A Function That Is Not Computable

Pick any programming language as powerful as Turing machines. Enumerate all possible programs, inputs and outputs. Let P(n) be the output of the n^th program and the n^th input. Let F(x) equal P(x) + 1 or 0, depending on whether P(x) exists. If F was computable, it would equal the k^th program for some k. That would imply F(k) = F(k) + 1 which is impossible.