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Proposition: Convergent Complex Sequences Are Cauchy Sequences

If the complex sequence $(a_n)_{n\in\mathbb N}$ is convergent, then it is also a complex Cauchy sequence.

Notes

• Together with the completeness principle for complex numbers, this proposition shows that in the set of complex numbers, the set of all convergent sequences is exactly the same as the set of all Cauchy sequences.
• A similar result can be proven for real sequences.

Table of Contents

Proofs: 1

Mentioned in:

Proofs: 1
Propositions: 2
Theorems: 3

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References

Bibliography

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