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:

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>>>> On 4 Apr., 19:40, William Hughes <wpihug...@gmail.com> wrote:

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>>>>> On Apr 4, 6:43 pm, WM <mueck...@rz.fh-augsburg.de> wrote:

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>>>>>> On 4 Apr., 18:21, William Hughes <wpihug...@gmail.com> wrote:

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>>>>>>> On Apr 4, 5:19 pm, WM <mueck...@rz.fh-augsburg.de> wrote:

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>>>>>>>> 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

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>>>>>>> However, you keep talking about two types of paths,

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>>>>>> Not at all. I talk about sets of nodes that are in the Binary Tree.

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>>>>> Indeed, and some of these subsets of nodes are paths and

>>>>> some are not.

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>>>> In the Binary Tree there is no stop at any path.

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>>>>> 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).

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>>>> All nodes that belong to a finite path, belong to an infinite path

>>>> too.

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>>> Since you refuse to say what makes a subset of nodes a path

>>> you cannot claim that a path without a last node exists.-

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>> 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?