Date: Feb 5, 2013 2:57 AM
Author: Virgil
Subject: Re: Matheology � 203
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.

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