> [!definition] > > Let $X$ be any [[Set|set]] and $Y$ be a [[Metric Space|metric space]], then let $f_n: X \to Y$, and $\seq{f_n}$ be a [[Sequence|sequence]] of [[Function|functions]]. The sequence converges to a function $f: X \to Y$ **pointwise** if $f(x) = \limv{n}f(x) \forall x \in X$.