Use the following outline to prove the theorem that every continuous function on a closed finite interval [a, b] must be bounded: Suppose false. Explain why |f| is not bounded above by any n E N, and why there exists xn E [a, b] such that \f (xn)| > n. Next show how you apply the Bolzano-Weierstrass Theorem to xn to deduce a contradiction of the fact that f E C[a, b].)

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