Let $(X,d)$ be a \reftext{def:metric-space-2026a}{metric space}, let $(x_m)_{m\in\mathbb{N}}$ be a \reftext{def:sequence-in-set-2026a}{sequence in $X$}, and let $x\in X$. We say that $(x_m)$ converges to $x$ in the metric space $(X,d)$ if for every real number $\varepsilon>0$ there exists $N\in\mathbb{N}$ such that

for every $m\in\mathbb{N}$ with $m\ge N$. In this case we write

and call $x$ the limit of $(x_m)$ in $(X,d)$.