```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
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