```Date: Apr 4, 2013 5:27 PM
Author: fom
Subject: Re: Matheology § 224

On 4/4/2013 3:45 PM, Virgil wrote:> In article> <8b76659f-69ea-4e51-8e7e-f99c0c598a9e@f18g2000vbs.googlegroups.com>,>   William Hughes <wpihughes@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 formal definition of a path in such a tree, finite or infinite tree,> is that it is a maximal sequence of parent to child connected nodes.> his requires it to start with the root node (which has no parent node)> and end, if it does end, with a terminal node which has no child nodes.>> Note that by this definition, a path in a Complete Infinite Tree, Binary> or otherwise, cannot have any terminal node as every node has at least> one child node.>> However WM does not allow sensibly defined trees and sensibly defined> paths in his Wolkenmuekenheim, so no one knows what goes on there.>"Sensible" is a secondary issue.  Has WM ever given an appropriatelystated definition to which references made in his "obvious" "proofsby reality" can be compared?
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