Date: Apr 4, 2013 4:48 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 224
On 4 Apr., 21:01, William Hughes <wpihug...@gmail.com> wrote:

> On Apr 4, 8:22 pm, WM <mueck...@rz.fh-augsburg.de> wrote:

>

>

>

>

>

> > On 4 Apr., 19:40, William Hughes <wpihug...@gmail.com> wrote:

>

> > > On Apr 4, 6:43 pm, WM <mueck...@rz.fh-augsburg.de> wrote:

>

> > > > 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.

>

> > > Indeed, and some of these subsets of nodes are paths and

> > > some are not.

>

> > In the Binary Tree there is no stop at any path.

>

> > > You talk about subsets of nodes with a last node

> > > and subsets of nodes without a last node. However,

> > > you refuse outright to indicate what makes a subset of nodes

> > > a path (certainly not all subsets of nodes are paths).

>

> > All nodes that belong to a finite path, belong to an infinite path

> > too.

>

> Since you refuse to say what makes a subset of nodes a path

> you cannot claim that a path without a last node exists.-

The construction principle of the Binary Tree (two child nodes to

every parent node) is obvious. If someone believes that there is a

difference between the Binary Tree that contains all infinite paths

and the Binary Tree that does not contain an infinite path, but

contains all finite paths, he has to define the latter. Good luck!

Regards, WM