# Number System - Rational Number - $\mathbb{Q}$

A rational number 1) is any number that can be expressed as the quotient or fraction p/q of two integers

Rational numbers are also known as:

• the rationals,
• the field of rationals
• or the field of rational numbers

## Syntax

The syntax of a rational number is expressed via a division operator:

$$\frac{\displaystyle p}{\displaystyle q} = \frac{\displaystyle \text{p (numerator)}}{\displaystyle \text{q (non-zero denominator)}}$$

Since the non-zero denominator q may be equal to 1, every integer is a rational number.

## Field

The rational numbers together with addition and multiplication form field which contains the integers and is contained in any field containing the integers.

The set of rational numbers is countable.