Definition: Subsequence

Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983
Forster Otto: "Analysis 2, Differentialrechnung im \(\mathbb R^n\), Gewöhnliche Differentialgleichungen", Vieweg Studium, 1984

Let \((X,d)\) be a metric space, \((a_n)_{n\in\mathbb N}\) be a sequence of points \(a_n\in X\) and let \[n_0 < n_1 < n_2 < \ldots\] be an ascending sequence of natural numbers \(n_k\in\mathbb N\). Then the sequence

\[(a_{n_k})_{k\in\mathbb N}\] is called the subsequence of \((a_n)_{n\in\mathbb N}\).

Proofs: 1 2 3 4
Theorems: 5