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Unformatted text preview: CPSC 121 Lecture 15 February 9, 2009 Menu February 9, 2009 Topics: Proof Techniques (cont’d) Summary of Learning Goals (Epp Chapter 3) (More) Examples (cont’d) Reading: Today: Epp 3.1, Theorem 3.4.1 (page 157), Representation of Integers (pages 159–163), Epp 3.6, and 3.7 Next: Epp 12.2 (pages 745–747), Designing a Finite Automaton (pages 752–754, skipping part b of the examples) Reminders: Look for on-line Quizzes 8 & 9 Marked Assignment 1 available in tutorials Assignment 2 due Friday, February 13 (by 17:00) Midterm exam Tuesday, February 24 (evening) Proof Techniques (cont’d) To illustrate proof techniques, many of our sample theorems have been drawn from elementary number theory. Here are the basic definitions to use when asked to prove results involving integers that are even, odd or prime. An integer n is even if and only if n equals twice some integer. An integer is odd if an only if n equals twice some integer plus 1 . Formally... Definition: Even and Odd Let n ∈ Z be an integer. Then n is even iff ∃ k ∈ Z such that n = 2 k n is odd iff ∃ k ∈ Z such that n = 2 k + 1 An integer n is prime if and only if n > 1 and for all positive integers r and s , if n = r s then r = 1 or s = 1 . An integer n is composite if and only if n > 1 and n = r s for positive integers r and s with r 6 = 1 and s 6 = 1 ....
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This note was uploaded on 01/09/2010 for the course CPSC 121 taught by Professor Belleville during the Spring '08 term at UBC.
- Spring '08