
Re: Grrrr! (was): infinite dimensional vector space
Posted:
Jun 25, 2003 8:40 PM


David Petry wrote: > David C. Ullrich <ullrich@math.okstate.edu> wrote in message news:<68bjfv0qpm20kt7fgnup431sch6ii38hus@4ax.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 honesttogod 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 nth digit of the nth number. If you can do this, you get .4545454545.... which is rational (45/99 = 5/11).
Martin Cohen

