Difference Between Natural Numbers and Whole Numbers

Difference Between Natural Numbers and Whole Numbers

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Vikram
Vikram Singh
Assistant Manager - Content
Updated on Dec 4, 2023 17:03 IST

Want to know more about natural and whole numbers and their differences? This article will help clear up all your doubts.

difference between natural number and whole number

 

When you start learning mathematics, you start with counting the numbers. In mathematics, there are different types of numbers, such as natural, whole, integers, rational, irrational, real, and complex numbers. All these numbers are different but also share some common characteristics. In this blog, we will learn the difference between Natural Numbers and Whole Numbers.

So, without further delay, let’s explore the article.

Table of Content

Difference Between Natural Number and Whole Number

Parameter Natural Number Whole Number
Definition Basic counting numbers starting from 1, i.e., positive integers A natural Number with zero is called a whole number, i.e., counting a number greater than or equal to zero.
Representation N = {1, 2, 3, 4, 5, …} W = {0, 1, 2, 3, 4, 5, …}
Purpose used for counting used for counting and set notation
Subset a subset of the whole number subset of integer
Smallest Number 1 0
Upper Bound No No
Example 1, 5, 10000, 55555555 0, 111, 2222, 3333, 4, 5
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What is a Natural Number?

Natural numbers are positive integers greater than zero. In simple terms, natural numbers are the counting numbers used to represent quantities. The set of natural numbers includes 1, 2, 3, 4, …… and so on, with no upper limit.

Notation: N (capital letter)

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What is a Whole Number?

Whole numbers are the union of natural numbers and zero, i.e., a set of positive integers, including zero, is known as a whole number. It represents a set of objects, including an empty set. The whole numbers include 0, 1, 2, 3, …… and so on with no upper limit.

Notation: W (capital letter)

Note: All natural numbers are whole numbers.

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Properties

If a, b, and c are three natural numbers (whole numbers), then 

Closure Property: When you add, subtract, multiply, or divide two natural numbers (whole numbers), the result is always a natural number (whole number).

Commutative Property: The order of addition or multiplication of two numbers (whole numbers) does not affect the result, i.e., 

  • a + b = b + a
  • a * b = b * a

Example: 

  • 2 + 3 = 5 = 3 + 2
  • 2 * 3 = 6 = 3 * 2

Associative Property: When you add or multiply three natural numbers ( whole numbers), the order in which numbers are grouped doesn’t affect the result., i.e.,

  • a + (b + c) = (a + b) + c
  • a * (b * c) = (a * b) * c

Example:

  • 2 + (3 + 4) = 9 = (2 + 3) + 4
  • 2 * (3 * 4) = 24 = (2 * 3) * 4

Distributive Property: Multiplication distributes over addition, i.e., 

  • a * (b + c) = a * b + a * c
  • (a + b) * c = a * c + b * c

Example

  • 2 * (3 + 4) = 2 * 3 + 2 * 4 = 6 + 8 = 14
  • (2 + 3) * 4 = 2 * 4 + 3 * 4 = 8 + 12 = 20

Identity Property: 

  • 0 is the additive identity, i.e., a + 0 = 0 + a = a

Example: 2 + 0 = 0 + 2 = 2

  • 1 is the multiplicative identity, i.e., 1 * a = a * 1 = a

Example: 1 * 2 = 2 * 1 = 2

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Key Differences and Similarities

  • Natural numbers are positive integers greater than zero, whereas whole numbers include zero.
  • A natural number is a subset of the whole number, whereas the whole number is a subset of integers and a superset of natural numbers.
  • The smallest whole number is 0, while the smallest integer is 1.
  • Both share similar properties: closure, associative, identity, commutative, and distributive.
  • Both numbers have no upper limits.
  • Natural and whole numbers are non-decimal, i.e., they do not include fractions or decimals.
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Conclusion

Natural numbers and whole numbers are the basic but fundamental concepts in mathematics. In this article, we have briefly discussed the difference between natural numbers and whole numbers.

Hope you will like the article.

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FAQs on Difference Between Natural Number and Whole Number

What is a Natural Number?

Natural numbers are positive integers greater than zero. In simple terms, natural numbers are the counting numbers used to represent quantities. The set of natural numbers includes 1, 2, 3, 4, ...., and so on, with no upper limit.

What is a Whole Number?

Whole numbers are the union of natural numbers and zero, i.e., a set of positive integers, including zero, is known as a whole number. It represents a set of objects, including an empty set. The whole numbers include 0, 1, 2, 3, 4,..., and so on with no upper limit.

What is the difference between Natural Number and Whole Number?

Natural number is a subset of the whole number, whereas the whole number is a subset of integers and a superset of natural number. The smallest whole number is 0 while the smallest natural number is 1.

What are the different properties of Natural Number and Whole Number?

If a, b, and c are three natural numbers (whole numbers), then 

Closure Property: When you add, subtract, multiply, or divide two natural numbers (whole numbers), the result is always a natural number (whole number).

Commutative Property: The order of addition or multiplication of two numbers (whole numbers) does not affect the result, i.e., 

  • a + b = b + a
  • a * b = b * a

Example: 

  • 2 + 3 = 5 = 3 + 2
  • 2 * 3 = 6 = 3 * 2

Associative Property: When you add or multiply three natural numbers ( whole numbers), the order in which numbers are grouped doesn’t affect the result., i.e.,

  • a + (b + c) = (a + b) + c
  • a * (b * c) = (a * b) * c

Example:

  • 2 + (3 + 4) = 9 = (2 + 3) + 4
  • 2 * (3 * 4) = 24 = (2 * 3) * 4

Distributive Property: Multiplication distributes over addition, i.e., 

  • a * (b + c) = a * b + a * c
  • (a + b) * c = a * c + b * c

Example

  • 2 * (3 + 4) = 2 * 3 + 2 * 4 = 6 + 8 = 14
  • (2 + 3) * 4 = 2 * 4 + 3 * 4 = 8 + 12 = 20

Identity Property: 

  • 0 is the additive identity, i.e., a + 0 = 0 + a = a

Example: 2 + 0 = 0 + 2 = 2

  • 1 is the multiplicative identity, i.e., 1 * a = a * 1 = a

Example: 1 * 2 = 2 * 1 = 2

What are the key difference and similarities between natural number and whole number?

  • Natural numbers are the positive integers greater than zero, whereas whole number includes zero.
  • Natural number is a subset of the whole number, whereas the whole number is a subset of integers and a superset of natural number.
  • The smallest whole number is 0, while the smallest integer is 1.
  • Both share similar properties: closure, associative, identity, commutative, and distributive.
  • Both numbers have no upper limits.
  • Natural and whole numbers are non-decimal, i.e., they do not include fractions or decimals.
About the Author
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Vikram Singh
Assistant Manager - Content

Vikram has a Postgraduate degree in Applied Mathematics, with a keen interest in Data Science and Machine Learning. He has experience of 2+ years in content creation in Mathematics, Statistics, Data Science, and Mac... Read Full Bio