Date: Apr 4, 2013 5:21 PM
Author: William Hughes
Subject: Re: Matheology § 224
On Apr 4, 10:48 pm, WM <mueck...@rz.fh-augsburg.de> wrote:

> 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!

If you take a set of nodes, and the parent/child

relationships, that contains all finite paths then

you have a tree that contains all finite paths. This tree contains

subsets of nodes that do not correspond to any finite path.

Some of these subsets are the subsets that correspond to what

might be termed infinite paths. However, if you use a definition

of path that excludes infinite paths, these subsets of nodes

remain, but they are not paths. So you have a Binary Tree that

does not contain an infinite path.