\begin{definition}[Definition:Real Hyperbolic Tangent/Definition 2]
The '''real hyperbolic tangent''' function is defined on the real numbers as:
:$\tanh: \R \to \R$:
:$\forall x \in \R: \tanh x := \dfrac {\sinh x} {\cosh x}$
where:
:$\sinh$ is the real hyperbolic sine
:$\cosh$ is the real hyperbolic cosine
\end{definition}