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.

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