number

A number is a mathematical object used to count, measure, and label.

A number is recorded via numerals, or symbols which represent the number.

Numbers can be classified into sets, called number sets or number systems.

The main number systems are:

Set	Name	Definition	$L A T E X$
$N$	natural numbers	$1, 2, 3, 4, 5, \dots$	`\mathbb{N}`
$Z$	integers	$\dots, - 3, - 2, - 1, 0, 1, 2, 3, \dots$	`\mathbb{Z}`
$Q$	rational numbers	$\frac{a}{b}$ where $a$ and $b$ are integers and $b \neq 0$	`\mathbb{Q}`
$R$	real numbers	the limit of a convergent sequence of rational numbers	`\mathbb{R}`
$C$	complex numbers	$a + b i$ where $a$ and $b$ are real numbers and $i^{2} = - 1$	`\mathbb{C}`

where each set down the table is a subset of the next one. Symbolically, $N \subset Z \subset Q \subset R \subset C$ .

Other common sets of numbers include