\begin{definition}[Definition:Inverse Tangent/Real]
Let $x \in \R$ be a real number.
The '''inverse tangent of $x$''' is the multifunction defined as:
:$\tan^{-1} \left({x}\right) := \left\{{y \in \R: \tan \left({y}\right) = x}\right\}$
where $\tan \left({y}\right)$ is the tangent of $y$.
\end{definition}