Definition:Reciprocal

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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:

$f: \R \setminus \left\{{0}\right\} \to \R: f \left({x}\right) = \dfrac 1 x$

is called the reciprocal function.


Examples

Reciprocal of $\pi$

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

This sequence is A049541 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).


Reciprocal of $e$

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

This sequence is A068985 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).


Warning

Note the domain of the function $f: \R \setminus \left\{{0}\right\} \to \R$.

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


Also see

  • Results about the reciprocal function can be found here.


Sources