"Aatu Koskensilta" <aatu.koskensilta@uta.fi> wrote in message news:87typ431fz.fsf@dialatheia.truth.invalid... > "Peter Webb" <webbfamily@DIESPAMDIEoptusnet.com.au> writes: > >> "WM" <mueckenh@rz.fh-augsburg.de> wrote in message >> news:62ae795b-1d43-4e1f-8633-e5e2475851aa@x21g2000yqa.googlegroups.com... >>> 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? >> >> Of course its computable. > > There is a computable real that differs from every computable real? >
Well, what I think he is really going on about is whether the diagonal number is computable, hence the reference to a "natural" number n in which the digits vary.
Taken at face value, that "there exists a natural number n such that r and r' disagree at the nth decimal place" is simply the statement that r <> r'. So (B) is equivalent to the statement "there exists an uncomputable number". Which is true, of course, although I acknowledge that I cannot provide the decimal expansion of one (by definition).
