Suppose there is some sequence [itex] \{x_n\}_{n\in\mathbb{N}}[/itex]. Say we have a set of all the limits of all possible subsequences, would the supremum of this set be the superior limit of [itex] \{x_n\}_{n\in\mathbb{N}}[/itex]? What about if this value turns out to be 5, but there is a member of the sequence that is equal to 500, but is not the limit of any subsequence. Can the superior limit be lower than the supremum of the sequence? Thanks!(adsbygoogle = window.adsbygoogle || []).push({});

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# Trying to understand lim sup

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