Limit Superior and Limit Inferior Part 1

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In this video we study the limit superior and the limit inferior. We prove that when they exist they are the maximum and minimum limit points respectively.
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Thank you so very much for this upload. I got it!

valeriereid
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If I say something has a limit, does that imply there is an ordering? If so, what degree of ordering is required? Just curious to hear your opinion.

I know there is a definition of limit in pure set theory, which doesn't have ordering at all, but that seems... unsatisfactory, like it stretches the intention of limits.

AlexBerg
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It seems like the limit superior/inferior is "max" if the set is finite. So, perhaps these notions are primarily interesting on infinite sets.

AlexBerg