In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 15 Jun., 22:24, Virgil <Vir...@home.esc> wrote: > > > > Note that it is possible to have an uncomputable number whose decimal > > expansion has infinitely many known places, so long as it has at least > > one unknown place. > > That is mathematically wrong.
It may not match every definition of 'uncomputable', but otherwise it is right.
> Nevertheless: Every number that can be determined, i.e., that is a > number, belongs to a countable set.
If every set of numbers is provably countable, that means that for every set there is a constructable surjection from N to that set, and for any such surjection, Cantor proves there is a real number not covered.
So one wonders what WM's definition of countability is?
onte that as soon as one has the standard N and powersets, WM loses.