On 2010-06-19, Peter Webb <webbfamily@DIESPAMDIEoptusnet.com.au> wrote: > If you give me a purported list of all computable Reals I can use a > diagonal argument to form a computable Real not on the list.
OK, here you go: define f:N->R by the method of my previous post. That is, it is the real computed by the n'th Turing machine within the set of Turing machines that compute a real, ordered by Godel numbering of their specifications. The function f defines a list of real numbers.
Your task is to find a real not on that list, and prove that it is a computable real.