HDTenEightyP/NetNews huggingface dataset:
From: frank@Cookie.secapl.com (Frank Adams)
Subject: Re: Easy (?) probability question
Date: Mon, 05 Oct 1992 19:57:21 GMT
Organization: Security APL, Inc.

In article <dak.718129100@tabaqui> dak@tabaqui.informatik.rwth-aachen.de (David Kastrup) writes:
>davidb@triangle.Berkeley.EDU (David T. Blackston) writes:
>>Let X be a random variable, and define the random variable Z by
>>Z=min{X, k} where k is some constant.  Show that var(Z) <= var(X).
>
>Well suppose X is realvalued. ...
>
>Since I am not familiar with complex variances, I cannot make any
>guesses.

To deal with complex variances, you'll have to restate the problem.  "min"
is not defined for complex numbers.
Newsgroups: sci.math
From: torkel@sics.se (Torkel Franzen)
Subject: Re: consequences of the Axiom of Choice
Organization: Swedish Institute of Computer Science, Kista
	<1992Oct1.152704.16387@CSD-NewsHost.Stanford.EDU>
	<1af9g6INN6d2@function.mps.ohio-state.edu>
Date: Fri, 2 Oct 1992 09:35:42 GMT

In article <1af9g6INN6d2@function.mps.ohio-state.edu> edgar@function.mps.
ohio-state.edu (Gerald Edgar) writes:

  >Explicitly find a countably infinite set S of (unordered) pairs,
  >for which a choice function is not obvious.  [More technical details.
  >The set S should be explicitly and uniquely specified in the language of ZF.
  >It should be provable in ZF that it is a countable set of pairs.]

  A suggestion: let S be the first countable ordinal definable set of
pairs of infinite sets of real numbers.
From: ara@zurich.ai.mit.edu (Allan Adler)
Newsgroups: sci.math
Subject: Re: Topos theory for mere mortals (?)
Date: 26 Sep 92 06:27:55 GMT
Organization: M.I.T. Artificial Intelligence Lab.

In article <90366@netnews.upenn.edu> weemba@sagi.wistar.upenn.edu (Matthew P Wiener) writes:

   Some group theorists can, in the wake of Shelah's solution to the
   Whitehead problem (if Ext(G,Z)=0, is G free?).  It's a theorem of
   Serre and somebody for G countable.  But for uncountable G, the
   question is dependent on assumptions beyond ZFC.


I think it is even true that there is a specific group G such that
whether Ext(G,Z) =0 or not is independent of set theory. 

Allan Adler
ara@altdorf.ai.mit.edu
From: hiraga@Csli.Stanford.EDU (Yuzuru Hiraga)
Subject: Re: Mattel says "Math is tough."
Organization: Stanford University CSLI
Date: Mon, 5 Oct 1992 19:10:34 GMT

>:         Mattel has just released a new product. A Barbie doll that says
>: "Math is tough".
>
>What would you have her say?: 

Not what I'd have her say, but if all of us filed a protest to Mattel,
it'll certainly be changed to "Mathematicians are tough".	:-)

-YH
From: mccoyje@wkuvx1.bitnet
Newsgroups: sci.math
Subject: Re: Roman Numerals
Date: 5 Oct 92 14:43:49 GMT
Organization: Western Kentucky University, Bowling Green, KY

In article <1992Oct4.203159.27522@umbc3.umbc.edu>, cs202144@umbc8.umbc.edu (cs202144) writes:
> This may be a dumb question, but I am curious...How are roman numerals larger
> than 3999 expressed? Is there an extended symbology or are the existing symbols
> altered in some way to express larger values?
> 
There are larger symbols which consist of the same letters with a line
across the top (as in the symbol for a line segment).

For instance:      _ _ _
		   M C X

I am not sure what they stand for exactly, but I think the x is
10,000; the C is 100,000; and the M is 1,000,000.
I believe you just multiply the original value of the letter by 1000.
                   _
So, 4000 would be MV (I think).
I could be wrong about these (they are from memory a long time ago.)

Jason McCoy
-- 
"Sleep -- those little slices of death -- how I loathe them!"
					-- Edgar A. Poe
"I am the way!"
	-- Pinhead
From: ara@zurich.ai.mit.edu (Allan Adler)
Newsgroups: sci.math
Subject: Re: Rename the Calculus sequence?
Date: 26 Sep 92 06:24:06 GMT
Organization: M.I.T. Artificial Intelligence Lab.

