> [!definition] > > Let $X$ be any [[Set|set]] and $(Y, d)$ 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 $f: X \to Y$ **uniformly** if > $ > \forall \varepsilon > 0, \exists N \in \nat: \forall n \ge N, x \in X, d(f_n(x), f(x)) < \varepsilon > $