On Jun 23, 1:49 pm, Virgil <Vir...@home.esc> wrote: > In article > <8cd5db0d-46a5-4deb-8fe5-9a28acad5...@k39g2000yqb.googlegroups.com>, > > Newberry <newberr...@gmail.com> 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
OK, so construct it assuming injection.
> 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.