Date: Apr 4, 2013 4:37 PM
Subject: Re: Matheology � 224
WM <firstname.lastname@example.org> 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
> 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
> 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.