The ancient Greeks had the following definition: two lengths (positive numbers) a,b are com- mensurable if there exists a common sublength m of a and b. Otherwise said, a = km and b = lm for some positive integers k,1. (a) Pythagoras is thought to have believed that all pairs of lengths a, b are commensurable, that is Va,b E Rt, 3m E R†, k,l e N such that a = km and b = lm State the negation of Pythagoras' claim using quantifiers. (b) Prove or disprove Pythagoras' claim. (You may use anything seen in the course without proof)

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.