Category:Division over Standard Number Field

This category contains results about Division over Standard Number Field.
Definitions specific to this category can be found in Definitions/Division over Standard Number Field.

The concept of division over a field is usually seen in the context of the standard number fields:

Rational Numbers

Let $\struct {\Q, +, \times}$ be the field of rational numbers.

The operation of division is defined on $\Q$ as:

$\forall a, b \in \Q \setminus \set 0: a / b := a \times b^{-1}$

where $b^{-1}$ is the multiplicative inverse of $b$ in $\Q$.

Real Numbers

Let $\struct {\R, +, \times}$ be the field of real numbers.

The operation of division is defined on $\R$ as:

$\forall a, b \in \R \setminus \set 0: a / b := a \times b^{-1}$

where $b^{-1}$ is the multiplicative inverse of $b$ in $\R$.

Complex Numbers

Let $\struct {\C, +, \times}$ be the field of complex numbers.

The operation of division is defined on $\C$ as:

$\forall a, b \in \C \setminus \set 0: \dfrac a b := a \times b^{-1}$

where $b^{-1}$ is the multiplicative inverse of $b$ in $\C$.