Question: Let M in R and let (an) be a sequence satisfying both of the following conditions: i. (sn) is smaller than M for all n

Let M in R and let (an) be a sequence satisfying both of the following conditions: i. (sn) is smaller than M for all n in N; ii. For every is greater 0, the set {n in N : |sn - M| is smaller than } is infinite. Prove that lim sup sn = M

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