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.