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Proposition: Uniqueness of the Limit of a Sequence

Let \((x_n)_{n\in\mathbb N}\) be a sequence in the metric space \((X,d)\), which is convergent against the limits \(x\) and \(x'\):

\[\lim_{n\rightarrow\infty} x_n=x\quad\quad\text{and}\quad\quad\lim_{n\rightarrow\infty} x_n=x'.\]

Then both limits are identical, or \(x=x'\)¹.

Table of Contents

Proofs: 1

Mentioned in:

Parts: 1
Proofs: 2
Propositions: 3

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References

Bibliography

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

Footnotes