>Cantor constructs the antidiagonal by taking the list and then computing a >missing Real based upon the decimal expansion of every Real on the list.
That's right, so Cantor showed how to compute an antidiagonal using the list of reals as an input. That shows that the antidiagonal is computable *relative* to the list. It does not show that the antidiagonal is computable. "Computable relative to a list" and "computable" are two different things.
This is a pretty simple concept, Peter. Mathematically, you have a function antidiagonal(L,n) which returns the nth digit of the antidiagonal, given the list L and n. That function is computable. But for the antidiagonal to be computable (not computable *relative* to L), you would have to be able to come up with a function
that, for *any* n, gives the nth digit of the antidiagonal.
Two different concepts: computable relative to L, and computable.