
Double Induction  A brief note that may help
Posted:
Jul 15, 2013 4:50 PM


The explanations of double induction online can be quite confusing. No doubt I am reinventing 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?
Dan Download my DC Proof 2.0 software at http://www.dcproof.com

