```Date: Apr 5, 2013 4:51 AM
Author: Virgil
Subject: Re: Matheology � 224

In article <9YedndChL-5hEcPMnZ2dnUVZ_vWdnZ2d@giganews.com>, fom <fomJUNK@nyms.net> wrote:> 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.But his definitions change their meaning in midstream.--
```