci.math:16988 sci.physics:21246 sci.bio:4594 sci.chem:5427 misc.education:5301
From: weemba@sagi.wistar.upenn.edu (Matthew P Wiener)
Newsgroups: sci.math,sci.physics,sci.bio,sci.chem,misc.education
Subject: Re: TIME HAS INERTIA - NewScientist Article
Date: 15 Dec 92 23:41:33 GMT
Reply-To: weemba@sagi.wistar.upenn.edu (Matthew P Wiener)
Followup-To: sci.physics
Organization: The Wistar Institute of Anatomy and Biology
In-reply-to: lachlan@dmp.csiro.au (Lachlan Cranswick)

In article <1992Dec14.023025.20353@dmp.csiro.au>, lachlan@dmp (Lachlan Cranswick) writes:
>>     There is a difference, Wegener at least had
>>     a physical theory that made predictions.

Yes.  And some of them were bogus.  His physical theory--involving
continents sliding around on the sea floor--was pretty much impossible.
It was easier to believe in coincidental shapes and a land bridge then
in his theory.

Contrast this with Charles Darwin, whose claims about the deep past were
immediately accepted, and decoupled from his theoretical explanations,
which took almost a century to be reinterpreted favorably in light of
genetics.

>Though I agree with your above assessment of Abian, what happened to
>Wegener is particularly sad and not unique to him.

What's sad is that he died (1930) on an expedition in deep Greenland, and
so there was no one to really push the theory afterward.

>						     With risk of
>rewriting history again, he was pretty thoroughly ridiculed because
>the technology for determining that the continents (plates) were
>moving did not exist at the time.

Not quite.  Wegener predicted movements about three orders of magnitude
greater than they were.  These were detectable--had they existed--in his
day, and of course the result was a disaster for his theory. 

>			     Was it in the 1950s that they
>showed the reversal of the earths magnetic field on sea-floor
>rock implying movement of the plates?

Early sixties.
-- 
-Matthew P Wiener (weemba@sagi.wistar.upenn.edu)
Newsgroups: sci.math,sci.physics,sci.bio,sci.chem,misc.education
From: hluce@well.sf.ca.us (Hudson Hayes Luce)
Subject: Re: TIME HAS INERTIA - NewScientist Article
Organization: Whole Earth 'Lectronic Link
Date: Mon, 14 Dec 1992 07:40:27 GMT


 Abian needs to submit his theory in an article to Physica D, the
 appropriate journal for this kind of thing. This has no place in
 sci.chem, it's a waste of bandwidth. Publications in the New Scientist
 are OK, but he really needs to get into some sort of refereed journal,
 and OUT OF THIS NEWSGROUP !!!!!
(he might also give Phys. Rev. Lett. a try......)