Date: Dec 13, 2012 2:28 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

moreover, they cannot be treated in a Cantor list.

> 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.

Explicit construction is onyl possible if every list number is

defined. That restricts the constructed diagonals to a countable set.

>

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

> either does not exist at all or is not countable.

You say it: The set of all definable real numbers is not countable.

You just admitted a contradiction of set theory.

Regaeds, WM