Question: Given that xn is bounded a sequence of real numbers, and given that an = sup{xk: k n} and bn = inf{xk: k n),

Given that xn is bounded a sequence of real numbers, and given that an = sup{xk: k n} and bn = inf{xk: k n), let the lim sup xn = lim an and lim inf xn = lim bn. Prove that if xn converges to L, then bn Lan, for all natural numbers n.

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