\begin{definition}[Definition:Lipschitz Continuity/Lipschitz Constant]
Let $M = \left({A, d}\right)$ and $M' = \left({A', d\,'}\right)$ be metric spaces.
Let $f: A \to A'$ be a (Lipschitz continuous) mapping such that:
: $\forall x, y \in A: d\,' \left({f \left({x}\right), f \left({y}\right)}\right) \le K d \left({x, y}\right)$
where $K \in \R_{\ge 0}$ is a positive real number.
Then $K$ is '''a Lipschitz constant for $f$'''.
\end{definition}