\begin{definition}[Definition:Sawtooth Wave]
A '''sawtooth wave''' is a periodic real function $S: \R \to \R$ defined as follows:
:$\forall x \in \R: \map S x = \begin {cases}
x & : x \in \openint {-\lambda} \lambda \\
\map S {x + 2 \lambda} & : x < -\lambda \\
\map S {x - 2 \lambda} & : x > +\lambda \end {cases}$
where $\lambda$ is a given real constant
\end{definition}