MIT6_042JS10_lec02

MIT6_042JS10_lec02 - Mathematics for Computer Science MIT...

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1 February 5, 2010 Albert R Meyer Mathematics for Computer Science MIT 6.042J/18.062J Proof by Cases Proof by Contradiction lec 1F.1 February 5, 2010 Albert R Meyer If so, 1332 Proof by Contradiction Is 1332 3 11 ? That’s not true , so lec 1F.3 1331 February 5, 2010 Albert R Meyer If an assertion implies something false , then the assertion itself must be false ! Proof by Contradiction lec 1F.4 February 5, 2010 Albert R Meyer Proof by Contradiction Suppose was rational So have n , d integers without common prime factors such that We will show that n & d are both even . This contradicts no common factor . Theorem: is irrational. lec 1F.5 February 5, 2010 Albert R Meyer Proof by Contradiction so can assume So d is even So n is even Theorem: is irrational. lec 1F.6 February 5, 2010 Albert R Meyer Quickie Proof assumes that if n 2 is even, then n is even . Why is this true? lec 1F.7
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2 February 5, 2010 Albert R Meyer Mathematics for Computer Science MIT 6.042J/18.062J Proof by Cases lec 1F.8 February 5, 2010 Albert R Meyer Java Logical Expression
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This note was uploaded on 05/27/2011 for the course CS 6.042J taught by Professor Prof.albertr.meyer during the Spring '11 term at MIT.

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MIT6_042JS10_lec02 - Mathematics for Computer Science MIT...

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