# Whole Numbers

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,…

 All the natural numbers are whole numbers. All counting numbers are W. There is no ‘largest’ whole number. All positive integers including zero are whole numbers. All W are real numbers.

### 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.