On Feb 7, 5:57 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > On 7 Feb., 15:56, William Hughes <wpihug...@gmail.com> wrote: > > > On Feb 7, 3:25 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > <snip> > > > >... a subset S of the countable set F of finite words bijects with > > > the set D of definable numbers > > by definition. > > > > > Nope. Every D corresponds to some finite word. > > No, D is a set or at least a collection. A definable number is an > element of D. > > > However, S, > > the collection of all the correspondences, may not be a subset > > of F (subsets must be computable). > > Need not be a subset. It is sufficient to know that there are not more > than countably many correspondences,
There is no set of correspondences thus there is no number of correspondences. You cannot know anything about the number of correspondences.