Date: Feb 5, 2013 3:13 AM
Author: fom
Subject: Re: Matheology § 203

On 2/5/2013 1:57 AM, Virgil wrote:
> In article <NrmdnTGwGq_kBo3MnZ2dnUVZ_tudnZ2d@giganews.com>,
> fom <fomJUNK@nyms.net> wrote:
>

>> On 2/4/2013 6:00 PM, fom wrote:
>>> On 2/4/2013 5:14 PM, Virgil wrote:
>>>> In article <tbCdnURtDtB9so3MnZ2dnUVZ_sWdnZ2d@giganews.com>,
>>>> fom <fomJUNK@nyms.net> wrote:
>>>>

>>>>>
>>>>> From the beginning (I showed up when Zuhair was asking questions)
>>>>> I have not understood terminology. A CIBT is the Cantor space.
>>>>> It is a topological construct and the C refers to topological
>>>>> completeness.

>>>>
>>>> In my disputes with WM, a "CIBT" or "COMPLETE INFINITE BINARY TREE"
>>>> is a countably infinite set of nodes, with a unique root node and such
>>>> that every node has two child nodes, a "left child" and a "right child",
>>>> and every node but the root node has one parent node for which it is
>>>> either a left child or a right child.
>>>>
>>>> One can model it with its nodes being positive naturals:
>>>>
>>>> 1
>>>> / \
>>>> / \
>>>> 2 3
>>>> / \ / \
>>>> 4 5 6 7
>>>> / \ / \ / \ / \
>>>>
>>>> So that the left child of any node n is 2*n and its right child is
>>>> 2*n+1, and the parent of any node n except 1 is floor(n/2).

>>>>>
>>>
>>>
>>> Yes. I gathered that and it is nice to see it
>>> framed classically.
>>>
>>> Would not infinite binary tree suffice? What
>>> confused me initially was the inclusion of the
>>> modifier "complete".

>>
>> I suppose not. In discrete presentations, the
>> length of a tree is probably described relative
>> to the length at the terminal node of the longest
>> branch (usually with a +1 somewhere). Consequently,
>> complete here means that every node has a branch
>> for every symbol of the alphabet -- in this case 2.

>
> A path in a binary tree is any maximal chain of parent-child linked
> nodes in a binary tree, and such a tree is complete if all paths are of
> equal length. In an infinite binary tree that means each path is a
> countably infinite set of nodes.
>


Thanks