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From: Maury Barbato on 17 Feb 2010 23:23
Arturo Magidin wrote:

> On Feb 17, 1:54 pm, Arturo Magidin
> <magi...(a)member.ams.org> wrote:
>
> > If you have the axiom of choice, then for each i
> the set of right
> > inverses of f_i is nonempty (by the Theorem), so
> now you have a
> > nonempty family of nonempty sets, so another
> application of the Axiom
> > of Choice lets you pick one right inverse g_i for
> each g_i.
>
> Oops; I didn't see your requirement that the g_i be
> distinct.

It doesn't matter, Arturo. I've appreciated very much
your explanation of the AC. I've perectly catched the
meaning of the AC: it seems to me an unassailable
assumption, or at least it perfectly agrees with
my intuitive and "pre-mathematical" idea of set.

> As
> Gerhard has pointed out, you may not have "enough"
> functions from Y to
> X to accomplish this in general, even if all the f_i
> are distinct, or
> even if your sets are infinite.

Thank you one more time for you great insights!
My Best Regards,
Maury Barbato

And we should consider every day lost on which we have
not danced at least once. And we should call every truth
false which was not accompanied by at least one laugh.
(F. Nietzsche)
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