rational number
The rational numbers are the fraction field of the ring of integers. In more elementary terms, a rational number is a quotient of two integers and , where is nonzero. Two fractions and are equivalent if the product
of the cross terms is equal:
Addition and multiplication of fractions are given by the formulae
The field of rational numbers is an ordered field, under the ordering relation defined as follows: if
- 1.
the inequality holds in the integers, and has the same sign as , or
- 2.
the inequality holds in the integers, and has the opposite sign as .
Under this ordering relation, the rational numbers form a topological space under the order topology. The set of rational numbers is dense when considered as a subset of the real numbers.