Virgil
Posts:
6,972
Registered:
1/6/11


Re: Distinguishability of paths of the Infinite Binary tree???
Posted:
Dec 25, 2012 3:59 PM


In article <76daea4039024687ae1c53fe5356b0a3@b11g2000yqh.googlegroups.com>, WM <mueckenh@rz.fhaugsburg.de> wrote:
> On 24 Dez., 20:14, Virgil <vir...@ligriv.com> wrote: > > In article > > <d85d67abaa3740919474a089288c3...@x10g2000yqx.googlegroups.com>, > > > > WM <mueck...@rz.fhaugsburg.de> wrote: > > > On 23 Dez., 21:20, Zuhair <zaljo...@gmail.com> wrote: > > > > > > Also the proof of Cantor is actually about uncountability of paths > > > > that are distinguishable on finite basis. > > > > > That is the point! > > > > The Cantor argument only deals with distinguishability on a finite basis > > (each individual listed entry differs from the "diagonal" at an > > "individual finite position") but shows that it can occur infinitely > > often > > without leaving the finite domain, i.e., the Binary Tree that contains > nothing but all finite paths.
Any such tree is incomplete as a binary tree, as it necessarily contains paths of all sorts of different lengths (different numbers of nodes or numbers of branches), while in a complete infinite binary tree all paths are of exactly the same length.
So that WM is WRONG! AGAIN!! AS USUAL!!! 

