In article <62ae795b-1d43-4e1f-8633-e5e2475851aa@x21g2000yqa.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 15 Jun., 12:26, stevendaryl3...@yahoo.com (Daryl McCullough) wrote: > > > (B) There exists a real number r, > > Forall computable reals r', > > there exists a natural number n > > such that r' and r disagree at the nth decimal place. > > > In what form does r exist, unless it is computable too? > > But if r is computable, then this theorem shows that the computable > numbers are uncountable. Contradiction.
Not if it is uncomputable. 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. > > And if r is not computable, then it is impossible to prove > disagreement with any r'.
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. > > Regards, WM
