\begin{definition}[Definition:Euclidean Metric/Real Vector Space]
Let $\R^n$ be an $n$-dimensional real vector space.
The '''Euclidean metric''' on $\R^n$ is defined as:
:$\ds \map {d_2} {x, y} := \paren {\sum_{i \mathop = 1}^n \paren {x_i - y_i}^2}^{1 / 2}$
where $x = \tuple {x_1, x_2, \ldots, x_n}, y = \tuple {y_1, y_2, \ldots, y_n} \in \R^n$.
\end{definition}