Date: Apr 4, 2013 4:37 PM
Author: Virgil
Subject: Re: Matheology � 224

In article 
<87f2e861-f89d-4a90-a2ef-83b821e9bd57@h1g2000vbx.googlegroups.com>,
WM <mueckenh@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.


By the time one has a path one has infinitely many nodes in it, at least
for a CIBT.
>
> > 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


There are no such things as finite paths in any Complete Infinite Binary
Tree.



> belong to an infinite path
> too. That is the character of the Binary Tree. There is no further
> limitation possible. There is no further indication necessary or
> possible.
>
> Abandon your untenable position.


It may be untenable inside Wolkenmuekenheim, but nowhere else, and much
of what WM claims is untenable anywhere else.




> Or try (and fail) to define a limit
> that distinguishes both Binary Trees.


The only binary tree of interest here is the Complete Infinite Binary
Tree in which each path is order isomorphic to |N.
--