In article <1686D9D43.R1STORY@VM1.CC.UAKRON.EDU> R1STORY@VM1.CC.UAKRON.EDU writes:

   When talking to my computer science colleagues, I have always been impressed
   with the titles they have given their courses: Data Structures; Discrete
   Structures; Analysis of Algorithms; Data Communication and Networks;
   Artificial Intelligence and Heuristic Programming; Automata, Computability and
   Formal Languages.

   I thought that I would make change of title for some of our tradional courses
   such as Calculus I, II, and III.

   Calculus I could be renamed "Limit Theory, Differential Structures, and
				Integral Algorithms"

   Calculus II:                "Calculus++, An Object Oriented Approach"

   Calculus III:               "Vector Data Structures, and Calculus of Arrayed
				Data"

   Any other suggested titles?
   --------------------------


How about "Calculus, a substance found on the teeth of mathematicians"?

Sorry, during my current dental crisis, I don't seem to be able to think
about anything else...

Allan Adler
ara@altdorf.ai.mit.edu
From: zeleny@husc9.harvard.edu (Michael Zeleny)
Newsgroups: sci.math
Subject: Re: Topos theory for mere mortals (?)
Date: 28 Sep 92 03:24:59 GMT
Organization: The Phallogocentric Cabal

In article <19qoafINNiqf@usenet.INS.CWRU.Edu> 
cxm7@po.CWRU.Edu (Colin Mclarty) writes:

>	There is a difference though for Platonists.  Set theoretic
>realists generally think there is some one universe of all sets, AC 
>is true in it or is not, and that universe is really the only place 
>to work.  So the question of what to "postulate" may be hard but
>it has some right answer--they are not "postulates" at all in the
>sense of "postulate theorists" like Huntingdon (of the many 
>axiomatizations of Boolean algebra).  Zeleny has made this point 
>well in another context.  Category theorists, even if realists, tend 
>to think it is worth working in all kinds of various ambient 
>categories for various purposes.  So that you always do need to say 
>what you postulate about your present ambient.

I have hesitated for a long time before following up on this claim,
especially since I don't recollect too well just what point it is that I
made in another context.  However, I wish to go on record as stating that,
though it probably is a sociological fact that most realists who bother
thinking about it, think that there is exactly one universe of all sets,
and that, conversely, some people have gone on record announcing their
conversion to formalism on the grounds of their loss of belief in the
unique existence of such a universe, I do not myself believe that a realist
philosophy of mathematics cannot accomodate a multiplicity of set-theoretic
(or type-theoretic) universes possessed of different size and structural
properties.  There is, after all, no good reason to suppose that everything
in the mathematical universe is a set, or equivalently, that the
development of a particular set theory is bound to yield privileged
insights into the nature of all mathematical objects.  So your contrast
between set theory and category theory may be right, but only for
accidental reasons.

>Colin McLarty

cordially,
mikhail zeleny@husc.harvard.edu
"Un de mes plus grands plaisirs est de jurer Dieu quand je bande."
Newsgroups: sci.math,sci.math.num-analysis
From: dfs@doe.carleton.ca (David F. Skoll)
Subject: Info wanted on "mps" format
Followup-To: sender
Reply-To: <dfs@doe.carleton.ca>
Organization: Dept. of Electronics, Carleton University
Date: Fri, 2 Oct 1992 16:00:02 GMT

I need to embed an LP or mixed integer-linear programming solver into
an application.  The solver requires input in the "MPS" format, apparently
a standard format.

If anyone could point me in the direction of documentation about MPS, I'd
appreciate it.

Thanks,

David F. Skoll
From: aspnes@molokini.almaden.ibm.com (J. Aspnes)
Newsgroups: sci.math
Subject: Re: A more virus resistant architecture
Keywords: computer,virus,Babbage,analytic engine
Date: 5 Oct 92 20:03:52 GMT
Reply-To: aspnes@molokini.almaden.ibm.com (J. Aspnes)
Organization: IBM Almaden Research Center


In article <BvMJAo.24F@world.std.com>, rjk@world.std.com (robert j
kolker) writes:
|> The question is this: Is a computer whose program space is totally
|> disjoint from the the data space less likely to be buggered by viruses
|> than a  Von Neuman Machine, where the data and the program are kept in the
|> same store.

