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.
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