\begin{definition}[Definition:Real Hyperbolic Cotangent/Definition 2]
The '''real hyperbolic cotangent''' function is defined on the real numbers as:
:$\coth: \R_{\ne 0} \to \R$:
:$\forall x \in \R_{\ne 0}: \coth x := \dfrac {\cosh x} {\sinh x}$
where:
:$\sinh$ is the real hyperbolic sine
:$\cosh$ is the real hyperbolic cosine
It is noted that at $x = 0$ we have that $\sinh x = 0$, and so $\coth x$ is not defined at that point.
\end{definition}