Introduction:

** Natural numbers: **The numbers by which counting is performed are called natural numbers, such as 1 2 3 4 5 .. There are natural numbers.

** Whole Numbers: **Includes 0 (zero) in the set of natural numbers, then a set of whole numbers is formed. I.e. 0 1 2 3 4. ………… etc. are whole numbers.

Note: 0 (zero) is not a natural number.

** Even Numbers: **The natural numbers which are divisible by 2 are called even numbers. Such as 2 4 6 8. e.t.c .

** Odd Numbers: **The natural numbers that are not divisible by 2 are called odd numbers. Such as 1 3 5 7 And so on.

** Prime numbers: **The natural numbers which are divisible by 1 or itself not by any other number, are called prime numbers. Such as 2 3 5 7 And so on.

** Composite Number: **The natural numbers which are divisible by 1 or by any other number, are known as composite numbers. Such as 4 6 8 9 10 And so on.

**Co-prime Numbers: **Those two natural numbers which have the greatest common divisor (HCF) 1 are called co-prime numbers. Like 4 and 9 are co-prime numbers.

** Prime Triplet Numbers: **Those three natural numbers which have the greatest common divisor (HCF) 1 are called prime triplet numbers. . Like – 8,9 and 25 are Prime triplet numbers.

** Rational Numbers: **The smallest form that a integer gets after dividing the other integer (apart from zero) is called a rational number. Like (where q = 0) is a rational number.

Note: Rational numbers are composed by collecting the composite numbers and fractions.

** Irrational Numbers: **The real number that is not a rational number is called an irrational number. Like Etc. are irrational numbers. Irrational numbers are non-recurring and non-terminating. That is, when it is converted into a decimal, neither it comes in the form of recurring nor does it have any definite end.

** Positive and Negative Integers: **Whole Numbers 1 2 3 4 5 are called positive integers. They are also written +1 + 2 +3 +4 +5. The positive numbers + a’s inverse -a is called negative integer. Therefore, the negative whole numbers -1 -2 -3 -4 … etc are the inverse of 1 2 3 4 ….

** Real numbers:** Rational and irrational numbers together are called real numbers.

**Unrealistic or Imaginary Quantities:** The numbers that are not real are called Imaginary numbers. Like Etc.

** Identity Element of Addition:** Adding 0 to any number does not make any difference in that number, therefore 0 is called the identity element of the addition.

** Identity Element of Multiplication: **By multiplying a number by 1, there is no difference in that number, therefore 1 is called the identity element of multiplication.

** The inverse element of addition : **-a is the rational number for each rational number a, where a + (-a) = (-a) + a = 0, So -a is called the inverse element of addition.

**Inverse Element of Multiplication: **For each rational number a, except for zero we get the rational number ^{ 1}/_{a} , Where a × ^{ 1}/_{a} = ^{ 1}/_{a} × a = 1 then a _{ }is called the Inverse element of Multiplication of ^{1}/_{a}.

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