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Topic: Problems with Infinity?
Replies: 72   Last Post: Apr 12, 2013 1:36 PM

 Messages: [ Previous | Next ]
 Frederick Williams Posts: 2,164 Registered: 10/4/10
Re: Problems with Infinity?
Posted: Feb 26, 2013 12:55 PM

Don Kuenz wrote:
>
> Joseph Nebus <nebusj-@-rpi-.edu> wrote:

> >
> > A couple recent posts on James Nicoll's LiveJournal ---
> >
> > http://james-nicoll.livejournal.com/4145868.html
> > http://james-nicoll.livejournal.com/4194844.html
> >
> > --- have left me aware that at least two Heinlein novels (_The Number
> > Of The Beast_ and _Time Enough For Love_) contain mentions dismissing
> > the Cantorian idea of there being different-size infinities, and that
> > at least one Christopher Anvil story in which a journey to hyperspace
> > reveals that the rationals and the integers *don't* have the same
> > cardinality.

>
> A question for the group, if you please.
>
> Let's say a Mobius strip goes to infinity "feedback style" (in layman's
> terms) while a line goes to two separate but equal infinities "linear
> style." How many different infinities does that make according to
> Cantor? One, two, or three?

If you're interested in infinity, here is something that I posted
recently:

A few years ago Zdislav V. Kovarik made a post listing a dozen or more
meaning of the word "infinity" as used in different branches of
mathematics. I'm hoping that he won't mind me reposting it:

There is a long list of "infinities (with no claim to exhaustiveness):
infinity of the one-point compactification of N,
infinity of the one-point compactification of R,
infinity of the two-point compactification of R,
infinity of the one-point compactification of C,
infinities of the projective extension of the plane,
infinity of Lebesgue-type integration theory,
infinities of the non-standard extension of R,
infinities of the theory of ordinal numbers,
infinities of the theory of cardinal numbers,
infinity adjoined to normed spaces, whose neighborhoods are
complements of relatively compact sets,
infinity adjoined to normed spaces, whose neighborhoods are
complements of bounded sets,
infinity around absolute G-delta non-compact metric spaces,
infinity in the theory of convex optimization,
etc.;

each of these has a clear definition and a set of well-defined rules
for handling it.

And the winner is...
the really, really real infinity imagined by inexperienced debaters of
foundations of mathematics; this one has the advantage that it need
not be defined ("it's just there, don't you see?") and the user can
switch from one set of rules to another, without warning, and without
worrying about consistency, for the purpose of scoring points in idle
and uneducated (at least on one side) debates.
--
When a true genius appears in the world, you may know him by
this sign, that the dunces are all in confederacy against him.
Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting

Date Subject Author
2/24/13 William Elliot
2/24/13 garabik-news-2005-05@kassiopeia.juls.savba.sk
2/24/13 Frederick Williams
2/24/13 David DeLaney
2/25/13 P. Taine
2/26/13 Butch Malahide
2/24/13 jsavard@ecn.ab.ca
2/25/13 ross.finlayson@gmail.com
2/25/13 Brian M. Scott
2/25/13 Shmuel (Seymour J.) Metz
2/25/13 jsavard@ecn.ab.ca
2/25/13 Brian M. Scott
2/26/13 ross.finlayson@gmail.com
2/26/13 Frederick Williams
2/26/13 Wayne Throop
2/26/13 Brian M. Scott
2/26/13 ross.finlayson@gmail.com
2/25/13 Frederick Williams
2/25/13 Shmuel (Seymour J.) Metz
2/25/13 Frederick Williams
2/26/13 Wayne Throop
2/26/13 Wayne Throop
2/26/13 Brian M. Scott
2/26/13 Wayne Throop
2/26/13 Brian M. Scott
2/26/13 Wayne Throop
2/27/13 David DeLaney
2/27/13 Shmuel (Seymour J.) Metz
2/28/13 David DeLaney
2/28/13 Shmuel (Seymour J.) Metz
2/28/13 David DeLaney
3/1/13 Shmuel (Seymour J.) Metz
3/1/13 David DeLaney
3/2/13 Shmuel (Seymour J.) Metz
2/28/13 jsavard@ecn.ab.ca
2/28/13 David Johnston
2/27/13 Shmuel (Seymour J.) Metz
2/26/13 Frederick Williams
2/26/13 David DeLaney
4/11/13 Walter Bushell
4/11/13 Brian M. Scott
4/11/13 Butch Malahide
4/12/13 fom
4/12/13 Wayne Throop
4/12/13 fom
4/12/13 Wayne Throop
4/12/13 fom
4/11/13 jsavard@ecn.ab.ca
4/11/13 Butch Malahide
4/12/13 Virgil
4/12/13 Brian M. Scott
4/12/13 jsavard@ecn.ab.ca
4/11/13 fom
4/11/13 Butch Malahide
4/11/13 Butch Malahide
4/12/13 Brian M. Scott
4/12/13 Butch Malahide
2/26/13 Brian M. Scott
2/26/13 Shmuel (Seymour J.) Metz
2/26/13 Brian M. Scott
2/26/13 David Bernier
2/26/13 Shmuel (Seymour J.) Metz
2/28/13 Shmuel (Seymour J.) Metz
4/11/13 Walter Bushell
4/11/13 Shmuel (Seymour J.) Metz
2/26/13 Frederick Williams
2/27/13 Scott Fluhrer