David Petry wrote: > David C. Ullrich <firstname.lastname@example.org> wrote in message news:<email@example.com>... > > >>(Or maybe I'm wrong - how _does_ one give a proof that there >>exist irrational numbers by "diagonalization"? > > > Start with a list of rational numbers between 0 and 1, and > diagonalize over the decimal expansions of those numbers. It > works just fine. The technical detail of what to do with > numbers that end in either all 9's or all 0's is easily > handled, and in the end you get an honest-to-god irrational > number. > > Comment: if the above proof were more widely known, there > would be much less confusion about Cantor's nonsense.
How do you know that you can't select alternately 4 and 5 as the digit that does not match the n-th digit of the n-th number. If you can do this, you get .4545454545.... which is rational (45/99 = 5/11).