An irrational number is a number that cannot be expressed as a fraction p/q for any integers p and q.

Irrational numbers have decimal expansions that neither terminate nor become periodic.

Every transcendental number is irrational.

There is no standard notation for the set of irrational numbers, but the notations R - Q

 or RQ, where minus sign or backslash indicates the set complement of the rational numbers Q

over the reals R, could all be used.