```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, thelength of a tree is probably described relativeto the length at the terminal node of the longestbranch (usually with a +1 somewhere).  Consequently,complete here means that every node has a branchfor every symbol of the alphabet -- in this case 2.
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