HDTenEightyP/NetNews huggingface dataset:
From: mknapp@casbah.acns.nwu.edu (Michael Knapp)
Subject: Re: Another Cute Math Joke (explanation of)
Organization: Northwestern University, Evanston Illinois.
Date: Tue, 6 Oct 1992 19:14:17 GMT

In article <a_rubin.718387119@dn66> a_rubin@dsg4.dse.beckman.com (Arthur Rubin) writes:
>In <1992Oct4.205137.29695@clark.edu> watson@clark.edu (Dennis Watson) writes:
>
>>Sometime back someone posted the following  joke?   
>
>>\epsilon < 0   
>
>There's a \delta for every \epsilon,

(some lyrics deleted.)

>(I can't remember the rest of the song.)
>
     Here it is, courtesy of the lyrics server.

AMM, 81 (1974) 612:
THERE'S A DELTA FOR EVERY EPSILON (Calypso)
Words and Music by Tom Lehrer

There's a delta for every epsilon,
It's a fact that you can always count upon.
There's a delta for every epsilon
	And now and again,
	There's also an N.

But one condition I must give:
The epsilon must be positive
A lonely life all the others live,
	In no theorem
	A delta for them.

How sad, how cruel, how tragic,
How pitiful, and other adjec-
Tives that I might mention.
The matter merits our attention.
If an epsilon is a hero,
Just because it is greater than zero,
It must be mighty discouragin'
To lie to the left of the origin.

This rank discrimination is not for us,
We must fight for an enlightened calculus,
Where epsilons all, both minus and plus,
	Have deltas
	To call their own.

Mike

-------------------------------------------------------------------------------
                              |       "The fight is what's important.  Doing
 Michael P. Knapp             |  what is good and right is why we're here.   
                              |  The end is variable and relative.  A person 
 mknapp@casbah.acns.nwu.edu   |  can only do what his heart tells him and  
 mknapp@isp.nwu.edu           |  break away from the terrible things      
                              |  around him.  We do what we can ... and live
                              |  with the consequences.
                              |                         -Marc Zanoni
                              |
-------------------------------------------------------------------------------

Newsgroups: sci.math
From: dan@cae.prds.cdx.mot.com (Dan Breslau)
Subject: Re: more on .999... = 10.0
Organization: none
Distribution: inet
Date: Tue, 29 Sep 1992 14:03:24 GMT

karr@cs.cornell.edu (David Karr) writes:


>I know infinitesimals were utilized to prove many important theorems
>in the eighteenth century and thereabouts, but they also led people to
>"prove" many falsehoods.  I thought they were abandoned for that
>reason.  What twentieth-century models of the real numbers have them?

Well, I can't cite the name of the text, but my high school calculus
class (78-79) used 'em. 

Then again, my college math teachers seemed to think that very odd...

Dan Breslau
dan@codex.com
Disc claimer:  "Hey!  That's my floppy!"



Newsgroups: sci.math
From: chalcraft@uk.tele.nokia.fi (Adam Chalcraft)
Subject: Re: Z <-> Q formula
Organization: cpd
Date: Mon, 28 Sep 1992 10:46:20 GMT

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

>   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.

Since noone else has mentioned it yet, there is a bijection which does not
involve discarding cancellable fractions or counting primes.
To make life easy for myself, I will enumerate the positive rationals:

0/1                                                                     1/0
                                       1/1
                   1/2                                   2/1
         1/3                  2/3               3/2               3/1
     1/4      2/5       3/5       3/4       4/3      5/3      5/2    4/1

The row with 1/1 is row 1.
On row n (n>0) there are 2^n fractions.
Each fraction is formed from the obvious two above it by the operation

  a/b           c/d
     (a+c)/(b+d)

Ignore the 0/1 and 1/0, which are just there to kick things off.
Now each positive rational occurs exactly once, and in its lowest form.

