\begin{definition}[Definition:Lipschitz Continuity]
Let $M = \struct {A, d}$ and $M' = \struct {A', d'}$ be metric spaces.
Let Let $f: A \to A'$ be a mapping.
Then $f$ is a '''Lipschitz continuous mapping''' {{iff}} there exists a positive real number $K \in \R_{\ge 0}$ such that:
:$\forall x, y \in A: \map {d'} {\map f x, \map f y} \le K \map d {x, y}$
That is, the distance between the images of two points lies within a fixed multiple of the distance between the points.
\end{definition}