Lecture 17(Monday) - using more of the de nition You may...

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Unformatted text preview: using more of the de nition You may have been disappointed that the last proof used only part of the de nition of oor. Here's a symbolic re-writing of the de nition of oor: V PR x y = x D y P Z y x (V P Z z ;z x A z y ) The full version of the de nition should prove useful to prove: V PR x ; x > x 1 slide 7 prove something is false De ne a sequence: = n=2 (of course, if you treat \/" as integer division, there's no need to take the oor. Now consider the claim: Wi P N; Vj P N; j > i A aj = ai The claim is false. Disprove it. n an V PN slide 9 cases Sometimes your argument has to split to take into account possible properties of your generic element: Vn P N; n2 + n is even A natural approach is to factor n2 + n as n(n + 1), and then consider the case where n is odd, then the case where n is even. slide 11 ...
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This note was uploaded on 10/13/2011 for the course COMPUTER S CSC 165 taught by Professor Dannyheap during the Fall '10 term at University of Toronto- Toronto.

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Lecture 17(Monday) - using more of the de nition You may...

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