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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