Definition:Multiplicative Inverse/Number

Definition

Let $\Bbb F$ be one of the standard number fields: $\Q$, $\R$, $\C$.

Let $a \in \Bbb F$ be any arbitrary number.

The multiplicative inverse of $a$ is its inverse under addition and can be denoted: $a^{-1}$, $\dfrac 1 a$, $1 / a$, and so on.

$a \times a^{-1} = 1$

Also known as

The multiplicative inverse of a number is often referred to as its reciprocal.

Sources

• 1967: Michael Spivak: Calculus ... (previous) ... (next): Part $\text I$: Prologue: Chapter $1$: Basic Properties of Numbers: $(\text P 7)$