Yes.  Unfortunately, it's also less likely to be infected by compilers.
Newsgroups: sci.math,sci.math.symbolic
From: Ray Zimmerman <Ray-Zimmerman@cornell.edu>
Subject: Re: Integral Tables
X-Xxmessage-Id: <A6EC95679001E0B5@ziklag.ee.cornell.edu>
X-Xxdate: Mon, 28 Sep 92 15: 56:39 GMT
Nntp-Posting-User: rz10@cornell.edu
Organization: Electrical Engineering, Cornell University
X-Useragent: Nuntius v1.1.1d11
Date: Mon, 28 Sep 1992 14:51:14 GMT

In article <10843.Sep2607.19.3092@virtualnews.nyu.edu> D. J. Bernstein,
brnstnd@nyu.edu writes:
>1-x positive or negative?'' whenever I gave it such an integral? Sure,
>Mathematica thinks that sqrt((-1)^2) = -1, but just because the new
>technology produces wrong answers doesn't mean that the old technology
>did.

Mathematica 2.0 on the Mac thinks that Sqrt[(-1)^2] = 1.  Please check
before posting this type of information.
 
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
 Ray Zimmerman            \ 397 Theory Center, Electrical Engineering
                           \ Cornell University, Ithaca NY  14853
 Ray-Zimmerman@cornell.edu  \ Phone: 607-254-8819  Fax: 607-255-9072
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Newsgroups: sci.math
From: stephen@mont.cs.missouri.edu (Stephen Montgomery-Smith)
Subject: Re: Opinions Sought (Why major in math?)
Organization: University of Missouri
Date:  1 Oct 92 01:14:57 GMT

In <1992Sep30.231548.1282@ncsu.edu> kbanerje@grad09.math.ncsu.edu (Kaushik Banerjee) writes:



>Why should one earn a math degree?

>Assume that you do not want to teach or conduct research.
>What types of jobs are available for an individuals with
>a math degree (at any level)?

I have interested in what careers there are for math majors, mainly
so that I can provide information for students.  It seems that there
are very few jobs out there that make use of the mathematics one has
learned.

A while ago, I phoned up alumni from our math dept, asking people
what career they had persued.  While many said that their math
degree helped them to think logically, none said that they actually
used their math.  The overall impression I got was that it is
better to double major math with something else.  The math degree
alongside the computer science, electrical engineering, whatever 
gives you an edge over other applicants, but by itself is not
sufficient to land one a job.

I also visited the careers fair by the M.A.A. given in Baltimore
either last Christmas or the year before.  It seemed to me that
the people there were either looking for mathematicians with expertise
in differential equations and modelling them on computers, or they
were acturial firms.

If anyone has any other information to offer, I would be very interested
to receive it.

Stephen
From: ara@zurich.ai.mit.edu (Allan Adler)
Newsgroups: sci.math
Subject: Re: Hyperbolic space?
Date: 29 Sep 92 22:29:48 GMT
Article-I.D.: camelot.ARA.92Sep29172948
	<1992Sep29.183907.6934@sun0.urz.uni-heidelberg.de>
Organization: M.I.T. Artificial Intelligence Lab.



Actually, I vaguely recall that around 1951 in the Journal of the
American Optical Society, there is an article about how what we 
see with out cyclopean vision is hyperbolic space.

Allan Adler
ara@altdorf.ai.mit.edu
Newsgroups: sci.math
From: matmcinn@nuscc.nus.sg (Mcinnes B T (Dr))
Subject: Re: Mattel says "Math is tough."
Organization: National University of Singapore
Date: Tue, 6 Oct 1992 04:50:01 GMT

mroussel@alchemy.chem.utoronto.ca (Marc Roussel) writes:
: In article <5840@tuegate.tue.nl> wsadjw@urc.tue.nl writes:
: >In article <1992Oct5.145314.2836@alchemy.chem.utoronto.ca>
: >mroussel@alchemy.chem.utoronto.ca (Marc Roussel) writes:
: >>The problem with Barbie saying that math is hard is that this doll will
: >>be not be given to college-aged women but to young girls.
: >
: >I get it.  To give a girl a doll that says "X is hard"  "Y is tough" or
: >anything like that, will brainwash the little brat and condemn her to a
: >lifetime of simpering weakness.  Presumably little boys who want to be
: >president or astronaut or fireman or whatever are not daunted by the 
: >possibility that it may require some effort.
: >But then, little boys don't get barbie dolls.  Maybe that is the problem.
: 
:      That is part of the problem.  Boys get toys that tell them that
: they can do things.  Dolls for boys are astronauts and firemen.  Boy

