## 26 Jun 2018

### Types of Numbers (Natural, Whole, Integer, Rational, Irrational, Real, Imaginary, Complex Numbers)

Following is the Classification of various types of numbers-

## Natural Numbers (N)

If N is a set of natural numbers, then we can write the set of natural numbers as N={1,2,3,4,5,6...}. So natural numbers are simply the counting numbers.

## Whole Numbers (W)

If w is the set of whole numbers, then whole numbers can be written as W={0,1,2,3,4...},
So it is clear that if we add 0 in the set of natural numbers then we get the set of whole numbers.

## Integers (I)

If we represent the set of integers by I, then we can write I={ ...-3, -2, -1, 1, 0,1, 2, 3...}
Here note that, {1,2,3...} is the set of positive integers while, {...-1, -2, -3} is the set of negative integers. But '0' is neither positive number nor negative number.

## Rational Numbers (Q)

Rational numbers are the numbers, that can be expressed in the form of p/q, where both p and q are integers and q is not equal to zero.
Following are the examples of Rational numbers-
0, 4, -4, 3/4, -5/7 etc.
It is very interesting to note here that between any two rational numbers, there exist infinite number of rational numbers.

## Irrational Numbers

Non recurring and non terminating decimals are called has irrational numbers. Unlike rational numbers, irrational numbers cannot be expressed in the form of p/q.
Irrational numbers are all the real numbers which are not rational numbers.
Some examples of irrational numbers are-
√3, √5, √7, √29...

On combining rational numbers and irrational numbers we get set of real numbers.
In other words, a real number is a value of a continuous quantity that can represent a distance along a line.
Ex. 2, -3, 3/4, √3, √5...

## Imaginary Numbers

It is a complex number that can be written as a real number multiplied by the imaginary unit i (iota).
Here i=√-1
Please note that 0 is both a real number and an imaginary number.
Examples of imaginary numbers
3i, 5i, ...

## Complex Numbers (C)

Complex numbers include real numbers, imaginary numbers, and also the sums and differences of real numbers and imaginary numbers.
Complex number can be expressed in the form of a+ib
Here a and b are real numbers and i=√-1
ex- 4, -7, 5/8, 3i, 8i etc