Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

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


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

Topic: Double Induction -- A brief note that may help
Replies: 13   Last Post: Jul 18, 2013 12:42 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
gnasher729

Posts: 418
Registered: 10/7/06
Re: Double Induction -- A brief note that may help
Posted: Jul 16, 2013 7:00 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Monday, July 15, 2013 9:50:39 PM UTC+1, Dan Christensen wrote:

> 1. Base case:
>
> Double induction: Prove P(1,1)
>
> 2. Inductive step: >
> Double induction: For x, y in N, assume P(x,y) and prove P(x+1,y) and P(x,y+1).
>
> Comments?


That would indeed prove P (x, y) for all pairs x, y. However, it may be impossible to prove one of these. For example, I might be able to prove P (x, y) implies P (x+1, y), and I might only be able to prove that if P (x, y) is true for all integers y, then P (x + 1, y) is true.



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

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.