Date: Apr 5, 2013 4:36 AM
Author: fom
Subject: Re: Matheology § 224

On 4/5/2013 3:25 AM, Virgil wrote:
> In article
> <baf421e7-181b-4d62-b014-2e323a6abad8@r8g2000vbj.googlegroups.com>,
> WM <mueckenh@rz.fh-augsburg.de> 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.

>>
> There cannot be any finite paths in any Complete Infinite Binary Tree,
> since all paths in trees are, by definition, maximal as sequences of
> nodes, and thus in CIBTs necessarily infinite.
> What WM is trying, but failing, to talk about may be labeled "FISONs"
> (Finite Initial Sequence Of Nodes).
>


Look closer. WH is giving WM a lesson in the
nature of construction based on definition.