Date: Jan 13, 2013 4:23 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 191
On 12 Jan., 23:21, Virgil <vir...@ligriv.com> wrote:

> In article

> <c971e75b-20e3-4761-b39a-aab5a20a6...@d10g2000yqe.googlegroups.com>,

>

>

>

>

>

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

> > On 12 Jan., 12:45, Zuhair <zaljo...@gmail.com> wrote:

> > > On Jan 12, 11:56 am, 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...

>

> > > No it cannot be constructed in that manner, simply because it would no

> > > longer be a BINARY tree.

>

> > No? What node or path would be there that is not a node or path of the

> > Binary Tree? This is again an assertion of yours that has no

> > justification, like many you have postes most recently, unfortunately.

>

> Your claim that there are only aleph_0 possible tails is falsified by

> the Cantor diagonal argument:

>

> Any listing of those tails as binary sequences allows the anti-diagonal

> constriction of a tail not listed. and if you cannot list them, you have

> no proof that they are only countable in number.

A listing of all finite initial segments of all possible tails is

possible.

Cantor's diagonal argument leads to an anti-diagonal that differs from

every finite initial segment by a finite initial segment which is a

self-contradiction since all possible finite initial segments that

possibly could differ are already there.

Regards, WM