```Date: Jul 15, 2013 10:12 PM
Author: David Petry
Subject: Re: Double Induction -- A brief note that may help

On Monday, July 15, 2013 1:50:39 PM UTC-7, 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? I don't think that's right.Base case: prove for all n, P(1,n)  and P(n,1)Inductive step:  Assume P(x,n) for all n <= y, and assume P(n,m) for all m and for all n < x,  prove P(x, y+1)
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