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Topic: Well Ordering
Replies: 4   Last Post: Feb 14, 2013 10:48 AM

 Messages: [ Previous | Next ]
 David C. Ullrich Posts: 21,553 Registered: 12/6/04
Re: Well Ordering
Posted: Feb 13, 2013 9:07 AM

On Wed, 13 Feb 2013 02:17:41 -0800, William Elliot <marsh@panix.com>
wrote:

>Let S be a set with cardinality aleph_nu.
>Since S is equinumerous with omega_nu, there's
>. . a bijection h:S -> omega_nu.
>
>Thus S is well ordered by x <= y when h(x) <= h(y);
>. . well ordered without using AxC. Hm...

Yes, if you begin by _assuming_ that S has cardinality aleph_nu
then you don't need AC to well-order S.

Now, given an arbitrary set S, how do you show that it _does_
have cardinality aleph_nu for some nu?

>
>

Date Subject Author
2/13/13 William Elliot
2/13/13 Butch Malahide
2/13/13 David C. Ullrich
2/13/13 magidin@math.berkeley.edu
2/14/13 Shmuel (Seymour J.) Metz