Whole Numbers: Definition, Properties, Comparison

Whole Numbers – Definition

Whole Numbers Definition :- Whole Numbers are numbers that don’t have fractions and is a collection of positive integers including zero. It is denoted by the symbol “W” and is given as {0, 1, 2, 3, 4, 5, ………}. Zero on a whole denotes null value or nothing.

• 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,….}

Whole numbers are positive integers along with zero and don’t have fractional or decimal parts. You can perform all the basic operations such as Addition, Subtraction, Multiplication, and Division.

Symbol

The Symbol to denote the Whole Numbers is given by the alphabet W = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,…

• All-natural numbers are whole numbers

• All positive integers including zero are whole numbers

• All whole numbers are real numbers

• All counting numbers are whole numbers

Properties of Whole Numbers

Whole Numbers Properties depend on arithmetic operations such as Addition, Subtraction, Multiplication, Division. When you multiply or add two whole numbers the result will always be a Whole Number. If you Subtract Two Whole Numbers the result may not always be a Whole Number and it can be an Integer too. Division of Whole Numbers can result in a Fraction at times. Let us see few more Properties of Whole Numbers by referring below.

Closure Property: Whole Numbers can be closed under addition or multiplication. If a, b are two whole numbers then a.b and a+b is also a whole number.

Commutative Property of Addition and Multiplication: Sum and Product of Two Whole Numbers will be the same no matter the order in which they are added or multiplied. If a, b are two whole numbers then a+b = b+a, a.b = b.a

Additive Identity: If a Whole Number is added to 0 the result remains unchanged. If a is a whole number then a+0 = 0+a = a

Multiplicative Identity: Whenever you multiply a whole number with 1 the result remains unchanged. Let us consider a whole number “a” then a.1 = 1. = a

Associative Property: If you are grouping the whole numbers and adding or multiplying a set the result remains the same irrespective of the order. If a, b, c are whole numbers then a + (b + c) = (a + b) + c and a. (b.c)=(a.b).c

Distributive Property: If a, b, c are three whole numbers then the distributive property of multiplication over addition is given by a.(b+c) =(a.b)+(a.c), Similarly Distributive Propoerty of Multiplication over Subtraction is given by a.(b-c) = (a.b)-(a.c)

Multiplication by Zero: If you multiply a Whole Number with Zero the result is always zero. i.e. a.0=0.a=0

Division by Zero: If you divide a Whole Number with Zero the result is undefined, i.e. a divided by 0 is not defined.