You can figure out where the rational p/q appears by using Euclid's
algorithm to show that p and q are coprime, and noticing when you do
"x:=x-y" and when you do "y:=y-x".
This gives you a finite sequence of x's and y's.
If you don't like the graphical method, then enumerate the xy-sequences
instead (length first, then alphabetical, as usual), which gives the same
answer.
Start with x=y=1, and then do "x:=x+y" or "y:=y+x" for x or y respectively.
The fraction is then x/y.
--
Adam Chalcraft -- Opinions are mine only, and probably wrong anyway.
Email: chalcraft@uk.tele.nokia.fi
       If that confuses your (uk) mailer, try chalcraft@cpdapo.tele.nokia.fi
       If that doesn't work, try ntl02.decnet.nokia.fi (zero-two)
       Alternatively, try dac11@phx.cam.ac.uk
Newsgroups: sci.math
From: lmitchel@nyx.cs.du.edu (lloyd mitchell)
Subject: Re: "Sneakers" & cryptography
Organization: University of Denver, Dept. of Math & Comp. Sci.
Date: Tue, 29 Sep 92 10:45:21 GMT

Thank you to all who posted or mailed a response to my question about the
cryptography method used in "Sneakers".  I appreciate the explanations and
the references.

Kerry Mitchell
From: hougen@vision.csl.uiuc.edu (Darrell Roy Hougen)
Newsgroups: sci.math
Subject: Re: Mattel says "Math is tough."
Date: 5 Oct 1992 20:02:35 GMT
Organization: Center for Reliable and High-Performance Computing, University of Illinois at Urbana-Champaign
NNTP-Posting-Host: vision.csl.uiuc.edu

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

*>What would you have her say?: 

How about, "Math is fun!" or "I like mathematical puzzles!" or
anything else that portrays in a positive light a subject that
children should have a positive attitude about.  

Darrell
Newsgroups: sci.math,sci.math.symbolic
From: dak@messua.informatik.rwth-aachen.de (David Kastrup)
Subject: Re: Integral Tables
Organization: Rechnerbetrieb Informatik  /  RWTH Aachen
Date: 29 Sep 92 11:49:14 GMT

Ray Zimmerman <Ray-Zimmerman@cornell.edu> writes:

>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.
So both are wrong. hooray. sqrt((-1)^2) = +- 1, that is either value,
depending on the choice of the Riemann leaf. And if you choose the leaf
you would expect from the squaring, you get -1. If you want to choose the
`main' leaf, you get 1. Fixing it one way or the other can always lead
to problems.
Xref: sparky sci.math:12463 sci.logic:1625
From: torkel@sics.se (Torkel Franzen)
Newsgroups: sci.math,sci.logic
Subject: Re: ZFC etc. (was Re: Report on Philosophies of Physicists)
Date: 29 Sep 92 22:29:27 GMT
	<TORKEL.92Sep28195555@bast.sics.se>
	<1992Sep29.145605.152967@Cookie.secapl.com>
Organization: Swedish Institute of Computer Science, Kista

In article <1992Sep29.145605.152967@Cookie.secapl.com> frank@Cookie.secapl.
com (Frank Adams) writes:

   >Similarly, in my hypothetical world where the disjunctive normal form
   >theorem was not proved, its disproof would not be a crisis.  The subsequent
   >proof, whenever it was found, would be a very serious crisis.  But that is
   >*because* it is an inconsistency.

  So what you are saying is that if we had somehow managed to avoid
proving that every formula has a disjunctive normal form, a proof that
some formulas do not have a disjunctive normal form would not have
caused an immediate furor, unlike a proof that propositional logic was
inconsistent. All that this seems to amount to is that we need to
think a little bit to see that every formula has a disjunctive normal
form, whereas the consistency of propositional logic is immediate.
Now, I've all but forgotten what was supposed to be the point of this.
Let's see. I said that a disproof of "every formula has a disjunctive
normal form" would show that our minds are seriously flawed, every bit
as much as a proof that propositional logic is inconsistent.  Is there
anything in your present reflections that tells against this?
Newsgroups: sci.math
Subject: Re: Infinity
From: wft@math.canterbury.ac.nz (Bill Taylor)
Date: Sat, 3 Oct 1992 08:29:31 GMT
 <1992Sep30.214743.18350@cs.rose-hulman.edu> <1371.2acabc99@atlas.nafb.trw.com> <1992Oct2.034803.14598@galois.mit.edu>
Organization: Department of Mathematics, University of Canterbury

|> >I can actually have "one" of something.  I don't know if it is possible
|> >for there to be "infinity" of anything.
|> 
|> Not anything that takes up any space, unless they are interpenetrable
|> or you have an infinite amount of room. 

