Question: ............. (1) Let X be a set, and (fn) be a sequence of functions fr : X - R. (a) Suppose that (fn) converges to

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(1) Let X be a set, and (fn) be a sequence of functions fr : X - R. (a) Suppose that (fn) converges to f: X - R uniformly and each (fn) is bounded. Prove that f is also bounded. (b) Find an example of (fn) converges to f: X - R pointwisely and each (fn) is bounded, but f is unbounded

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