My book says that if the set of all cluster points is empty, then we write lim sup = [itex]-\infty[/itex] and if the sequence is not bounded above, we write limsup = [itex]+\infty[/itex].(adsbygoogle = window.adsbygoogle || []).push({});

But what if both happen at the same time? for instance consider x_n=1/n. There are no accumulation points and it is unbounded above.

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# Homework Help: Lim sup, lim inf definition/convention

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