Let $M = (X, \mathcal{T}_d, d)$ be a D1107: Metric space such that
(i) | $x : \mathbb{N} \to X$ is a D62: Sequence |
Then $x$ is a D336: Convergent sequence in $M$ if and only if
\begin{equation}
\exists \, a \in X :
\forall \, \varepsilon > 0 :
\exists \, N \in \mathbb{N} :
\forall \, n \geq N :
d(x_n, a) < \varepsilon
\end{equation}