A [[sequence|sequence]] \(\{x_n\}_{n\in\mathbb{N}}\) in [[knowledge-mathematics-analysis-functional-analysis-metric-spaces|metric space]] \((X,d)\) is said to be convergent if there exists some limit point \(x\in X\) such that \[ \forall\epsilon>0,~\exists N\in\mathbb{N},~\forall n\geq N:d(x_n,x)<\epsilon~. \] We write \(x_n\rightarrow x~(n\rightarrow \infty)\) or \(\lim_{n\rightarrow\infty}x_n=x\).