Rational numbers

Description

A rational number is a number of the form $a / b$, where $a$ and $b$ are integers and $b \neq 0$. We write $\mathbb{Q}$ for the set of rational numbers. Two fractions $a / b$ and $c / d$ are the same rational number when $a d = b c$. With addition and multiplication, $\mathbb{Q}$ is a field, and with its usual order it is an ordered field. The set $\mathbb{Q}$ contains $\mathbb{Z}$, because each integer $a$ is the fraction $a / 1$.