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



