Common Number Sets in Mathematics

Symbol	Name	Description	Origin
$\mathbb{N}$	Natural numbers	$1, 2, 3, \dots$ (sometimes includes $0$ )	English Natural
$\mathbb{Z}$	Integers	$\dots, -2, -1, 0, 1, 2, \dots$	German Zahlen
$\mathbb{Q}$	Rational numbers	Numbers that can be written as $\tfrac{p}{q}$ , $q \neq 0$	English Quotient
$\mathbb{R}$	Real numbers	Rational and irrational numbers ( $\pi$ , $\sqrt{2}$ , $\dots$ )	English Real
$\mathbb{C}$	Complex numbers	Numbers of the form $a + bi$ , $i^2 = -1$	English Complex

The symbols $\mathbb{N}, \mathbb{Z}, \mathbb{Q}, \mathbb{R}, \mathbb{C}$ are written in blackboard bold.
This style comes from mathematicians writing bold letters on the blackboard to distinguish special sets of numbers.

These symbols are mainly used in set notation.
For example:

$1 \in \mathbb{N}$ : $1$ is a natural number.
$\pi \in \mathbb{R}$ : $\pi$ is a real number.

They also follow an inclusion relationship:
$\mathbb{N} \subset \mathbb{Z} \subset \mathbb{Q} \subset \mathbb{R} \subset \mathbb{C}$