On 13 Jun., 15:43, William Hughes <wpihug...@hotmail.com> wrote: > On Jun 13, 8:53 am, WM <mueck...@rz.fh-augsburg.de> wrote: > > > On 13 Jun., 14:17, 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. > > > > You agree that there is a path p in the tree > > > > You agree that path p can be distinguished > > > from every element of P. > > > If actually infinite paths exist! > > Ok. We make the assumption explicit.
> You agree that if actually infinite paths > exist, there is a path p in the tree > > You agree that if actually > infinite paths exist, path p > can be distinguished > from every element of P.
by using nodes of the tree only without additional knowledge. > > You do not agree that > if actually infinite paths exist, > the tree contains a path that > can be distinguished from every element of P.
I prove that it is impossible to distinguish a give path p from the paths in P using only the information stored in the tree, i.e. using only digit sequences to identify numbers, thereby proving that no actual infinity exists.
Instead of grumbling about this fact, you either should accept it and confess that I am right and that set theory is wrong, or you should be able to distinguish your path p from the set P of paths that I have used for construction, but without any other knowledge than the final result, namely the digits, i.e., the nodes of the binary tree.