In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 15 Jun., 16:18, stevendaryl3...@yahoo.com (Daryl McCullough) wrote: > > Peter Webb says... > > > > >"WM" <mueck...@rz.fh-augsburg.de> wrote in message > > >news:firstname.lastname@example.org... > > >> 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. > > > > No, it's computable *relative* to the list of all computable reals. > > But that list is not computable. > > That is nonsense!
Only in WM's world. It makes perfectly good sense everywhere else. > > The list of all definitions is possible and obviously contains all > definitions of real numbers.
That claim has been disproved, at least in standard mathematics, many times. What WM does in his own tiny world is of no consequence, except to his poor captive students.
As well as the definitions of as many uncomputable numbers. For any undecidable proposition ,P, the number defined by "if P then x else y", where x and y are computable numbers and not equal, defines an uncomputable number.