On 16 Jun., 12:38, William Hughes <wpihug...@hotmail.com> wrote: > On Jun 15, 4:44 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > On 15 Jun., 22:04, 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." > > > > You agree that if actually infinite paths exist > > > your claim is false. > > > No. I see that my claim is correct under any circumstances. That fact > > is independent of whether or nor actually infinite paths exist. > > Nope. You have repeatedly agreed that if actually infinite paths > exist, then a path p exists that can be distinguished from > every element of P. > > WM: If actually infinite paths exist, then there is a path p that can > be > WM: distinguished from every path of P.
A ==> B > > You also claim > > WM: And: > WM: There is no path p that can be distinguished from every path of > P.
((A ==> B) & ~B) ==> ~A > > > > > Every path of the tree is is from P. > > > > Nope. Every *node* of the tree is from P. > > > Every path of the tree is from P. I explicitly forbid every other path > > to enter my tree. > > Nope. You cannot forbid every other path to enter the > tree. You add nodes to the tree.
I add infinite paths.
> When you add a node to the tree you add subsets of nodes > to the tree as well. You add a subset of nodes that is > not in a single element of P.
Wrong. I add a path p_n like 0.himpidimpydowadididum000... That path p_n is different from any other path p_m and there is no path p_m that together with p_n produces anything different from all finite subsets that are already contained in p_n or p_m.
You are dreaming of an ideal set theoretic world - without paradoxes and antinomies. But this world has come to an end in 2004 with the first construction, recognition and careful interpretation of the binary tree.