$\mathbb {N} \,$ is the set of **positive** integers, also called the **natural numbers**.

$\mathbb {Z} \,$ is the set of all **integers**.

$\mathbb {Q} \,$ is the set of all **rational** numbers.

$\mathbb {A} \,$ is the set of **algebraic** numbers.

$\mathbb {R} \,$ is the set of **real** numbers.

$\mathbb {C} \,$ is the set of **complex** numbers.