The whole numbers are the number without fractions and it is a collection of positive integers and zero. It is represented by the symbol “W” and the set of numbers are {0, 1, 2, 3, 4, 5, 6, 7, 8, 9,……………}. Zero as a whole represents nothing or a null value.
 Whole Numbers: W = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10……}
 Natural Numbers: N = {1, 2, 3, 4, 5, 6, 7, 8, 9,…}
 Integers: Z = {….9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,…}
 Counting Numbers: {1, 2, 3, 4, 5, 6, 7,….}
Symbol
The number shows with the symbol ‘W’. W = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,…

Difference Between Whole Numbers and Natural Numbers
Whole Numbers  Natural Numbers 
W: {0, 1, 2, 3, 4, 5, 6,…..}  N: {1, 2, 3, 4, 5, 6,……} 
Counting starts from 0  Counting starts from 1 
All W are not natural numbers  All Natural numbers are W 
The symbol to represent with the alphabet ‘W’  All Natural numbers are represented with ‘N’ 
Properties of Whole Numbers
 Closure Property: They can be closed under addition and multiplication, i.e., if x and y are two whole numbers then x. y or x + y is also a whole number.
 Commutative Property of Addition and Multiplication: The sum and product of two W will be the same whatever the order they are added or multiplied in, i.e., if x and y are two whole numbers, then x + y = y + x and x. y = y . x
 Additive identity: When a whole number is added to 0, its value remains unchanged, i.e., if x is a whole number then x + 0 = 0 + x = x.
 Multiplicative identity: When a whole number is multiplied by 1, its value remains unchanged, i.e., if x is a whole number then x.1 = x = 1.x
 Distributive Property: If x, y and z are three W, the distributive property of multiplication over addition is x. (y + z) = (x.y) + (x.z), similarly, the distributive property of multiplication over subtraction is x. (y – z) = (x.y) – (x.z)
 Multiplication with zero: When a whole number is multiplied to 0, the result is always 0, i.e., x.0 = 0.x = 0.
 Division with zero: The division of a whole number by o is not defined, i.e., if x is a whole number then x/0 is not defined.