Date: Apr 4, 2013 11:19 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 224
On 4 Apr., 16:08, William Hughes <wpihug...@gmail.com> wrote:

> On Apr 2, 10:45 pm, WM <mueck...@rz.fh-augsburg.de> wrote:

>

> > On 2 Apr., 00:14, William Hughes <wpihug...@gmail.com> wrote:

> > > The difference between the trees is not which

> > > subsets of nodes exist, but which subsets are

> > > considered to be paths.

>

> > The tree of all finite paths and the tree of all paths like every tree

> > has infinite paths. Therefore there is no tree which has only finite

> > subsets that are considered paths.

>

> You confuse subsets of nodes, which belong

> to both trees, with paths which are defined

> differently for the two different trees.

> Only in one of the trees

> can a subset of nodes without a last

> node be considered a path.

>

>

>

> > Is this tree

>

> > 0.

> > 0 1

> > 0 1 0 1

> > ...

>

> > that one with infinite subsets not considered paths?

>

> I do not know. You have shown

> me a set of nodes, but have not

> told me which subsets are considered

> paths.

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 - in mathemativs. Every path that you can form by unioning finite

paths is of course a path of the Binary Tree. Every node you point to,

is a node of a path, in fact even of a finite path. And this does not

change, whether or not the Binary Tree is defined so or so.

Regards, WM