Zeno strikes again !!!

*Or* ,  they may all take up nonzero but rapidly decreasing amounts of room.

( Nitpicking:- the nation's favorite indoor sport. )
Newsgroups: sci.math
From: tao@potato.princeton.edu (Terry Tao)
Subject: Re: Most important event in the history of mathematics
Originator: news@nimaster
Organization: Princeton University
Date: Mon, 28 Sep 1992 20:47:34 GMT

In article <1992Sep28.174237.26784@Cookie.secapl.com>, frank@Cookie.secapl.com (Frank Adams) writes:
|> In article <1992Sep28.145025.4059@guinness.idbsu.edu> holmes@opal.idbsu.edu (Randall Holmes) writes:
|> >In article <1992Sep25.201622.40255@Cookie.secapl.com> frank@Cookie.secapl.com (Frank Adams) writes:
|> >>[the proof of the inconsistency of naive set theory]
|> >>was nevertheless probably the most [important] event in the history of
|> >>mathematics.
|> >
|> > It was not the most important
|> >event in the history of math by a long shot.
|> 
|> All right; what was the most important event in the history of mathematics?
|> My vote is in; what do the rest of you think?

Feynman said that in his HO Tartagalia's solving of the cubic.  Not because
that this was really important in itself, but because it showed that we could
beat the ancient Greeks.

I don't think there were many single events, though: more of a long, gradual
process.  The gradual acceptance of Arabic numerals, for example, or symbolic
algebra.  Individuals did do a huge amount of work which then changed mathematics
forever, but not with one single achievement.
From: ags@seaman.cc.purdue.edu (Dave Seaman)
Newsgroups: sci.math
Subject: Re: Another Cute Math Joke  (explanation of)
Date: 2 Oct 92 14:31:34 GMT
Organization: Purdue University

> In article <marc.717947769@vieta.math.uni-sb.de>  
marc@vieta.math.uni-sb.de (Marc Conrad) writes:
> )dms@krang.vis.citri.edu.au (David Mcgregor SQUIRE) writes:
> )
> )>Q: What do you get if you cross an elephant with a grape?
> )
> )>A: |elephant||grape|sin(theta)
> )I'm stupid, but can someone explain this to me ??
> )Marc

Actually, the problem is that it wasn't told properly. It should be:

Q: What do you get if you cross an elephant with a mosquito?

A: |elephant| |mosquito| sin(theta)

Q: What do you get if you cross a mosquito with a mountain climber?

A: You can't cross a vector with a scaler.

(Puzzled? Look up "vector" and pay attention to non-mathematical  
definitions.)

--
Dave Seaman
ags@seaman.cc.purdue.edu
Newsgroups: sci.math
From: frank@Cookie.secapl.com (Frank Adams)
Subject: Most important event in the history of mathematics
Date: Mon, 28 Sep 1992 17:42:37 GMT
Organization: Security APL, Inc.

In article <1992Sep28.145025.4059@guinness.idbsu.edu> holmes@opal.idbsu.edu (Randall Holmes) writes:
>In article <1992Sep25.201622.40255@Cookie.secapl.com> frank@Cookie.secapl.com (Frank Adams) writes:
>>[the proof of the inconsistency of naive set theory]
>>was nevertheless probably the most [important] event in the history of
>>mathematics.
>
> It was not the most important
>event in the history of math by a long shot.

All right; what was the most important event in the history of mathematics?
My vote is in; what do the rest of you think?
Newsgroups: sci.math
From: edc323usft@vx24.cc.monash.edu.au
Subject: 200 Digit Integer C Code Wanted
Organization: Computer Centre, Monash University, Australia
Date: Mon, 28 Sep 1992 14:55:20 GMT

G'Day

       I have posted messages in other newsgroups, but I feel that this
is
probabily the most appropriate...

