Date: Apr 5, 2013 2:29 AM
Author: fom
Subject: Re: Matheology § 224

On 4/5/2013 1:00 AM, WM wrote:
> On 4 Apr., 23:21, William Hughes <wpihug...@gmail.com> wrote:
>> On Apr 4, 10:48 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>>
>>
>>
>>
>>

>>> On 4 Apr., 21:01, William Hughes <wpihug...@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 construction principle of the Binary Tree (two child nodes to
>>> every parent node) is obvious. If someone believes that there is a
>>> difference between the Binary Tree that contains all infinite paths
>>> and the Binary Tree that does not contain an infinite path, but
>>> contains all finite paths, he has to define the latter. Good luck!

>>
>> If you take a set of nodes, and the parent/child
>> relationships, that contains all finite paths then
>> you have a tree that contains all finite paths. This tree contains
>> subsets of nodes that do not correspond to any finite path.
>> Some of these subsets are the subsets that correspond to what
>> might be termed infinite paths. However, if you use a definition
>> of path that excludes infinite paths, these subsets of nodes
>> remain, but they are not paths.

>
> They are path in an infinite Binary Tree. And that is the tree
> constructed from all finite paths.


Is it any surprise that WM has absolutely no understanding
with regard to the use of definitions?