My niece has a vast collection of dinosaur toys. Guess I had better ask
my brother to ensure that none of them is carnivorous........

s
Newsgroups: sci.math
From: mms@euphemia.math.ucla.edu (Murray Schacher)
Subject: Re: "Sneakers" & cryptography
Organization: UCLA Mathematics Department
Date: Tue, 29 Sep 92 20:02:39 GMT

In article <19qiosINN8ht@function.mps.ohio-state.edu> edgar@function.mps.ohio-state.edu (Gerald Edgar) writes:
>>
>>>>The mathematician's office was also weird.
>>>
>>>I didn't think that it was all that weird: I'd sure like to have an
>>>office with that much space.
>>
>>That's what was weird.
>>
>
>I'll bet that no mathematician (except possibly an ex-mathematician, now an
>administrator) at the real UCLA has an office that big.  Also, I have never
>heard of a mathematician's office with a workbench where he makes his own
>computer chips...

Yes, no mathematician at UCLA has an office that big.  However, UCLA was
put into the discussion by some wayward netter.  The lecture is supposed
to take place at Berkeley.  No mathematician at Berkeley has an office
that big either.  Neither UCLA nor Berkeley normally get that many
people to a math lecture, but we can dream...
From: zeleny@husc9.harvard.edu (Michael Zeleny)
Newsgroups: sci.math
Subject: Re: Z <-> Q formula
Date: 27 Sep 92 16:07:55 GMT
Organization: The Phallogocentric Cabal

In article <1992Sep27.085952.7534@Csli.Stanford.EDU> 
hiraga@Csli.Stanford.EDU (Yuzuru Hiraga) writes:

YH:
># This may be a FAQ, but...
>
>The set of intergers Z and the set of rationals Q have the same cardinality,
>i.e. there exist a bijection between them.  So we all know that.
>But then, is there a "simple" formula that expresses any such mapping?
>You may use any device you please, but note that the subjective little
>"simple" is the criterion.

Cantor's device for coding the plane \omega \times \omega is fairly
simple.  Recall that the idea is to order the pairs first by their
sum, and within the sum in a lexicographic manner.  So we get the
enumeration of (x,y):

J(x,y) = (\sum_{i<x+y}(i+1))+x = (x+y)^2+3x+y \over 2

Note that this doesn't answer your question, as each rational number
is counted infinitely many times.  In order to come up with a simple
bijection between N and Q (which could be trivially modified to yield
one between Z and Q), we might modify the above procedure to exclude
the cases of pairs (x,y), in which x and y are not relatively prime.
Unfortunately, I don't know of a simple way to do that.

>-Yuzuru Hiraga

cordially,
mikhail zeleny@husc.harvard.edu
"Un de mes plus grands plaisirs est de jurer Dieu quand je bande."
From: nakada@ntttsd.ntt.jp (Hiroshi Nakada)
Newsgroups: sci.math
Subject: Re: a graph problem
Date: 6 Oct 92 00:54:18 GMT
Organization: NTT Transmission Systems Laboratories, Yokosuka, JAPAN

In article <MARCOS.92Oct5145828@iota.ece.ucsb.edu> marcos@nu.ece.ucsb.edu writes:
>I came across this problem and I believe it must have been already solved
>by someone. Please send me the solution and/or references if you know it.
>
>What is the maximum number of nodes possible in a graph if all nodes have
>degree at most d (in my case d=16) and the distance between any two nodes
>is at most dist (i.m.c. dist=4) ??

Let n(d,D) be a number of nodes of a graph with a given maximum degree
d and diameter D (D is the maximum distance between any two nodes).
A theoretical upper bound on n(d,D) is giben by Moore (see [1]) as

                 n(d,D) <= (d(d-1)^D -2)/(d-2)

for d>2. This bound is called the Moore bound.  The graphs 
satisfying the equality are called the Moore graphs.
Unfortunately, the Moore graphs can exist only if D=2 and 
d=3, 7 or 57.  A nearly optimum solution of this problem
is often called a dense graph. Many dense graphs have been 
reported (see forexample [2,3]), but it is very difficult 
to find such graphs systematically.  The case of d=16, D=4
is difficult, too.  The same problem for a directed graph has also 
been discussed in [4,5].  The related topics are mentioned in [6,7].