       I need some source code ('C') to handel integers that are
between 150 and 200 digits long.  I don't need anything fancy, as
long as the four basic operations are supported.  In case your wondering
it is for a RSA encryption algorithim.  If anyone can offer any help
i would appriciate it greatly

Travis
From: tedh@cylink.COM (Ted Hadley)
Newsgroups: sci.math
Subject: Re: Mattel says "Math is tough."
Date: 5 Oct 92 16:55:10 GMT
Organization: Cylink Corp.

In article <1992Oct5.084002.25808@nuscc.nus.sg> matmcinn@nuscc.nus.sg (Mcinnes B T (Dr)) writes:
>iltiss@owlnet.rice.edu (Steven Patrick Iltis) writes:
>: I don't normally read this news group, so I apologize if this is not
>: the appropriate place to post this. But I believe this is relevant.
>: 
>:         Mattel has just released a new product. A Barbie doll that says
>: "Math is tough".
>
>What would you have her say?: 

How about "Math is Important" or "Learn math well and get a good job as a
[computer scientist | engineer | physicist | ...]"


-- 
Ted A. Hadley  tedh@cylink.COM         "Credo qvia absvrdvm est" -- Tertullian
Cylink Corporation, 310 N. Mary Ave., Sunnyvale, CA 94086  USA    408-735-5847
All opinions expressed are my own, and probably not liked by my employer.
From: tao@ginger.princeton.edu (Terry Tao)
Newsgroups: sci.math
Subject: Re: Easy (?) probability question
Date: 2 Oct 92 18:08:18 GMT
Organization: Princeton University
Originator: news@nimaster

The variance of X is the minimum value of

E((X-a)^2)

for a variable a over the reals.  It is minimized, of course, when a is the
expectation of X.

Now it is obvious that if Z = min{X, k}, then the optimal value of a for Z
is less than k, as E(Z)<k.  But for a < k,

E((X-a)^2) \geq E((Z-a)^2)

as you can no doubt easily verify.

That's it!

Terry

alternatively:

var(Z) = E((Z-E(Z))^2) \leq E((X-E(Z))^2) \leq E((X-E(X))^2) = var(X)

the first inequality comes from the fact that X > Z if Z > E(Z), and X=Z
otherwise, and the second you can figure out yourself. 
Xref: sparky sci.math:12433 rec.puzzles:6505 comp.theory:2079
From: jpm10@cd.amdahl.com (Jim Millar)
Newsgroups: sci.math,rec.puzzles,comp.theory
Subject: Re: more on 9.999... = 10.0
Date: 29 Sep 92 17:03:47 GMT
Distribution: usa
Organization: Amdahl Corporation, Sunnyvale CA

Regarding why .333..=3/9 is more acceptable than .999...=9/9:

I remember when learning repeating decimals that .333..=1/3 was the first
example we learned. Everyone accepted it as truth. We learned a lot of other
repeating decimal representation of fractions, but never encountered .999...

In later math courses we learned limits. When talking about taking the limit
as x approaches a value such as 1, we talked about being able to get 
arbitrarily close, such as .9, .99, .999, .999... and never reaching 1.
Everyone accepted .999... as an example of being as close to 1 as possible
without being equal to 1 as truth.

When I pointed out to the teacher that I believed that .999... = 1, he agreed
but said he was only using .999... not equal to 1 as an example to demonstrate
his point. While I agreed with his reasoning, I can see why there is a lot
of confusion.

Jim Millar
Xref: sparky sci.math:12540 comp.theory:2104
From: watson@maths.uwa.oz.au (David Watson)
Newsgroups: sci.math,comp.theory
Subject: Re: Convex hulls in higher dimensions: applications?
Date: 30 Sep 1992 23:58:21 GMT
Organization: The University of Westrn Australia
Distribution: inet
NNTP-Posting-Host: madvax.maths.uwa.oz.au

orourke@sophia.smith.edu (Joseph O'Rourke) writes:

>I am interested in learning of practical applications of algorithms
>for constructing the convex hull of a set of points in dimensions
>greater than three.  What I have in mind is the application
>that Cohen & Hickey used a decade ago:  they analyzed the
>branching probabilities in programs as ratios of volumes of
>polytopes whose dimension depended on the complexity of the
>code.  Any other such applications?  Thanks!

