Definition:Homogeneous Function/Real Space

Definition
Let $f: \R^2 \to \R$ be a real-valued function of two variables.

$\map f {x, y}$ is a homogeneous function of degree zero :
 * $\exists n \in \Z: \forall t \in \R: \map f {t x, t y} = t^n \map f {x, y}$

Thus, loosely speaking, a homogeneous function of $x$ and $y$ is one where $x$ and $y$ are both of the same "power".

Zero Degree
A special case is when $n = 0$: