Re: infinity ...

In article <1129946611.902596.262670@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
"William Hughes" <wpihughes@xxxxxxxxxxx> wrote:

> Dave Rusin wrote:
> > In article <1129901285.084347.34810@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
> > William Hughes <wpihughes@xxxxxxxxxxx> wrote:
> >
> > >Yes all sets have a cardinality.
> >
> > That's your Choice.
>
> Am I assuming AC here?
>
> My understanding was that, while AC was needed to
> put a total ordering on the equivalence classes
> under bijection, one could assert the existence
> of these classes even without AC. Or are the
> cardinalities defined not as all possible
> equivalence classes but as the equivalence classes
> on the ordinals?
>
> -William Hughes

As I understand it, without AC, one cannot be sure of creating any sort
of function at all from one arbitrary set to another, much less
guarantee that such a function, even if creatable, be an injection or a
surjection.
.

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