We use the convex hull as a prepocessing step for natural neighbour
interpolation in higher dimensions.  This interpolation method is
usually applied only within the convex hull because natural neighbour
local coordinates are defined only within convex hulls.  By finding
the convex hull of the data and fitting a linear function by least
sum of squared differences, pseudo-data can be assigned at the
vertices of a large simplex enclosing the data.  Then interpolation
can be performed at locations which are outside the convex hull of
the real data.
Then time-series data can be embedded in 2, 3, 4, 5, or 6, dimensions
and the resulting manifold explored by natural neighbour interpolation
to give predictions about the behavior of the time-series.


--
Dave Watson                          Internet: watson@maths.uwa.edu.au
Department of Mathematics            
The University of Western Australia               Tel: (61 9) 380 3359
Nedlands, WA 6009  Australia.                     FAX: (61 9) 380 1028
Newsgroups: sci.math
From: iltiss@owlnet.rice.edu (Steven Patrick Iltis)
Subject: Mattel says "Math is tough."
Organization: Rice University
Date: Sun, 4 Oct 1992 17:43:24 GMT

I don't normally read this news group, so I apologize if this is not
the appropriate place to post this. But I believe this is relevant.

        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.

        Do not assume that corporate actions like these are final and
that your voice means nothing. Every complaint made over the telephone
lines is recorded and every complaint received by mail is collected
by the Consumer Affairs Division. I was informed that many people
have already voiced their upset.  Let's continue letting Mattel know
that their thoughtlessness treatment of our young people and science
will not be tolerated.

        Please call and write lodging your dissatisfaction with
Mattel's action. 
Joe Juliano Associate Director for Administration

Here is the information for your protest for Mattel.

Call 1-800-421-2887

Write
        Mattel
        Consumer Affairs Division
        333 Continental Boulevard
        El Segundo, California 90245

-- 
Steve Iltis, iltiss@owlnet.rice.edu
"People should get beat up for stating their beliefs." -They Might Be Giants
From: dseal@armltd.co.uk (David Seal)
Newsgroups: sci.math
Subject: Re: "Solvability" in Chess
Date: 30 Sep 92 13:49:13 GMT
Distribution: sci
Organization: A.R.M. Ltd, Swaffham Bulbeck, Cambs, UK

In article <1992Sep29.090457.25696@ucsu.Colorado.EDU>
cuffell@spot.Colorado.EDU (CUFFELL TIMOTHY MICH) writes:

>The rules also describe a tournament director who can decide the outcome of
>games that take too long.

Interesting, but is this a chess rule or a rule about chess tournaments? If
the former, it presumably means that you technically cannot play a game of
chess outside a tournament - you may play something that looks similar, but
it isn't actually strictly chess :-).

If the latter, I'm afraid it isn't directly relevant to this discussion -
i.e. it may help us solve "chess under tournament conditions", but it won't
help us solve "chess".

David Seal
dseal@armltd.co.uk

All opinions are mine only...
From: greil@guug.de (Anton Greil)
Newsgroups: sci.math
Subject: action of a semigroup on a set ?
Keywords: semigroup,action
Date: 27 Sep 92 19:08:33 GMT
Organization: Technical University of Munich, Germany


Is there a theory/calculus about the action of a semigroup on a set ?
(in analogy to the action of a group on a set) 

I'm looking for a text, where such a concept is defined.
Thank you !

Toni Greil, greil@guug.de
Newsgroups: sci.math
From: sassoj@rs6412.ecs.rpi.edu (John J. Sasso Jr.)
Subject: INTERESTING TOPOLOGY QUESTION
Keywords: Dense sets
Organization: Rensselaer Polytechnic Institute, Troy NY
Distribution: usa
Date: Mon, 5 Oct 1992 22:08:02 GMT

QUESTION:  Given the interval [0,1], does there exist two sets A and B such
           that A is dense in [0,1], B is dense in [0,1], and the Lebesgue
           outer measure of A and B is |A| = |B| = 1/2 ? 


