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Let S be the set {(-1)^n +1 - (1/n): all n are natural numbers}. 1. find...

Let S be the set {(-1)^n +1 - (1/n): all n are natural numbers}.

1. find the infimum and the supremum of S, and prove that these are indeed the infimum and supremum.

2. find all the boundary points of the set S. Prove that each of these numbers is a boundary point.

3. Is the set S closed? Compact? give reasons.

4. Complete the sentence: Any nonempty compact set has a....

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