Date: Dec 13, 2012 2:17 PM
Author: Virgil
Subject: Re: On the infinite binary Tree
In article

<f46dba51-46fc-4354-985c-27665000dbf4@x3g2000yqo.googlegroups.com>,

WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 13 Dez., 09:26, Virgil <vir...@ligriv.com> 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?

Undefineable or unreconstructable paths are not needed to prove

uncountability because every list of defineable/constructable paths

proves the existence, by explicit definition/construction of it, of a

path which has been omitted from that list.

Thus it is your alleged set of all defineable/constructable paths that

either does not exist at all or is not countable.

--