References:
[1] B.Bollobas, Extremal graph theory, London Math. Soc. Monograph
    No.11 (Academic Press, London, 1978).
[2] J.C.Bermond, et al., Tables of large graphs with given degree
    and diameter, Inform. Proc. Letters 15(1) (1982) 10-13.
[3] J.C.Bermond, et al., Large graphs with given degree and 
    diameter II, J. Combin. Theory Ser.B 36 (1984) 32-48.
[4] N.G.de Bruijn, A combinatorial problem, Proc. Akad. Westeschappen,
    Vol.49 Part 2, (1946) 758-764.
[5] M.Imase and M.Itoh, A design for directed graphs with minimum
    diameter, IEEE Trans. Comput. 32 (1983) 782-784.
[6] T.Soneoka, H.Nakada, M.Imase and C.Peyrat, Sufficient conditions
    for maximally connected dense graphs, Discrete Mathematics 63
    (1987) 53-66.
[7] T.Soneoka, H.Nakada and M.Imase, Design of a d-connected digraph
    with a minimum numter of edges and a qusiminimal diameter,
    Discrete Applied Mathematics 27 (1990) 255-265.

----
  HIROSHI NAKADA                nakada@ntttsd.NTT.JP
  NTT Transmission Systems Labs. Phone (0468)59-8537
From: kasdan@cs.columbia.edu (John Kasdan)
Newsgroups: sci.math
Subject: Re: Movie mathematicians
Date: 28 Sep 92 22:56:04 GMT
Organization: Columbia University Department of Computer Science

In article <1252@kepler1.rentec.com> andrew@rentec.com (Andrew Mullhaupt) writes:
>In article <1992Sep23.162424.26946@nas.nasa.gov> asimov@wk223.nas.nasa.gov (Daniel A. Asimov) writes:
>>I believe also Straw Dogs had Dustin Hoffman playing a math'n as well.
>>
>>Any others????
>
>There were rumors that the Eudaemonic Pie was being made into a movie, but
>those guys I think of as physicists.
>

Which reminds me that, in my favorite James Bond movie, Casino Royale
(you know, the one where 007 is played by, among others, Woody Allen
and David Nivens) Ursulla Andress spends some time vamping Peter
Sellers playing a mathematician (presumably modeled on Thorpe) who
has invented a blackjack system.

>
>Later,
>Andrew Mullhaupt
From: zeleny@husc9.harvard.edu (Michael Zeleny)
Newsgroups: sci.math
Subject: Re: Topos theory for mere mortals (?)
Date: 26 Sep 92 20:06:45 GMT
Article-I.D.: husc3.1992Sep26.160647.15869
Organization: The Phallogocentric Cabal

In article <1992Sep25.152726.2075@maths.tcd.ie> 
tim@maths.tcd.ie (Timothy Murphy) writes:

>cxm7@po.CWRU.Edu (Colin Mclarty) writes:

CML:
>>	There is just no way that what Halmos calls naive set theory
>>can be regarded as the common heritage of all rational humans.  It
>>takes training to learn to think that way.

TM:
>Pardon me for stepping into the middle of a train of thought
>which I have not been following,
>but could one not usefully distinguish here
>between _finite_ set theory and general set theory?
>Can't we agree that finite set theory at least
>is "the common heritage of all rational humans"?

Since you were kind enough to set the precedent, I'll commit another
egregious breach of protocol by answering a question not addressed to me.
THe distinction you are suggesting may be arrived at by distinguishing
between the logical sense of `set', which presupposes a universe of
discourse fixed within the theory, and the iterative sense of `set',
whereby the structure of the universe in question becomes, in a sense, the
proper object of the theory, and hence is fixed only indirectly within the
metatheory: in ZFC, the universe V is just what our quantifiers are taken
as ranging over.  (This distinction is discussed very nicely in the recent
book by Stewart Shapiro, _Foundations without Foundationalism: A Case for
Second-order Logic_.)  Logical sets owe more to the work of Boole and
Schr\"oder than to the developments of the Cantorian set theory, either
under the iterative conception, or on the doctrine of the limitation of
size; the salient difference between the two approaches consists in the
plausibility of interpreting the former as part of "the common heritage of
all rational humans", in the fashion of the logicist program.  So the
"size" of set theory is, indeed, an issue, but not in the way you are
suggesting.

TM:
>And can one not regard topos theory,
>or one aspect of it,
>as a study of infinite set theory
>from the viewpoint of finite set theory?

