# Number System

Number system is a mathematical notation for representing numbers using different kind of symbols or digits and it allows us to operate arithmetic operations like addition, subtraction, multiplication.

## Natural Numbers

The natural numbers are the numbers used for counting and ordering, they are also known as counting numbers and they are represented by N.
e.g ➤ N= 1, 2, 3, 4, 5............ ∞ ( infinite )
Note ➠ zero should not be included

## Whole Numbers

When we include zero in natural numbers then it becomes whole number, and we represent it by W.
Whole Number = Zero + Natural Numbers
e.g ➤ W= 0, 1, 2, 3, 4, 5...........∞ ( infinite )
Note ➠ (i) All natural numbers are whole numbers, but not all whole numbers are natural numbers.
(ii) Zero is a whole number, but not a natural number.

## Integer Numbers

When we represent whole numbers with positive and negative signs then we call it integer numbers or integers, and we represent it by I.
e.g ➤  I =   -∞ ......-3, -2, -1, 0, 1, 2, 3......∞

### (i) Positive Integer Numbers

Natural numbers are called positive integer numbers. e.g ➤ 1, 2, 3, 4, ..............

### (ii) Negative Integer Numbers

If natural numbers are written with minus sign, then those numbers are called negative integer numbers. e.g ➤ -1, -2, -3, -4, ..............

## Rational Numbers

The numbers which can be written in the form of P/Q is called rational numbers.
e.g ➤ 1/2, 3/2, 7/8, √1.........
Where (i) in P/Q,  Q ≠ 0
(ii) P and Q are Integers

## Irrational Numbers

The number which can not be written in the form of P/Q is called irrational numbers.
Where P and Q are integers and ( Q ≠ 0 )
Note ➠ π is a irrational number but the value of π (3.14) is a rational number.

## Real Numbers

A group of rational numbers and irrational numbers is called real numbers, and we represent it by R.
e.g ➤ R= 0, -2, 2/3, -6/15, √2 etc

## Imaginary Numbers

Numbers that are not real but just imagined, those are called imaginary numbers.
e.g ➤ √-3, √-15
Note ➠ (i) Thus the square root of these negative numbers cannot be derived.
(ii) They are also written as follows in the language of mathematics (a+ib), (a-ib), (x+iy),(-ix+y), we add I with them and this is very important for higher mathematics.

## Even Numbers

Natural numbers which can be completely divided by 2 are called even numbers.
e.g ➤ 2, 4, 6, 8, 10, 12, ............
Commonly these are represent as 2m where m= Natural Number

## Odd Numbers

Natural numbers which cannot be completely divided by 2 are called odd numbers.
e.g ➤ 1, 3, 5, 7, 9, ............
Commonly these are represent as 2m - 1 where m= Natural Number

## Prime Numbers

All numbers greater than 1, which only can be divided by itself or by 1 are called prime numbers.
e.g ➤ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, ..............

## Composite Numbers

All numbers greater than 1, which has at least one divisor other than 1 and itself, is called composite number.
e.g ➤ 4, 6, 9, 15, etc

## Co - Prime Numbers

Two natural numbers whose HCF is equal to 1 is called co-prime numbers.

## Important Points

Zero is called identity element of addition because when we add zero to any number it do not change the result.

### Identity Element of Multiplication

1 is called identity element of multiplication because when we multiply 1 to any number it do not change the result.

Adding a number to the number which make the sum zero is called additive inverse.

### Multiplicative Inverse

Multiplying a number to the number which make the product 1, that number is called multiplicative inverse
e.g ➤ Multiplicative inverse of x is 1/x

If you have any doubt or question let me know in the comments.