Date: Dec 13, 2012 2:25 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: On the infinite binary Tree

On 13 Dez., 20:17, Virgil <vir...@ligriv.com> wrote:
> In article
> <f46dba51-46fc-4354-985c-27665000d...@x3g2000yqo.googlegroups.com>,
>
>
>
>
>
>  WM <mueck...@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.
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