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.
--