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. --