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Proposition: Relationship between Limit, Limit Superior, and Limit Inferior of a Real Sequence

A real sequence $(a_n)_{n\in\mathbb N}$ is convergent, if and only if its limit equals its limit superior and its limit inferior, formally

$$\lim_{n\to\infty} a_n=\overline{\lim_{n\to\infty}} a_n=\underline{\lim_{n\to\infty}} a_n.$$

Table of Contents

Proofs: 1

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References

Bibliography

1. Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983