(1)Natural Numbers:They are counting numbers,the set of natural numbers denoted by N.
N={1,2,3,.....}

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(2)Whole Numbers:When we include "zero" in natural number it is called as whole numbers, the set of whole numbers denoted by W.
W= {0,1,2,3,.....}

(3)Integers:Are whole number (None fractional number),that can be positive,negative or zero and set of integers denoted by Z or I.
Z={....-3,-2,-1,0,1,2,3,....}

(i) Negative integers={....-3,-2-1}
(ii) Positive integers={1,2,3,....}
(iii)Non-negative integers={0,1,2,3....}

Note:Fractional numbers are not integers,
So , 3/5,1/2,4/9,2.21,9.6,3.68 etc.
are not integers.

(4)Prime Numbers:A number other than 1 is known as a prime number if it divisible by 1 and itself only.

Note:(i) Prime number are not divisible by any other numbers, except 1 and itself.
(ii) 1(one) is not a prime number.
(iii) 2 is only even prime number.
(iv) There are 25 prime numbers, between 1 and 100.

(5) Co-Prime: Pair of two natural numbers having no common factor,other than 1,is called a pair of Co-prime.

eg , (6,13), (11,17), (19,21) etc.
Note: H.C.F of co-prime number is 1 (one).

(6) Twin Primes: Prime numbers differing by two are called twin prime numbers.
eg.(11,13), (17,19), (29,31) etc.

(7) Prime Triplet: The set of three consecutive primes is called a prime triplet.
eg. {3,5,7}.

(8)Composite numbers: These numbers have more than two factors(one and itself),are known as composite numbers.

Note: (i) 1(one) is not a composite number.
(ii) Composite number may be even or odd.

(9) Even Numbers:Which are exactly divisible by 2.

(10)Odd Numbers:Which are not exactly divisible by 2.
Note:Zero is neither even nor odd.

(11)Rational Numbers:A number that can be written in the form p/q is called a rational number, where p and q are integers ,q is not equal to zero.
The set of rational numbers denoted by Q.
Note:
(i) Every integer is a rational number.
(ii) A rational number is either an integer or a non-integer.
(iii) Zero is an rational number.
e.g. 0, 1, 2, -3 etc.

(12) Irrational Numbers:A number that can't be written in the form p/q is called an irrational number, where p and q are integers, q is not equal to 0.

Note:(i) Surds are irrational numbers.
(ii) 0(zero)is not an irrational number.
eg.(2)^1/2, 0.30,3000 ....

(13) Real Numbers:The set of all rational and irrational numbers are known as real numbers.
eg. 0, 1/2, (3)^1/2 etc.