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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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David Chmelik

Posts: 16
Registered: 2/14/08
Re: Double Induction -- A brief note that may help
Posted: Jul 15, 2013 8:22 PM
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On Mon, 15 Jul 2013 13:50:39 -0700 (PDT)
Dan Christensen <Dan_Christensen@sympatico.ca> 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?
>
> Dan
> Download my DC Proof 2.0 software at http://www.dcproof.com


Sounds like an interesting idea... is there an example proof somewhere?



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