
Re: Cantor's diagonal argument.
Posted:
Oct 5, 2001 1:26 PM


g.d.redgrave@elostirion.freeserve.co.uk (Giles) says...
>Why can't you apply the same inductive argument to sets of natural >numbers. > >1. A_1 has a finite number of elements >2. For each n, if A_n has a finite number of elements, then A_{n+1} >has a finite number of elements. >3. Therefore, each set of natural numbers has finite size. > >This seems to me to be exactly the same argument.
No. It would be a correct proof by induction if you replace 3. by "Therefore, for each n, A_n is finite." That doesn't imply that every set of naturals is finite, only those sets that happen to equal A_n for some n.
 Daryl McCullough CoGenTex, Inc. Ithaca, NY

