Similarly, the set of all non-zero rational numbers given by

is a set on which the binary operation division is closed. Now add the number (zero) to the above set and define the set of all rational numbers, denoted by , as

Observe that the set of rational numbers is closed under addition, subtraction and multiplication and the set is closed under division also.

We shall look at these number systems from a different point of view. Can you find a natural number satisfying the equation . You can immediately say that . Now, can you find a natural number satisfying the equation ? You will arrive at a conclusion that there is no natural number satisfying this equation.