```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:>>>>>>>>>>>>>>>>>>>>> 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?
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