Date: Dec 13, 2012 8:00 AM
Subject: Re: On the infinite binary Tree

On 13 Dez., 09:26, Virgil <> wrote:

> > No. I proved that the number of infinite paths is countable by
> > constructing all nodes of the Binbary Tree by a countable set of
> > infinite paths.

> WM is again, or should I say still, self-deluded in all sorts of ways.
> The only way WM could actually have CONSTRUCTED all nodes of a INFINITE
> binary tree is by completing infinitely many construction steps himself
> which he has often claimed that no one can ever do.

If actual infinity exists (and I assume that for the sake of
contradiction) then the CIBT can be constructed.

> Such trees can exist only in the imagination, as is the case with a
> great many mathematical "constructions".
> But the set of paths of such an imagined tree, to be consistent, must
> have a different path for every different subset of the set of all
> naturals numbers, being the set of levels at which that path branches
> left, and there are uncountably many such subsets of N.

Alas most of them are not definable. Why does no Cantor-list contain
undefinable elements?

Regards, WM