ThmDex – An index of mathematical definitions, results, and conjectures.
Formulation F10782 on R246: Cauchy sequence is bounded
F10782
Formulation 2
Let $M = (X, d)$ be a D1107: Metric space such that
(i) $x : \mathbb{N} \to X$ is a D65: Cauchy sequence in $M$
Then \begin{equation} \exists \, a \in X, r > 0 : x(\mathbb{N}) \subseteq B(a, r) \end{equation}