In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 14 Jun., 22:33, Virgil <virg...@nowhere.com> wrote: > > > > 2) Path p cannot be distinguished from every path of P. > > > > Whatever countable set of paths, P, may be used to build a maximal > > infinite binary tree, there are too many paths in the resulting tree to > > be contained in the original P. > > I have built a complete maximal binary tree by means of a countable > set P of path.
The issue is not whether my path is in the tree but whether it is in WM's original list of paths, P. And for any such list, Cantor provides an infallible method of producing an unlisted path. an with trivial variations, produce as many new paths as originally listed.
> You may choose a path and prove wether it is in the > tree or not. I will tell you afterwards what P is.
Unless you tell me in advance what P is, I would have to be guessing, but once you tell me, I can be quite sure that mine is not one of yours.
> But this is of no > relevance, because every countable set of terminating paths or paths > withg a special tail like 31415... or 121212... will yield the same > tree.
Including lots and lots of paths not used explicitly in the construction.
Given any set of binary sequences, the very proof that it is countable, if it actually is, provides a method for finding sequences not included in it.