CISC 102 Lecture Notes - Lecture 30: Mathematical Induction, Complex Instruction Set Computing
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6 Dec 2017
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An informal proof of this result could be that either a or a+1 must be divisible by 2, so their product must also be divisible by 2. however, we have seen a similar template" for proving this result. Familiar facts from high school math, as well as results that we have seen this term and used repeatedly can be assumed without further proof. In practice for a course like this there is usually a very similar proof that you have seen that can be used as a template. and this will implicitly use assumptions that you may use. Proof by cases: prove that 2|a(a+1) for all natural numbers a, prove that 3|a(a+1)(a+2) for all natural numbers a. 3|a, so by result 1. 2|(a+1)(a+2). so 6|a(a+1)(a+2). Proof: who have met or not met x. Amongst those who have met x, at least one pair have met each other. since.
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