In Mathematics, we frequently come across simple equations to be solved.The solution 11 is a natural number. On the other hand, for the equationthe solution gives the whole number 0 (zero). If we consider only natural numbers, equation (2) cannot be solved. To solve equations like (2), we added the number zero to the collection of natural numbers and obtained the whole numbers. Even whole numbers will not be sufficient to solve equations of typeDo you see ‘why’? We require the number –13 which is not a whole number. This led us to think of integers, (positive and negative). Note that the positive integers correspond to natural numbers. One may think that we have enough numbers to solve all simple equations with the available list of integers. Consider the equations
(1) Whole numbers Let us revisit the closure property for all the operations on whole numbers in brief.Check for closure property under all the four operations for natural numbers.
(2) Integers Let us now recall the operations under which integers are closed.
You have learnt to represent natural numbers, whole numbers, integers and rational numbers on a number line. Let us revise them.Also, the first of the equally spaced points that divides the distance between 0 and 1 into three equal parts can be labelled
Can you tell the natural numbers between 1 and 5? They are 2, 3 and 4. How many natural numbers are there between 7 and 9? There is one and it is 8. How many natural numbers are there between 10 and 11? Obviously none. List the integers that lie between 5 and 4.