Let {xn] be a sequence of real numbers and let yn = max{x1, x2, . positive...

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Let {xn] be a sequence of real numbers and let yn = max{x1, x2, . positive integer n. Xn} for each a) Suppose that {x} is bounded. Prove that {yn} converges to sup{x, : n Z }. b) Suppose that {x,} is not bounded above. Prove that {yn} converges to . c) Give an example of an unbounded sequence {xn} for which {yn} converges. Let {xn] be a sequence of real numbers and let yn = max{x1, x2, . positive integer n. Xn} for each a) Suppose that {x} is bounded. Prove that {yn} converges to sup{x, : n Z }. b) Suppose that {x,} is not bounded above. Prove that {yn} converges to . c) Give an example of an unbounded sequence {xn} for which {yn} converges.