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 the

nature of construction based on definition.