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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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 Dan Christensen Posts: 8,219 Registered: 7/9/08
Double Induction -- A brief note that may help
Posted: Jul 15, 2013 4:50 PM
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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?

Dan
Download my DC Proof 2.0 software at http://www.dcproof.com

Date Subject Author
7/15/13 Dan Christensen
7/15/13 Virgil
7/15/13 David Chmelik
7/15/13 Dan Christensen
7/16/13 William Elliot
7/16/13 Brian Q. Hutchings
7/15/13 David Petry
7/16/13 William Elliot
7/15/13 Tucsondrew@me.com
7/16/13 gnasher729
7/16/13 gnasher729
7/16/13 gnasher729
7/16/13 Tucsondrew@me.com
7/18/13 Dan Christensen

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