lecture24 - Lecture 24 Induction, Recursive Definitions...

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Lecture 24 Induction, Recursive Definitions
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Announcement Quiz on Friday Chapters: three (excluding 3.7 and 3.8) and four (4.1, 4.2, 4.3)
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Basic Induction Goal. Prove that n P(n) n = {1,2,3,…} We show two things: 1. Basis: P(1) is true 2. Inductive Step: k (P(k) P(k+1)) is true
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Strong Induction We will show two things: 1. Basis: P(1) is true 2. Inductive Step: k [ (P(1) P(k)) P(k+1)] is true i.e. We assume that all of P(1), P(2), …, P(k) is true, and show that this implies that P(k+1) must be true.
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Prime Factorization (existence) If n is an integer greater than 1, then n can be written as a product of primes.
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Prime Factorization (existence) Every prime p number can be written as a product of primes (using the book’s terminology: p can be written as a product of one prime, itself) If n is an integer greater than 1, then n can be written as a product of primes.
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Prime Factorization (existence) Reworded: If n is an integer greater than 1, then n can be written as a product of primes and 1.
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geometry Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry. Many applications in robotics, computer
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This note was uploaded on 10/21/2011 for the course CSCI 2011 taught by Professor Staff during the Spring '08 term at Minnesota.

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lecture24 - Lecture 24 Induction, Recursive Definitions...

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