On 13 Jun., 13:30, William Hughes <wpihug...@hotmail.com> wrote: > On Jun 13, 12:13 am, WM <mueck...@rz.fh-augsburg.de> wrote: > > > On 13 Jun., 02:16, William Hughes <wpihug...@hotmail.com> wrote: > > Your claim is that "no possibility exists to construct or to > distinguish by one or many or infinitely many nodes > of the tree another path."
Yes. > > > The path p is distinguished > from every element of P.
1/pi is distinct from any terminating path. > > All of the nodes of path p > are in the tree. > All nodes of the path 1/pi are in the tree (together with all nodes of any other path of the unit interval).
> The binary tree does not contain a path > p that can be distinguished from > every element of P.
The binary tree does not contain any path that can be distinguished from every element of the set P of paths by which it was constructed. If this were no true, then you could determine whether a given path p differs from every element of P without knowing P.
Note: Cantor's diagonal method uses only digits respective nodes, no additional information like the age of the writer or so. Same holds for my tree.