WM says... > >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?
r is computable *relative* to the list L of all computable reals. That is, there is an algorithm which, given an enumeration of computable reals, returns a real that is not on that list.
In the theory of Turing machines, one can formalize the notion of computability relative to an "oracle", where the oracle is an infinite tape representing a possibly noncomputable function of the naturals.
