# Power Series - Boundedness

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(a) Suppose E and F are nonempty closed bounded subsets of C. Show that there exist z_0 E E and w_0 E F such that

| z_0 - w_0 | = inf {| z - w | ; z E E, w E F}.

(b) Show that this is not true if the boundedness condition on E and F is dropped.

(c) What if only one of E or F is bounded (but both are still closed)?

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#### Solution Summary

In an attached Word document, this solution is determined through step-by-step computations and accompanying explanations.

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