```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 pathThere 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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