## Natural Number

Any number that matches to a number from **1, 2, 3, 4, ….** is called a **natural number** or
**counting number**.

**4, 9 , 11, 35, 99, 500** or **9876** are natural numbers.

Natural numbers are used for counting and ordering. On the basis of that they can be further divided into cardinal and ordinal numbers.

### 1. Cardinal numbers

Cardinal numbers are used for counting of objects. For example, there are 7 apples in a box or there are 7 days in a week. In both examples, we are counting objects which are 7.

### 2. Ordinal numbers

Ordinal numbers are used to order the positions of objects or in other words, we can tell the position of an object.

**Example 1**

Ist position or 2nd position and so on. The example of ordinal numbers is, girls stood Ist
in the race.
**Example 2**

This is the second largest country in the world.

Set of natural numbers is denoted by **N**.

## Whole Number

Any number that matches to a number from **0, 1, 2, 3, 4, ….** is called a Whole Number.

**0, 2, 14 , 23, 48, 172, 623** or **1245** are whole numbers.

Set of whole numbers is denoted by **W**.

## Integers

All natural numbers and negative of natural numbers including zero are called Integers. It includes 0 and all negative numbers and positive natural numbers.

**-65, -12, -5, 0, 56, 89** or **354** are Integers.

Also, the negative numbers are **additive inverse** of positive corresponding numbers.

What are additive inverse? Additive inverse refers to the sum of a positive number and corresponding
negative
number is equal to 0.

2 is **additive inverse** of -2.

Because -2 + 2 = 0.

Zero is neither a negative number nor positive number. It is a neutral number.

Set of integers is denoted by **Z**.

## Rational Numbers

The numbers each of which can be expressed in the form of
$\frac{\mathrm{p}}{\mathrm{q}}$ , where p and q are integers and q is
not equal to zero, are called Rational Numbers.

Besides, the rational numbers are also non terminating and repeating numbers.

$\frac{2}{5}$ , $\frac{1}{3}$ , $\frac{8}{9}$ , $\frac{3}{10}$ etc.

Set of rational numbers is denoted by **Q**.

Rational number is also a **real number.**

## Irrational Numbers

The numbers which are not rational are called irrational numbers. Besides, irrational numbers are also non terminating and non repeating numbers.

$\sqrt{2}$ , $\sqrt{5}$ etc.

## Real Numbers

Set of rational numbers and irrational numbers is called Real Numbers. In other words, real numbers include all rational and irrational numbers.

$\sqrt{7}$ , $\frac{1}{8}$ , $\frac{3}{10}$ etc.

All real numbers can be represented on a number line which is also called a real line.

Set of real numbers is denoted by **R**.