```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 thenature of construction based on definition.
```