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I j h n _ k k b h g Z e v g u c i Z d _ l,Let X be a nonempty set The characteristic function of a subset E of X is the function given by χ E(x) = n 1 if x ∈ E, 0 if x ∈ Ec A function f from X to IR is said to be simple ifP n 1 implies that p ij1 = (p 1 p n 1) (p 1 p n) Which is impossible as p i 2 Hence none of the p i's divides p 1 p n 1 15 Prove that there are in nitely many primes (Hint Use the previous exercise) Solution Assume that there exists only nitely many primes say the list of all primes fp 1;p 2;p ng Then

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