# Mathematics: Number System: Natural, Whole Numbers and Integers (For CBSE, ICSE, IAS, NET, NRA 2022)

Glide to success with Doorsteptutor material for CBSE/Class-10 : get questions, notes, tests, video lectures and more- for all subjects of CBSE/Class-10.

There are four different types of numbers that represent in detail.

## Natural Numbers

- Recall that the counting numbers 1,2, 3, … constitute the system of natural numbers. These are the numbers which we use in our day-to-day life.
- Recall that there is no greatest natural number, for if 1 is added to any natural number, we get the next higher natural number, called its successor.
- We have also studied about four-fundamental operations on natural numbers.

For, example,

again, a natural number.

again, a natural number, but

is not defined in natural numbers.

Similarly, again a natural number

again, a natural number

is a natural number but is not defined in natural numbers? Thus, we can say that

- Addition and multiplication of natural numbers again yield a natural number but Subtraction and division of two natural numbers may or may not yield a natural number
- The natural numbers can be represented on a number line as shown below.

- Two natural numbers can be added and multiplied in any order and the result obtained is always same. This does not hold for subtraction and division of natural numbers.

## Whole Numbers

When a natural number is subtracted from itself, we cannot say what is the left-out number. To remove this difficulty, the natural numbers were extended by the number zero (0) , to get what is called the system of whole numbers. Thus, the whole numbers are

Again, like before, there is no greatest whole number.

The number 0 has the following properties:

Division by zero (0) is not defined.

Four fundamental operations can be performed on whole numbers also as in the case of natural numbers (with restrictions for subtraction and division) .

Whole numbers can also be represented on the number line as follows:

## Integers

- While dealing with natural numbers and whole numbers we found that it is not always possible to subtract a number from another.
- For example, (2 – 3) , (3 – 7) , (9 – 20) etc. are all not possible in the system of natural numbers and whole numbers. Thus, it needed another extension of numbers which allow such subtractions.
- Thus, we extend whole numbers by such numbers as (called negative 1) , (negative 2) and so on such that
- Thus, we have extended the whole numbers to another system of numbers, called integers.
- The integers therefore are