\begin{definition}[Definition:Euclidean Metric/Real Number Line]
Consider the Euclidean space $\struct {\R^n, d}$.
On the real number line, the Euclidean metric can be seen to degenerate to:
:$\map d {x, y} := \sqrt {\paren {x - y}^2} = \size {x - y}$
where $\size {x - y}$ denotes the absolute value of $x - y$.
\end{definition}