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.