Re: abundance of irrationals!)


Virgil wrote:

> >
> > Of course neither of these sets can exist. You see it best by
> > investigating the definition. From the axioms, be it Peano's
induction
> > or set theoretic axiom of infinity, step by step another number is
> > included, but, as we have been told several times, this does by no
> > means lead to N or to any of its infinite subsets.
>
> Who has told us this? Only WM himself, and he offers no valid
evidence
> of his claims.

By no means I did so. You have a very bad memory. I hope, your CPU is
somewhat better. On the contrary, I said that induction shows that the
set of al even numbers is not infinite, because there is always a
number z in any non-empty set of positive finite even numbers, which
surpasses the cardinal number of that set. It is easily proven by
induction. And, of course, it is valid.

Regards, WM

.

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