Difference Between Natural and whole Numbers

A number is a mathematical value used for measuring or counting. Numbers are essential for calculations in math. They come in different types like whole numbers, natural numbers, integers, rational numbers, irrational numbers, real numbers, and complex numbers. The decimal system, commonly used in math, is one example of a number system.

Now, let's understand the difference between natural and whole numbers with an example in this article.

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Introduction

Whole numbers include the value '0', which sets them apart from natural numbers. A number represents a quantity in arithmetic. Mathematics categorizes numbers into various types:

  • Real Numbers
  • Integers
  • Numbers from Nature
  • Logical Numbers
  • Complete Numbers
  • Numbers with Irrational Exponents
  • Complex Numbers

These types are defined based on their unique properties.

Number System

The number system uses digits or symbols to represent numbers. It's a way of notation that defines which values can be used to represent quantities. Typically, the digits used range from 0 to 9.

Natural Numbers

Natural numbers, also called counting numbers, are used for counting objects. They are positive integers starting from 1. Natural numbers don't include zero, negative numbers, fractions, decimals, or complex numbers.

Examples:

  • 43 is a natural number (positive).
  • -51 is not a natural number (not positive).

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Whole Numbers

Whole numbers are all the positive integers (like 1, 2, 3), including zero (0). They are shown on a number line starting from zero and going towards infinity with positive numbers. For example, 0, 1, 2, 3, 4, and so on are whole numbers.

Natural numbers are a part of whole numbers because they are all positive integers starting from 1 onwards. However, not all whole numbers are natural numbers, except for zero.

Numbers like fractions (1/2, 3/4), decimals (0.5, 1.25), and complex numbers (like √-1) are not considered whole numbers.

You can do basic math operations like adding, subtracting, and multiplying with whole numbers.

Examples:

  • 232 is a whole number because it is a positive integer.
  • -344 is not a whole number because it's not a positive integer.

Difference Between Natural Numbers and Whole Numbers

Natural Numbers

Whole Numbers

Natural numbers are the fundamental counting numbers. In set notation, the natural number is 1, 2, 3, 4, 5,.....

The set of natural numbers and zero is defined as whole numbers. In set notation, the whole numbers are 0, 1, 2, 3, 4, 5,....

The letter "N" is used to represent natural numbers.

The letter "W"  is used to represent whole numbers.

Counting number starts from 1.

Counting number starts from 1.

We can say that all natural numbers are thought of as whole numbers.

All whole numbers, we can say, are not considered natural numbers.

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Frequently Asked Questions on Difference Between Natural and whole Numbers

Natural numbers are all the positive numbers starting from 1 and going up to infinity. Whole numbers include all the positive numbers starting from 0 and going up to infinity. So, 0 is a whole number, but it is not a natural number.

Natural numbers are positive whole numbers that start at 1 and go on forever. They are used for counting, like 1, 2, 3, 4, 5, and so on. While all natural numbers are whole numbers, not all whole numbers are natural numbers because whole numbers also include zero and negative numbers.

Real numbers include all the numbers we can think of: both rational numbers (like fractions and whole numbers) and irrational numbers (like the square root of 2 or pi).

 Every whole number is a natural number but every natural number is not a whole number.

The 23, isn't because it is a fraction.