# Definition:Real Hyperbolic Cotangent/Definition 3

## Definition

The real hyperbolic cotangent function is defined on the real numbers as:

$\coth: \R_{\ne 0} \to \R$:
$\forall x \in \R_{\ne 0}: \coth x := \dfrac 1 {\tanh x}$

where $\tanh$ is the real hyperbolic tangent.

It is noted that at $x = 0$ we have that $\tanh x = 0$, and so $\coth x$ is not defined at that point.