Search All of the Math Forum:

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

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

Topic: Proposed Schema for Double Induction
Replies: 4   Last Post: Jul 18, 2013 12:00 PM

 Search Thread: Advanced Search

 Messages: [ Previous | Next ]
 Dan Christensen Posts: 8,219 Registered: 7/9/08
Re: Proposed Schema for Double Induction
Posted: Jul 18, 2013 11:53 AM
 Plain Text Reply

Compare...

SCHEMA FOR ORDINARY INDUCTION

P(1)
& ALL(a):[a in N & P(a) => P(a+1)]
=> ALL(a):[a in P => P(a)]

where P is a unary predicate

SCHEMA FOR DOUBLE INDUCTION

P(1,1)
& ALL(b):[b in N => [P(1,b) => P(1,b+1)]]
& ALL(a):ALL(b):[a in N & b in N => [P(a,b) => P(a+1,b)]]
=> ALL(a):ALL(b):[a in N & b in N => P(a,b)]

where P is a binary predicate

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

Date Subject Author
7/18/13 Dan Christensen
7/18/13 Dan Christensen
7/18/13 Dan Christensen
7/18/13 Dan Christensen
7/18/13 Dan Christensen

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