A real convergent sequence is a real sequence \((x_n)_{n\in\mathbb N}\), which is convergent in the metric space of real numbers \((\mathbb R,|~|)\). In other words, \((x_n)_{n\in\mathbb N}\) is convergent to the number \(x\in\mathbb R\), i.e. for each \(\epsilon > 0\) there exists an \(N\in\mathbb N\) with
\[ | x_n-x | < \epsilon\quad\quad \text{ for all }n\ge N.\]
Further Reading
[581] Forster Otto: “Analysis 1, Differential- und Integralrechnung einer Veränderlichen”, Vieweg Studium, 1983
[582] Forster Otto: “Analysis 2, Differentialrechnung im \(\mathbb R^n\), Gewöhnliche Differentialgleichungen”, Vieweg Studium, 1984
All logical predecessors and all successors of the current node are:
Found a mistake? Fix it by editing the definition above!
