On 2010-06-20, Peter Webb <webbfamily@DIESPAMDIEoptusnet.com.au> wrote: > "Daryl McCullough(" <email@example.com> wrote in message >> Cantor's proof assumes the *existence* of such a list. It doesn't >> assume that you know how to compute it. > > If that is what you believe, then I am happy for the same rules to > be applied to the purported list of all computable Reals.
Chaitin's Omega exists. Its binary expansion exists, in which there exists an n'th digit for all n, which we can denote Omega_n. So a list L:N->R exists for which L(n) = (1 - Omega_n) / 2^n.
For all k, the k'th entry in L is either 0 or 1/2^n. Both of these are computable, so L is a list of computable numbers.