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.independent

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 ]
Virgil

Posts: 7,005
Registered: 1/6/11
Re: Double Induction -- A brief note that may help
Posted: Jul 15, 2013 5:34 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

In article <cac54bbd-1fb4-4509-9197-e1aa3860ab95@googlegroups.com>,
Dan Christensen <Dan_Christensen@sympatico.ca> wrote:

> The explanations of double induction online can be quite confusing. No doubt
> I am re-inventing wheel here, but you may find the following analogy to
> ordinary induction to be useful.
>
> With ordinary induction, we want to prove that for all x in N, we have P(x)
> where P is a unary predicate.
>
> With double induction, we want to prove that for all x, y in N, we have
> P(x,y) where P is a binary predicate.
>
> 1. Base case:
>
> Ordinary induction: Prove P(1)
>
> Double induction: Prove P(1,1)
>
> 2. Inductive step:
>
> Ordinary induction: For x in N, assume P(x) and prove P(x+1)
>
> Double induction: For x, y in N, assume P(x,y) and prove P(x+1,y) and
> P(x,y+1).
>
> Comments?
>


Seems adequate!
--





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.