On Wed, 13 Feb 2013 02:17:41 -0800, William Elliot <firstname.lastname@example.org> 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?