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

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Registered: 1/6/11
Re: Double Induction -- A brief note that may help
Posted: Jul 15, 2013 5:34 PM
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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!

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