**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**

**Identity Element of Addition**

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.

**Additive Inverse**

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.

## 1 Comments

Nice information

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