Prove the lemma

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Prove the lemma.

Let {cn, n ≥ 1} be a sequence of real numbers. If for every subsequence there exists a further subsequence with a limit superior that does not exceed some number, a, say, then lim supn→∞ cn ≤ a. Similarly, if for every subsequence there exists a further subsequence with a limit inferior that exceeds some number, b, say, then lim infn→∞ cn ≥ b.

Reference no: EM131830216

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