Difference Between Natural Numbers and Whole Numbers

# Difference Between Natural Numbers and Whole Numbers

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

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

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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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Taylor Series Approximation: Definition, Formula, and Example
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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.
Types of Matrix
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A skew-symmetric matrix is a square matrix whose transpose is equal to its negative. In other words, it is a matrix that satisfies the condition A^T = -A. This type...read more

## 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.

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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.