Integers

In order to be able to perform subtraction of arbitrary natural numbers, the set $\mathbb{N}$ is extended to the set $\mathbb{Z}$ of integers.

The integers are closed under addition, multiplication and subtraction.

$\mathbb{Z} = {\dots, -3, -2, -1, 0, 1, 2, \dots}$

The quotient of two integers need not be an integer:

$22 : 7 \not\in \mathbb{Z}$