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Proposition: Limit Superior is the Supremum of Accumulation Points of a Bounded Real Sequence

Let $H$ be the non-empty¹ set of all accumulation points of a bounded real sequence $(a_n)_{n\in\mathbb N}.$ The limit superior of $a_n$ equals the supremum of $H$, formally $$\overline{\lim_{n\to\infty} a_n}=\sup H.$$

Table of Contents

Proofs: 1

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References

Bibliography

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

Footnotes