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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