In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> 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).
That is not the issue. WM has presented a countable list of paths, P, from which he claims to build a maximal infinite binary tree, T.
While the union of P, as a set of nodes, can well be the set of all nodes of T, the members of P, being sets of nodes which for paths, d not exhaust the set of all paths, where a path is any maximal set of nodes totally ordered by the ancestor relation. > > > 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.
On the contrary, the tree contains more of those paths than the ones from 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.
Nonsense. There is difference between knowing that there ARE paths not in P and knowing WHICH paths are not in P. The cardinalities involved require that there be paths not in P, but do not identify which paths are not in P.
If Card(A) > Card(B), then there are elements of A which are not members of B. At least outside of WM's world of MathUnrealism. > > 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.
How does the age of the writer of your tree affect its structure? > > Regards, WM