Identifying Numbers

1 Identifying Numbers

$\hbox{ Particular subsets of the set of real numbers } \mathbb{R} \hbox{ are the sets of }$

$\hbox{ natural numbers } \quad \mathbb{N}= \{ 1, 2, 3, 4, \ldots \}$
$\hbox{ integers } \quad \mathbb{Z} = \{ \ldots, -4, -3, -2, -1, 0, 1, 2, 3, 4, \ldots\}$
$\hbox{ rational numbers } \quad \displaystyle{\mathbb{Q}= \{ \frac{p}{q} : \quad p, q \in \mathbb{Z}, \quad q \neq 0\} }$
$\hbox{ irrational numbers } \quad\mathbb{R} \setminus\mathbb{Q}.$