The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Cantor's diagonal argument.
Replies: 24   Last Post: Oct 12, 2001 5:16 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Daryl McCullough

Posts: 502
Registered: 12/8/04
Re: Cantor's diagonal argument.
Posted: Oct 5, 2001 1:26 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply (Giles) says...

>Why can't you apply the same inductive argument to sets of natural
>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

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.