Question: Suppose S R is bounded above. (a) Prove { x n } S such that lim n x n = s u p S .

Suppose S R is bounded above.

(a) Prove {xn} S such that limnxn=supS .

(b) Prove that sup S is a maximum of S or is a limit point of S.

(c) Give examples of sets S for each of the following cases:

i. sup S is a maximum of S and a limit point of S

ii. sup S is a limit point of S and not a maximum of S iii. sup S is a maximum of S and not a limit point of S

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