The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Dan Christensen

Posts: 8,219
Registered: 7/9/08
Double Induction -- A brief note that may help
Posted: Jul 15, 2013 4:50 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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).


Download my DC Proof 2.0 software at

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.