Date: Apr 4, 2013 4:45 PM
Author: Virgil
Subject: Re: Matheology � 224
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.

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