Re: CANTOR's theorem

In article <1117026663.273526.7580@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:

> Randy Poe wrote:
> > mueckenh@xxxxxxxxxxxxxxxxx wrote:
> > > Randy Poe wrote:
> > >
> > > >
> > > > > but of non-existence of a special self-reflexive set
> > > > > {M, m, f'}.
> > > >
> > > > I don't know what that means.
> > >
> > > Say, there is no set {M, m, f} where f is a mapping, M is the set of
> > > all nongenerators under f, and m is a generator which is not a
> > > generator.
> >
> > I agree there is no m which is a generator and also
> > not a generator.
>
> But that is just what is required if all n e N are to map on the power
> set.

It is easy to map all n in N into P(N), what is not so easy is to make
each S in P(N) the target of some n in N in such a mapping.

If is easy to see that for finite sets T, T -> P(T) cnot be a surjection
(onto) mapping. For T infinite is may be less easy to see, but it is
still true.
.

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