Date: Apr 4, 2013 12:43 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 224

On 4 Apr., 18:21, William Hughes <wpihug...@gmail.com> wrote:
> On Apr 4, 5:19 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>

> > On 4 Apr., 16:08, William Hughes <wpihug...@gmail.com> wrote:
> > There is no need to say what numbers belong to mathematics - in
> > mathematics. There is no need to say what paths belong to the Binary
> > Tree

>
> However, you keep talking about two types of paths,


Not at all. I talk about sets of nodes that are in the Binary Tree.

> paths with a last node and paths without a last node.
> You have to say which subsets of nodes correspond to
> paths.


Not at all. I have not to say what sequences of digits I use when I
write digits. That is just the clue of my proof: In mathematics
numbers are represented by digits and nothing else. This is also the
case in Cantor's list. When you require further information, then you
concede that your matheology is not only based upon digits but on
additional information that may be given by God but does not belong to
mathematics.

In mathematics a sequence of digits is infinite, if it does not end.
No further information is required. And the paths are infinite in a
Binary Tree that contains all finite initial segments of paths.
>
> Nope, you can form a subset of nodes without a last node
> by unioning finite paths.  You have to decide if you wish
> to call this set of nodes a path.


There is no decision possible. And there is no letter in mathematics
responsible for expressing that decision. The paths are automatically
infinite in the Binary Tree constructed by finite paths only.

Regards, WM