Date: Apr 5, 2013 2:00 AM Author: mueckenh@rz.fh-augsburg.de Subject: Re: Matheology § 224 On 4 Apr., 23:21, William Hughes <wpihug...@gmail.com> wrote:

> 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.

They are path in an infinite Binary Tree. And that is the tree

constructed from all finite paths.

Regards, WM