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?