```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.--
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