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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: 10/7/06
Re: Double Induction -- A brief note that may help
Posted: Jul 16, 2013 7:00 PM
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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.

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