Types of Number Natural, Whole, Integer, Real Rational

Natural Number

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

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.

Whole Number

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

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.

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.

Based on integers, there are more classification of numbers like even numbers, odd numbers, prime numbers, composite numbers and polygon numbers.

1. Even numbers

Any integer which is multiple of 2 is called as an even number.

2. Odd numbers

Any integer which is not multiple of 2 is called as an odd number.

3. Prime numbers

A positive integer which is divisible by itself and 1 only is called as prime number.

4. Composite numbers

Any number which can be expressed as product of smaller positive integers is called as Composite number.

5. Polygonal numbers

The numbers which can be expressed as dots and can be arranged in the shape of regular polygon are called polygon numbers.
Such numbers are classified into triangular numbers, square numbers, pentagonal numbers, hexagonal numbers, heptagonal numbers, octagonal numbers, nonagonal numbers, decagonal numbers, hexdecagonal numbers and dodecagonal numbers.

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.

Irrational Numbers

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

Real Numbers

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

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

Imaginary numbers

Square root of a negative number is called as imaginary number.

Square root of negative 1 is called as imaginary unit. It is denoted by symbol i. It is pronounced as iota.
The value of i, i², i³ and i⁴ can be calculated as following:

Value of i
$\text{i}=\sqrt{-1}$

Value of i²
$\text{i²}=\mathrm{i}.\mathrm{i}$
$=\sqrt{-1}.\sqrt{-1}=-1$

Value of i³
$\text{i³}=\mathrm{i²}.\mathrm{i}$
$=\mathrm{(-1)}.\mathrm{i}=\mathrm{-i}$

Value of i⁴
$\text{i⁴}=\mathrm{i²}.\mathrm{i²}$
$=\mathrm{(-1)}.\mathrm{(-1)}=1$

The value of i^-1 and i^-2 are calculated as following:
Value of i^-1
$\mathrm{i^-1}=\frac{1}{\mathrm{i}}$ $=\frac{1}{\mathrm{i}}\times \frac{\mathrm{i}}{\mathrm{i}}$ $=\frac{\mathrm{i}}{\mathrm{i²}}$ $=\frac{\mathrm{i}}{-1}=\mathrm{-i}$
Value of i^-2
$\mathrm{i^-2}=\frac{1}{\mathrm{i²}}$ $=\frac{1}{-1}=-1$

Complex numbers

A number which can be expressed in the form of a + ib is called as complex number. In the complex number a + ib, a and b are real numbers and i is an imaginary unit. It has two parts real part and imaginary part. The real part is a and the imaginary part is ib.