There exist several mathematical concepts and sources today that help us humans carry out various tasks smoothly. These terms and concepts have been coined by various intellects and mathematicians.

These mathematicians and intellects made sure that their knowledge of the subject reached various people.

Some people find mathematics and statistics complicated and insurmountable, but they don’t know that once a person understands a particular concept, mathematics can be very interesting and fun to study.

The basic concepts of mathematics and statistics involve a thorough understanding of different types of numbers. There are several types of numbers in mathematics. Two of these are 1. Natural numbers, and 2. Whole numbers.

## Key Takeaways

- Natural numbers include all positive integers starting from 1, while whole numbers include all positive integers and zero.
- Both sets of numbers are infinite and fundamental in mathematics.
- Whole numbers are more versatile in calculations as they include zero, essential for various mathematical operations.

## Natural vs Whole Numbers

Natural numbers are the set of positive integers (1, 2, 3, 4, 5, …). They are the numbers used to count objects or quantities and are sometimes called counting numbers. Whole numbers are the set of non-negative integers (0, 1, 2, 3, 4, 5, …). They include the natural numbers and also include the number 0.

The numbers that are used for counting and the numbers that are non-negative or positive are known as natural numbers. Natural numbers are used for counting.

A set of natural numbers is represented as “N.” It is an infinite set of numbers that start with the number “one.”

There are several properties and functions of natural numbers. Every natural number is followed by another natural number is one of the most commonly known properties.

The set of numbers that consists of the number “zero” is known as whole numbers. All whole numbers are considered real numbers, but on the other hand, not all real numbers are considered whole numbers.

They consist of positive numbers and integers, but they do not consist of fractions. A set of whole numbers is represented by “W.”

## Comparison Table

Parameters of Comparison | Natural Numbers | Whole Numbers |
---|---|---|

Meaning/ Definition | The numbers that are used for counting and the numbers that are non-negative or positive are known as natural numbers. | The set of numbers that consists of the number “zero” is known as whole numbers. |

Number “Zero” | Absent | Present |

Set | An infinite set is represented by “N”. | An infinite set is represented by “W”. |

Counting Number | The counting number starts from the number “one”. | The counting number starts from the number “zero. |

Set Notation | {1,2,3,4,5,6,7,…….} | {0,1,2,3,4,5,6,7,8,……} |

## What are Natural Numbers?

The numbers that are used for counting and the numbers that are non-negative or positive are known as natural numbers. Several properties are theorised regarding natural numbers.

The history of natural numbers dates back several years and is quite ancient. Various intellects have postulated several theories and properties regarding natural numbers.

Natural numbers are used for counting. A set of natural numbers is represented as “N.” It is an infinite set of numbers that start with the number “one”.

There are several properties and functions of natural numbers. Every natural number is followed by another natural number is one of the most commonly known properties.

Several discussions regarding the numerical system were held in Europe during the 19th century. Both mathematical and philosophical discussions were held.

Some intellects even postulated that natural numbers were the results of the human intellect. Self-theoretical meanings and definitions were initiated by Frege.

There are several properties and functions regarding natural numbers. The set of natural numbers is infinite, but it is known as countable infinity.

Counting and Ordering are two of the most significant generalizations of natural numbers. These numbers help many people with various tasks.

## What are Whole Numbers?

The set of numbers that consists of the number “zero” is known as whole numbers. All whole numbers exist on a number line, and they all are real numbers.

Examples of whole numbers include 0, 44, 19, 13, 45, 67, 24, 5, etc. Whole numbers do not contain fractions and include the number “zero”.

All whole numbers are considered real numbers, but on the other hand, not all real numbers are considered whole numbers. They consist of positive numbers and integers, but they do not consist of fractions.

A set of whole numbers is represented by “W”. There are several facts and properties regarding whole numbers.

All the natural numbers, counting numbers, and positive integers are whole numbers, including the number “zero”. It is also said that all whole numbers are real numbers, but not all real numbers are whole numbers.

These facts and properties are postulated by several intellects and mathematicians over the course of time.

The various arithmetic operations are the base of the properties regarding the whole numbers. These operations include addition, subtraction, multiplication, and division.

Multiplication or addition of two whole numbers results in a whole number, unlike the subtraction of two whole numbers may or may not result in a whole number as sometimes the results are also in integers.

If two whole numbers are divided, they may result in a fraction.

## Main Differences Between Natural and Whole Numbers

- The numbers that are used for counting and the numbers that are non-negative or positive are known as natural numbers. On the other hand, the set of numbers that consists of the number “zero” is known as whole numbers.
- The set of natural numbers does not consist of the number “zero”. On the other hand, the set of whole numbers does consist of the number “zero”.
- A set of natural numbers is represented by “N”. On the other hand, a set of whole numbers is represented by “W”.
- The counting number in natural numbers starts from the number “one”. On the other hand, the counting number in the whole numbers is the number “zero”.
- The set notation of natural numbers is {1,2,3,4,5,6,7,8,9…….}, on the other hand, the set notation of whole numbers is {0,1,2,3,4,5,6,7,8,9….}.
- All natural numbers are considered whole numbers, but not all whole numbers are considered natural numbers.

**References**

- https://www.researchgate.net/profile/Grzegorz-Bancerek/publication/243767436_Segments_of_Natural_Numbers_and_Finite_Sequences/links/5470776e0cf216f8cfa9f888/Segments-of-Natural-Numbers-and-Finite-Sequences.pdf
- https://library.oapen.org/bitstream/handle/20.500.12657/27709/1002297.pdf?sequence=1

Last Updated : August 4th, 2023

Piyush Yadav has spent the past 25 years working as a physicist in the local community. He is a physicist passionate about making science more accessible to our readers. He holds a BSc in Natural Sciences and Post Graduate Diploma in Environmental Science. You can read more about him on his bio page.