Re: Orlow cardinality question

In article <MPG.1d24dfb63c4cd5d0989ebb@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:

> Virgil said:

> > For each finite natural, n in N, let n* represent the set of naturals up
> > to and including that value, so that, for example, 3* = {1,2,3}, and for
> > all "finite" n in N, Card(n*) = n.
> >
> > Now let N* be the union of these n*'s for all finite n in N.
> >
> > Then N* is an infinite set of "finite" naturals, such as TO claims
> > cannot exist.
> >
> I simply stated, and proved, that such a set is finite.

And I simply stated and proved it to be not finite:

Successor: N* -> N* injects N* into a proper subset of itself.

Ergo, N* is not finite. QED.

So TO's proof is garbage.
.

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