On 14 Jun., 14:49, William Hughes <wpihug...@hotmail.com> wrote: > On Jun 14, 8:26 am, WM <mueck...@rz.fh-augsburg.de> wrote: > > > On 14 Jun., 14:01, 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." > > > > > > Assuming infinite paths exist: > > > > The path p is in the tree > > > > The path p can be distinguished from > > > every element of P. > > > For every path p_n of P there is a digit such that p differs from p_n. > > But there is no digit of p that differs from every path p_n of P > > because, if p exists as binary representation, then p is the union of > > all p_n and as such cannot differ from the union. > > The statement says nothing about p being distinguished from the union > of all p_n, the statment says that p can be distinguished from every > *element* > of the union of all p_n. Do you wish to repudiate your repeated > agreement to > > The path p can be distinguished > from every element of P > > ?
No. The union of paths is not larger than every element - unless we agree to magic.
In particular p cannot be distinguished from the paths of P, used to construct the tree, if I had included p in P. I agree that p was not included. But that does not play a role unless you are able to obtain that from the complete tree. But you are not! > > > > > > > > > > You refuse to agree to > > > > Assuming infinite paths exist: > > > > There is a path p in the tree that can > > > be distinguished from every element of P. > > > > Until you explain this, no other argument as > > > to why you refuse to accept this statment > > > will be considered. > > > It is obviously impossible to distinguish p from all paths p_n that > > are in the binary tree after construction has been completed. > > Indeed. However, the statement is not about > distinguishing p from paths in the > tree, it is about distinguishing p from paths in P.
If this was possible before, then it would also be possible post festum, because only P was used to construct the tree. But it is not. Therefore it turns out that the original assumption "p can be distuinguished from every path of P" is contradicted. A classical proof by conradiction. By the way, one of the finest proofs that exists in mathematics.