Date: Feb 5, 2013 12:41 AM
Author: fom
Subject: Re: Matheology § 203

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.