Sheer prudency demands that I withhold my half-baked opinions on this
subject.

>-- 
>Timothy Murphy  
>e-mail: tim@maths.tcd.ie
>tel: +353-1-2842366
>s-mail: School of Mathematics, Trinity College, Dublin 2, Ireland

cordially,
mikhail zeleny@husc.harvard.edu
"Un de mes plus grands plaisirs est de jurer Dieu quand je bande."
Newsgroups: sci.math
From: cyeomans@ms.uky.edu (Charles Yeomans)
Subject: Re: Square root of i
    <1992Sep22.134545.21209@ms.uky.edu> 
    <1992Sep24.160754@gruc18.nor.chevron.com>
Date: Sun, 27 Sep 1992 18:19:22 GMT
Organization: University Of Kentucky, Dept. of Math Sciences

In article <1992Sep24.160754@gruc18.nor.chevron.com> hbtnn@gruc18.nor.chevron.com (Brian Tanner) writes:
>In article <1992Sep22.134545.21209@ms.uky.edu>, cyeomans@ms.uky.edu (Charles Yeomans) writes:
>|> In article <1992Sep21.185742.17360@pellns.alleg.edu> frisinv@alleg.edu writes:
>|> >   This problem has been plauging me for the past seven years. In the  
>|> >sixth grade, my math teacher assigned as extra credit to find the square  
>|> >root of i (i=Sqrt[-1]). I messed it up then but she wouldn't tell us the  
>|> >answer. I solved it once with DeMoirve's(sp?) theorem but forgot that.  
>|> >Could someone tell me the official answer so I can get off this  
>|> >distraction and back to my homework?
>|> >
>|> >THIS IS NOT A HOMEWORK PROBLEM ANYMORE. THE TEACHER WHO ASSIGNED IT IS  
>|> >RETIRED.
>|> >
>|> >----------
>|> >Vincent
>|> 
>|> We know sqrt(i) is a complex number.  So write sqrt(i) = a+bi qns 
>|> square both sides to get 
>|> 
>|> i = (a^2 - b^2) + (2ab)i..
>|> 
>|> Since a complex number can be written in the form a + bi in a unique way,
>|> we get the two equations (a^2- b^2) = 0 and (2ab) = 1.  Find all 
>|> simultaneous solutions of these equations to get the square roots of i.
>|> 
>|> Charles Yeomans
>|> yeomans@austin.onu.edu
>|> cyeomans@ms.uky.edu
>
>too much work.
>
>use r * exp(i theta) notation.
>
>    i = 1 * exp(pi/2)
>i^0.5 = (1 * exp(pi/2))^0.5
>i^0.5 = 1 * exp(pi/4) = (2^0.5/2) + i * (2^0.5)/2
>
>((2^0.5)/2 + i * (2^0.5)/2)^2 = (2/4 - 2/4) + i * (2 * 2/4) = i
>
>Q.E.D.
>(Latin for 'full credit' ;^) )
>
>Brian Tanner

Doesn't i have two square roots?

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

Xref: sparky sci.math:12314 rec.puzzles:6482 comp.theory:2063
From: markh@csd4.csd.uwm.edu (Mark)
Newsgroups: sci.math,rec.puzzles,comp.theory
Subject: Re: more on .999... = 10.0
Date: 28 Sep 1992 12:25:30 GMT
Organization: Computing Services Division, University of Wisconsin - Milwaukee
Distribution: inet
NNTP-Posting-Host: 129.89.7.4

In article <1992Sep22.142321.29598@watson.ibm.com>, mittle@watson.ibm.com (Josh Mittleman) writes:
|> Neal Howard writes:
|> 
|> > >	   x =  9.999...
|> > >     10x = 99.999...
|> >       ^^^^^^^^^^^^^^^^
|> >       NOT !!!!!!!
|> > 
|> >       10x would equal 99.999...9990 with the "0" at the infinity(th)
|> >       rightmost position !!!!!
|> 
|> How creative.

In article <1992Sep22.162133.2554@Princeton.EDU> tao@ginger.princeton.edu (Terry Tao) writes:
>Does this actually make sense in some strange 10-adic space?

Yes.  Not some strange 10-adic space, but in the set of real numbers itself.

All models of the real number axioms have infinitesimals in them, except one.
So choose any garden variety interpretation of the real number system, it has
infinitesimals in it with probability 1.