Date: Apr 4, 2013 5:27 PM
Author: fom
Subject: Re: Matheology § 224
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?