In article <email@example.com>, Newberry <firstname.lastname@example.org> wrote:
> Cantor's proof starts with the assumption that a bijection EXISTS, not > that it is effective.
Actually, a careful reading shows Cantor's proof merely assumes an arbitrary INJECTION from N to R (originally from N to the set of all binary sequences, B) which is NOT presumed initially to be surjective, and then directly proves it not to be surjective by constructing the "antidiagonal"as a member of the codomain not in the image.
Thus proving that ANY injection from N to R (or B) fails to be surjective.
For some unknown reason, the DIRECT "anti-diagonal" proofs given by Cantor, and his followers, are often misrepresented as being proofs by contradiction, but they never were.