Question: a) Suppose that {xn} is a monotone increasing sequence in R (not necessarily bounded above). Prove that there is an extended real number x such

a) Suppose that {xn} is a monotone increasing sequence in R (not necessarily bounded above). Prove that there is an extended real number x such that xn → x as n → ∞.
b) State and prove an analogous result for decreasing sequences.

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