WM says... > >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! > >The list of all definitions is possible and obviously contains all >definitions of real numbers.
I was talking about the list of all *computable* reals. There are definable reals that are not computable, and Cantor's proof shows how to define one.
You can similarly get a list of all definable reals for a specific language L. Then Cantor's proof allows us to come up with a new real that is not definable in language L. (It is definable in a new language that extends L).