Date: Jan 13, 2013 3:47 PM
Author: Virgil
Subject: Re: Matheology � 191
In article

<91cc9673-aa94-45c5-ba92-f50a1c7012ea@b8g2000yqh.googlegroups.com>,

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

> On 12 Jan., 22:58, Virgil <vir...@ligriv.com> wrote:

> > In article

> > <f62302b5-c3c6-4b54-8437-6f9d7bc00...@4g2000yqv.googlegroups.com>,

> >

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

> > > Matheology § 191

> >

> > > The complete infinite Binary Tree can be constructed by first

> > > constructing all aleph_0 finite paths and then appending to each path

> > > all aleph_0 finiteley definable tails from 000... to 111...

> >

> > > 0

> > > 1, 2

> > > 3, 4, 5, 6

> > > 7, ...

> >

> > > This Binary Tree contains aleph_0 * aleph_0 = aleph_0 paths.

> >

> > Aleph_0 * aleph_0 = aleph_0 but 2 ^ aleph_0 > aleph_0, and that is the

> > number of paths.

>

> Can you name, define, or at least "discern" one of the paths missing

> in my Binary Tree? Note: I do not hide my receipe of construction any

> longer. I use every tail that can be described and communicated in any

> language.

If your set of paths ( as infinite binary sequences) is capable of being

listed then that very capability proves, a la Cantor, that it is

incomplete, and if it cannot be listed then it is, by definition, not

countable.

> >

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