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: 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 ]

Posts: 8,833
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 <>,
Dan Christensen <> 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]

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