```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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