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.
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.
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).
Therefore the first statement is falsified. This means that there are no actually infinite digit sequences, but only potentially infinite digit sequences.