Category:Definitions/Division over Standard Number Field

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This category contains definitions related to Division over Standard Number Field.
Related results can be found in Category: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 $\C$.

Subcategories

This category has the following 3 subcategories, out of 3 total.