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