Date: Apr 4, 2013 5:32 PM
Author: Virgil
Subject: Re: Matheology � 224

In article <Va6dnYv5KPWzbcDMnZ2dnUVZ_h6dnZ2d@giganews.com>,
fom <fomJUNK@nyms.net> wrote:

> On 4/4/2013 3:45 PM, Virgil wrote:
> > In article
> > <8b76659f-69ea-4e51-8e7e-f99c0c598a9e@f18g2000vbs.googlegroups.com>,
> > William Hughes <wpihughes@gmail.com> wrote:
> >

> >> On Apr 4, 8:22 pm, WM <mueck...@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.
> >>>

> >>>> 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, belong to an infinite path
> >>> too.

> >>
> >> Since you refuse to say what makes a subset of nodes a path
> >> you cannot claim that a path without a last node exists.

> >
> > The formal definition of a path in such a tree, finite or infinite tree,
> > is that it is a maximal sequence of parent to child connected nodes.
> > his requires it to start with the root node (which has no parent node)
> > and end, if it does end, with a terminal node which has no child nodes.
> >
> > Note that by this definition, a path in a Complete Infinite Tree, Binary
> > or otherwise, cannot have any terminal node as every node has at least
> > one child node.
> >
> > However WM does not allow sensibly defined trees and sensibly defined
> > paths in his Wolkenmuekenheim, so no one knows what goes on there.
> >

>
> "Sensible" is a secondary issue. Has WM ever given an appropriately
> stated definition to which references made in his "obvious" "proofs
> by reality" can be compared?


Not to my knowledge. For example, WM has used the word "path" unmodified
to mean both a necessarily finite sequence of nodes and later a
necessarily infinite and maximal sequence of nodes in the same sentence.
--