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

 Messages: [ Previous | Next ]
 Virgil Posts: 8,833 Registered: 1/6/11
Re: Problems with Infinity?
Posted: Apr 12, 2013 12:50 AM

In article
Butch Malahide <fred.galvin@gmail.com> wrote:

> On Apr 11, 8:49 pm, Quadibloc <jsav...@ecn.ab.ca> wrote:
> >
> > However, there is a set known to have cardinality aleph-1, the set of
> > well-orderings of the integers.

>
> Well, sort of. Actually, the set of well-orderings of the integers has
> the cardinality of the continuum, which may or may not equal aleph_1.
> It's the set of *order types* of well-orderings of the integers that
> absolutely has cardinality aleph_1. That is, you definite an
> equivalence relation on that set of well-orderings, two orderings
> being called equivalent just in case they are isomorphic, and the the
> resulting equivalence classes are aleph_1 in number. (That's what you
> meant, but mathematicians make a big deal of saying what you mean and
> meaning what you say.)

Which rules out WM.
--

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