REAL NUMBERS, R

2. Rational Numbers, Q

The rational numbers are those real numbers, which can be expressed as the ratio of two integers. We denote the set of rational numbers by Q. Accordingly,

                Q = {x|x = p q where p €z, q€z}

Notice that each integer is also a rational number since, for example, 5 = 5/1;

hence Z is a subset of Q.

The rational numbers are closed not only under the operations of addition, multiplication and subtraction but also under the operation of division (except by 0). In other words, the sum, product, difference and quotient (except by 0) of two rational numbers is again a rational number.