"Daryl McCullough" <stevendaryl3016@yahoo.com> wrote ... > |-|ercules says... >> >>"Daryl McCullough" <stevendaryl3016@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. >
