In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 12 Jan., 22:58, Virgil <vir...@ligriv.com> wrote: > > In article > > <f62302b5-c3c6-4b54-8437-6f9d7bc00...@4g2000yqv.googlegroups.com>, > > > > WM <mueck...@rz.fh-augsburg.de> wrote: > > > Matheology § 191 > > > > > The complete infinite Binary Tree can be constructed by first > > > constructing all aleph_0 finite paths and then appending to each path > > > all aleph_0 finiteley definable tails from 000... to 111... > > > > > 0 > > > 1, 2 > > > 3, 4, 5, 6 > > > 7, ... > > > > > This Binary Tree contains aleph_0 * aleph_0 = aleph_0 paths. > > > > Aleph_0 * aleph_0 = aleph_0 but 2 ^ aleph_0 > aleph_0, and that is the > > number of paths. > > Can you name, define, or at least "discern" one of the paths missing > in my Binary Tree? Note: I do not hide my receipe of construction any > longer. I use every tail that can be described and communicated in any > language.
If your set of paths ( as infinite binary sequences) is capable of being listed then that very capability proves, a la Cantor, that it is incomplete, and if it cannot be listed then it is, by definition, not countable. > > --