In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 14 Jun., 16:49, 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." > > > > Your answer to "Do you wish to repudiate your repeated > > agreement to" > > > > The path p can be distinguished from > > every element of P. > > > > is "No". Then you claim > > > > p cannot be distinguished from the paths of P, > > used to construct the tree, > > > > You agree to the stamentemt > > > > The path p is in the tree. > > > > then you say > > > > 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 are becoming incoherent. > > There are two statements: > 1) Path p can be distinguished from every path of P. > 2) Path p cannot be distinguished from every path of P. > > The first is assumed to be correct before P was used to construct the > tree. > The second is assumed to be correct after P was used to construct the > tree.
BOTH WRONG! At least if P is a countable and fixed set of paths.
Unless P is allowed to change as it is used, every p that exists before the construction must be in P (as there is as yet no tree from which to get others), but after the construction is complete, the tree necessarily contains uncountably many paths some of which could not have been in the original P. > > One of them is false, unless it is a magic tree where something > happens during construction. But I do not believe in magic, least in > mathematics.
Something happens during construction, but it is only magic to those too thick to understand it. > > The second statement can be proved to be correct, because in fact you > are not able to distinguish p from P (by means of digits).
Cantor could and did. And those using his methods still can anddo. > > Therefore the first statement is falsified. This means that there are > no actually infinite digit sequences, but only potentially infinite > digit sequences.
Then WMcan never build a maximal infinite binary tree at all, even though others can still build them.
But since WM conceded complete paths at the onset of this discussion, he is not now allowed to renege now.