On 15 Jun., 21:46, stevendaryl3...@yahoo.com (Daryl McCullough) wrote: > |-|ercules says... > > > > >"Daryl McCullough" <stevendaryl3...@yahoo.com> wrote... > >> That's *all* that matters, for Cantor's theorem. The claim > >> is that for every list of reals, there is another real > >> that does not appear on the list. > > >Yes but HOW does Cantor show that? > > You've been told many times. He shows that for every > list L of reals, there is another real antidiag(L) that > is defined in such a way that > > forall n, antidiag(L) differs from the nth real in L at > the nth decimal place. > > From this, it follows: > > forall n, antidiag(L) is not equal to the nth real. > > From this, it follows: > > antidiag(L) is not on the list L.
No, that is the conclusion of a crank. It follows for all n: The antidiagonal is not in the first n lines. That is true. But it cannot be extrapolated to the whole set N.
