In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 24 Dez., 20:14, Virgil <vir...@ligriv.com> wrote: > > In article > > <d85d67ab-aa37-4091-9474-a089288c3...@x10g2000yqx.googlegroups.com>, > > > > WM <mueck...@rz.fh-augsburg.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.