WM says... > >On 15 Jun., 16:17, stevendaryl3...@yahoo.com (Daryl McCullough) wrote: > >> In this sense, the antidiagonal of the list of all computable reals >> is definable (but not computable). > >That is nonsense. To define means to let someone know the defined. If >he knows it, then he can compute it.
That's just not true. For example, we can define a real r as follows:
r = sum from n=0 to infinity of H(n) 2^{-n}
where H(n) = 1 if Turing machine number n halts on input n, H(n) = 0 otherwise.
That's definable, but it is not computable.
This is very basic stuff. I'm a little surprised that you are so unfamiliar with it.
