Lecture 13(Wedneday) - CSC 165 proof Danny Heap...

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Unformatted text preview: CSC 165 proof Danny Heap heap@cs.toronto.edu http://www.cdf.toronto.edu/ f heap/165/F10/ slide 1 a proof foretold A proof communicates why and how you believe something to be true. You'll need to master two things: 1. Why do you believe the thing is true? This step is messy, creative, but then increasingly precise to identify (and then strengthen) the weak parts of your belief. 2. Write up (express) why you believe the thing is true. Each step of your written proof should be justi ed enough to convince a skeptical peer. If you detect a gap in your reasoning, you may have to go back to step 1. Although I present a great deal of symbolic notation, we will accept carefully-structured, precise English prose. The structure, however, is required, and is the main topic of Chapter 4. slide 2 nding a proof of universally-quanti ed ) To support a proof of a universally-quanti ed implication 8 x 2 X; P ( x ) ) Q ( x ), you usually need to use some already-proven statements and axioms (de ned, or assumed, to be true for...
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Lecture 13(Wedneday) - CSC 165 proof Danny Heap...

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