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Lecture13Induction - Lecture 13 CS 2603 Applied Logic for...

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CS2603 Applied Logic for Hardware and Software Rex Page – University of Oklahoma 1 Lecture 13 — CS 2603 Applied Logic for Hardware and Software The m o st impor tant th ing you will learn … th is y ear … next year … o r the year after t ha t Induction the original blue-light special
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CS2603 Applied Logic for Hardware and Software Rex Page – University of Oklahoma 2 Mathematical Induction Principle of Induction Starting point 9 Predicate P 9 Universe of discourse: N = {0, 1, 2, …} Process 9 Prove: P(0) 9 Prove: n.(P(n) P(n+1)) Conclusion: n. P(n) P(0) n.(P(n) P(n+1)) ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ {Ind} n. P(n) Induction Induction is a tremendous bargain You get: proofs for an infinite number of propositions 9 P(0), P(1), P(2), … But, you only have to prove one of them: P(0) Also, you have to prove the implication: P(n) P(n+1) 9 That is, you prove P(n+1), but you get to assume P(n) blue -li g h t s pecial a new inference rule for our formal system
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