           John



Newsgroups: sci.math
From: ledwards@leland.Stanford.EDU (Laurence James Edwards)
Subject: Re: Elliptic, hyperbolic and plane geometries
Organization: DSG, Stanford University, CA 94305, USA
Date: Fri, 2 Oct 92 08:07:04 GMT

In article <1992Oct1.130121.1@tnclus.tele.nokia.fi>, hporopudas@tnclus.tele.nokia.fi writes:
|> 
|>   About elliptic geometry and hyperbolic geometry with aid of algebra
|> 
|> 
|>       I refer here to my article 'Surface Algebras'


Ahhh, Hannu of space-potato fame is the one who posted that surface algebra
stuff ... a lot becomes clear now. Oh, and Hannu, I do apologize, as Scott
Chase pointed out, "wises" is an english word although your usage was
incorrect.

Anyway, take care Hannu, best of luck, I hope you find that space-potato.

Larry Edwards

Xref: sparky sci.math:12621 rec.puzzles:6574
From: hart@corona.math.vt.edu (Heath David)
Newsgroups: sci.math,rec.puzzles
Subject: Re: EASY NUMBER SEQUENCE PUZZLE...
Date: 2 Oct 92 14:46:25 GMT
Followup-To: sci.math
Organization: Mathematics Department, Virginia Tech University

In article <1992Oct2.113505.22990@kth.se> TordM@VanA.PhySto.SE writes:
>
> I see the pattern
> x_n=(-1905950809n^3+13341650526n^2-26683285691n)/6+2541264354
> which would yield the above series AND x_4=0
>

You *see* THAT pattern?  I snork profusely.
Newsgroups: sci.math
From: seh@neutron.physics.arizona.edu (Steven E. Hoell)
Newsgroups: sci.math
Subject: Re: Could have Archimedies invented Calclus?
Date: 27 Sep 92 20:40:21 GMT
Distribution: na
Organization: University of Arizona, Tucson AZ

I missed most of this discussion, but my freshman calculus instructor
said that Archimides would have discovered calculus had he been
familiar with the concept of limit.

Steve Hoell		seh@neutron.physics.arizona.edu
Newsgroups: sci.math
From: chungy2@aix.rpi.edu (Yau Felix Chung)
Subject: Books for Sale
Organization: Rensselaer Polytechnic Institute, Troy, NY
Date: Sat, 3 Oct 1992 19:32:04 GMT


				BOOK SALE!!



Through The Telescope by Michael R. Porcellino (hard cover)........$14.00              
Local Area Networks: The Next Generation by Thomas W. Madron.......$20.00           
The Boundary Value Problems in Mathematical Physics by 
	O. A. Ladyzhenskaya (hard cover)...........................$52.00           
Subatomic Physics by H. Frauenfelder & E. M. Henley (hard cover)...$57.00           
Applications of Group Theory in Physics and Mathematical Physics
	by M. Flato, P. Sally & Gregg Zuckerman (hard cover).......$70.00             
A First General Relativity by Bernard F. Schutz (hard cover).......$20.00                 

	* All prices are negociable
	* Shipping charges are not included it the prices above.

		If interested please e-mail chungy2@aix.rpi.edu
From: bbm@po.CWRU.Edu (Brian B. Mathewson)
Newsgroups: sci.math
Subject: Closed form solution to Sum[1/x,{x,1,n}] ?
Date: 30 Sep 1992 06:07:35 GMT
Organization: Case Western Reserve University, Cleveland, OH (USA)
Reply-To: bbm@po.CWRU.Edu (Brian B. Mathewson)
NNTP-Posting-Host: thor.ins.cwru.edu


Is there a closed form formula for:
  
  x=n
  Sum [  1/x  ]    where  x = {1,2,3,...n}  ?
  x=1

I have found other closed form formulas, such as for Sum[x^y,{y,1,n}]
but cannot find this one.

I am not looking for a solution for an infinite series, but just up to
a certain limit.

Thanks,

-- 

Brian Mathewson   bbm@r2d2.eeap.cwru.edu
                  bbm at Cleveland Freenet