The set of rational numbers is an extension of the set of integers. The set formed by positive rational numbers, negative rational numbers, and zero is a new set that we call set of rational numbers, represented by Q.
Notice the picture:
The set of Q is an extension of the set Z.
Other subsets of Q:
Q* is the set of nonzero rational numbers;
Q+ is the set of positive rational numbers and zero;
Q- is the set of negative rational numbers and zero;
Q+* is the set of rational and positive numbers;
Q-* is the set of negative rational numbers.