# Definition(s) > [!NOTE] Definition (Euclidean Metric) > The Euclidean metric is the function $d:\mathbb{R}^n \times \mathbb{R}^n\to \mathbb{R}$ such that for all $\underline{x},\underline{y}\in \mathbb{R}^n,$ $d(x,y)=\lvert \lvert \underline{x} - \underline{y} \rvert \rvert $where $\lvert \lvert x \rvert \rvert$ denotes the [[Euclidean Norm|Euclidean norm]] of $x.$ > [!Example] Example > Contents # Properties(s) # Application(s) **More examples**: # Bibliography