Definition:Rational Number

Definition
A number in the form $\dfrac p q$, where both $p$ and $q$ are integers ($q$ non-zero), is called a rational number.

The set of all rational numbers is usually denoted $\Q$.

Thus:
 * $\Q = \set {\dfrac p q: p \in \Z, q \in \Z_{\ne 0} }$

Also denoted as
Variants on $\Q$ are often seen, for example $\mathbf Q$ and $\QQ$, or even just $Q$.

Some sources use $R$, and for the real numbers use $\mathfrak R$.

Also see

 * Definition:Irrational Number
 * Equality of Rational Numbers


 * Definition:Dedekind Cut