Definition:Homogeneous Function/Real Space

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

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

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 $n = 0$: