One of the most fundamental sets of numbers is whole numbers. We use numbers in our daily lives, such as the money left in our wallets, the amount of fuel in our vehicles’ tanks, the number of students in a class, and the number of subjects we will have to study over the course of an academic year. All of the examples given are situations in which we explicitly use numbers in our daily lives. Let’s take a closer look at whole numbers.

## What are whole numbers?

A set of natural numbers along with zero is referred to as a set of all whole numbers. Whole numbers always start with 0 and go up to infinity. 0 is the predecessor of 1; it is the smallest whole number. We can use whole numbers to represent cardinality.** Whole numbers are represented by the notation 𝕎.**

Whole numbers are represented using a set notation as

𝕎 = {0, 1, 2, 3, … ∞}

It is read as 𝕎 is a set of all whole numbers from 0 to infinity. 𝕎 is the notation used to represent whole numbers. { } is the curly brackets used to denote the set. ∞ is the symbol used to represent infinity.

## Number Line Representation

We can represent whole numbers on the number line similar to that of natural numbers. **A number line in which the numbers starting from 0 followed by 1, 2, 3, 4, … are marked at equal intervals is referred to as a number line representing whole numbers.** The red part on the number line shows the part of it that needs to be considered for representing whole numbers.

For example, a set of natural numbers from 0 to 10 is represented on the number line as pictured.

## Differences between Natural numbers and Whole numbers

Natural Numbers | Whole Numbers |
---|---|

Numbers starting from 1, 2, 3, 4, … ∞ are natural numbers. | Numbers starting from 0, 1, 2, 3, … ∞ are whole numbers. |

1 is the least natural number. | 0 is the least whole number. |

All whole numbers are considered as natural numbers except 0. | All natural numbers are considered as whole numbers. |

Example: length, time, weight, and so on | Example: phone numbers, TV channels, speedometer, and so on |

## Math Facts

Know more about other concepts of Number Systems on Fibonacci Numbers, Fractions, Natural Numbers, Prime Numbers and Unit Conversions.

**Online Math Classes > Math Concepts > Number Systems > Whole Numbers
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