# Definition:Reciprocal

## Definition

Let $x \in \R$ be a real number such that $x \ne 0$.

Then $\dfrac 1 x$ is called the reciprocal of $x$.

The real function $f: \R_{\ne 0} \to \R$ defined as:

$\forall x \in \R_{\ne 0}: \map f x = \dfrac 1 x$

is called the reciprocal function.

## Examples

### Reciprocal of $\pi$

$\dfrac 1 \pi \approx 0 \cdotp 31830 \, 98861 \, 83790 \, 67153 \, 77675 \, 26745 \, 02872 \, 40689 \, 19291 \, 480 \ldots$

### Reciprocal of $e$

$\dfrac 1 e \approx 0 \cdotp 36787 \, 94411 \, 71442 \, 32159 \, 55237 \, 70161 \, 46086 \, 74458 \, 11131 \, 031 \ldots$

## Warning

Note the domain of the function $f: \R \setminus \set 0 \to \R$.

That is, $\dfrac 1 0$ is not defined.

## Also see

• Results about reciprocals can be found here.