Date: Apr 4, 2013 5:51 PM
Author: fom
Subject: Re: Matheology § 224

On 4/4/2013 4:21 PM, William Hughes 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:
>>
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>>> 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. So you have a Binary Tree that
> does not contain an infinite path.
>


Nice. But, when has WM respected any defined terms?