Let p1 and p2 be points in a metric space X. Prove that the set p1 ⋃ p2 is compact in X. Now, let p1, p2, p3, ... , pn be points in a metric space X. Prove that the set p1 ⋃ p2 ⋃ p3  ⋃, ... ,  ⋃ pn (where n is a positive integer), is compact in X.  Note: Because a metric is not explicitly defined, we can use the standard metric of d(p,q)=|p-q|.

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