\begin{definition}[Definition:Scaled Euclidean Metric]
Let $\R_{>0}$ be the set of strictly positive real numbers.
Let $\delta: \R_{>0} \times \R_{>0} \to \R$ be the metric on $\R_{>0}$ defined as:
:$\forall x, y \in \R_{>0}: \map \delta {x, y} = \dfrac {\size {x - y} } {x y}$
Then $\delta$ is the '''scaled Euclidean metric''' on $\R_{>0}$.
\end{definition}