Question: Let (xn) be a bounded sequence and for each n N let sn := sup{xk : k > n} and S := inf{sn}. Show

Let (xn) be a bounded sequence and for each n ∈ N let sn := sup{xk : k > n} and S := inf{sn}. Show that there exists a subsequence of (xn) that converges to S.

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