\begin{definition}[Definition:Homogeneous Function/Real Space]
Let $f: \R^2 \to \R$ be a real-valued function of two variables.
$\map f {x, y}$ is a '''homogeneous function''' {{iff}}:
:$\exists n \in \Z: \forall t \in \R: \map f {t x, t y} = t^n \map f {x, y}$
Thus, loosely speaking, a '''homogeneous function''' of $x$ and $y$ is one where $x$ and $y$ are both of the same "power".
\end{definition}