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Remark 41

[20G](Solved on 2022-11-29) Using the properties of $inf, sup$ , we obtain for example these characterizations

\underset{x \to x_{0}}{lim sup} f (x) \leq l ⟺ \forall z > l, eventually for x \to x_{0}, f (x) < z;

\underset{x \to x_{0}}{lim sup} f (x) \geq l ⟺ \forall z < l, frequently for x \to x_{0}, f (x) > z;

and so on. (In this simplified writing, we assume that $x \in I$ ).

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Authors: "Mennucci , Andrea C. G." .

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