In school mathematics, you are familiar with the natural numbers ,,,, which is usually denoted by . You may remember that, after teaching ,,, the teacher taught you to add and multiply two numbers. Now you can realize that you need minimum two numbers to add (or multiply). That is why, these operations are called the binary operations. What do you get as an answer, if you add (or multiply) two natural numbers? Whenever you add two natural numbers, you always get the result as a natural number. We can state this property as: Given any two natural numbers and , the sum (addition) of and , denoted by , is again a natural number. Similarly, the multiplication of any two natural numbers is again a natural number. We describe this property of school mathematics in the language of college mathematics as on the set of natural numbers , the binary operations addition and multiplication are closed .

Just think, what are the other binary operations we know to perform on numbers? It is subtraction and division. If you subtract a natural number from a natural number, you may not get a natural number as a result. For example, if you subtract from , the answer is which is not a natural number. That is, is not closed under `subtraction'. So, we want to expand the set of natural numbers to form a bigger set of numbers which is closed under the binary operation subtraction also. You can find that the set of integers, denoted by , and defined by

is a set on which the binary operations addition, multiplication and subtraction are closed.