◀ ▲ ▶Branches / Analysis / Proposition: Relationship between Limit, Limit Superior, and Limit Inferior of a Real Sequence
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
- Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983
