(a) If S is a nonempty bounded set, show that SC (inf S, sup S. (b)...

 

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(a) If S is a nonempty bounded set, show that SC (inf S, sup S. (b) If S is as in (a) and I is a closed interval with SCI, show that [inf S, sup S] CI (c) If S is as in (a), show that [inf S, sup S]=I, where the intersec- tion is taken over all closed intervals containing S. (d) What is I, where the intersection is taken over all open intervals containing S? (a) If S is a nonempty bounded set, show that SC (inf S, sup S. (b) If S is as in (a) and I is a closed interval with SCI, show that [inf S, sup S] CI (c) If S is as in (a), show that [inf S, sup S]=I, where the intersec- tion is taken over all closed intervals containing S. (d) What is I, where the intersection is taken over all open intervals containing S?