Definition: Bounded Complex Sequences

Let \((a_n)_{n\in\mathbb N}\) be a complex sequence. Since the absolute value of a complex number is a real number, we can compare it to other real number using the order relation for real numbers "\(\le\)".

We call the complex sequence \((a_n)_{n\in\mathbb N}\) bounded, if there is a positive real number \(B\) with \(|a_n|\le B\) for all \(n\in\mathbb N\).

  1. Proposition: Convergent Complex Sequences Are Bounded

Proofs: 1 2
Propositions: 3 4

Thank you to the contributors under CC BY-SA 4.0!




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