\begin{definition}[Definition:Lipschitz Continuity/Real Function]
Let $A \subseteq \R$.
Let $f: A \to \R$ be a real function.
Let $I \subseteq A$ be a real interval on which:
:$\exists K \in \R_{\ge 0}: \forall x, y \in I: \size {\map f x - \map f y} \le K \size {x - y}$
Then $f$ is '''Lipschitz continuous on $I$'''.
The constant $K$ is known as '''a Lipschitz constant for $f$'''.
\end{definition}