lecture22 - Lecture 22 Induction Recap Algorithms for...

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Lecture 22 Induction
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Recap Algorithms for integer operations Addition, multiplication, div, mod Modular exponentiation GCD Not covered: 3.7 Applications of number theory CSCI 5271 - Introduction to Computer Security 3.8 Matrices CSCI 2031 - Introduction to Numerical Computing Calc 3
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Induction A powerful technique to prove statements of the form n P(n) Examples: n, n < 2 n 2 ) 1 ( , 1 n n i n n i As usual, we need to specify the domain of n
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Strategy We will show two things: 1. Basis: P(1) is true 2. Inductive Step: k (P(k) From these two, we can infer that: n P(n) n = {1,2,3,…} So, let’s start. . Well Ordering Property: Every non-empty set of positive integers has a least element
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Prove the following by induction For all positive integers n:
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lecture22 - Lecture 22 Induction Recap Algorithms for...

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