Re: abundance of irrationals!)

In article <1115327162.940942.66840@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:

> imaginator...@xxxxxxxxxxxxx wrote:
>
>
> > In other words, it is _true_ that (if n and p are naturals):
> > For all n, exists p, s.t. p>n
> >
> > It is not true that:
> > Exists p, s.t. for all n, p>n
> >
> > This is the standard reversal of quantifiers that is behind
> practically
> > every crank argument about infinity.
>
> But this is precisely the way to deduce the existence of the whole
> numbers aleph_0 or omega from the axiom of infinity.

Since Wm has repeatedly demostrated that his notion of the axiom of
infinity to be nothing like the Zermelo-Frankel version or the von
Neumann-Bernays-Goedel (NBG) version, nor any mathematical version known
to mathematics, what he deduces from it need not be consistent with what
one can deduce from any accepted version of it.
>>
> Or is there another axiom leading to aleph_0? It must have escaped me,
> though I studied carefully different axiom systems of set theory.

Try Googling for the actual axiom of infinity either the Zermelo-Frankel
version or the Neumann-Bernays-Goedel version by preference.
.

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