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Natural numbers

A number that represents a real whole object is called a natural number.


Firstly, it is essential to know the meaning of natural numbers. The term “Natural numbers” is introduced by combining the meanings of the words “Natural” and “Number”.

The number is a symbolical representation of a quantity or the objects. Now, let us discuss the meaning of the word “natural”. There are two suitable definitions for the word “natural” in English language.

  1. Existing in nature
  2. Derived from nature

In the real world, the nature gives us everything completely. So, the natural numbers are used to represent the real objects or whole quantities by the numbers. Natural numbers are part of the real numbers and they are started from one, written as $1$ in mathematics.


The natural numbers are mainly used in two cases.

  1. Counting
  2. Labeling


The following two examples help us to understand how to use them in mathematics.


The natural numbers are mainly used to count the objects or things but they should be whole (not the fractions).

counting numbers

There is an apple in the first example. It is a whole object, not a fraction. Hence, the total number of apples is one, and it is symbolically denoted by a number $1$.

There are some cars and count them. The total number of cars are two and it is denoted by a number $2$.

There are some footballs. Now, count them and the total number of footballs are three. Hence, it is denoted by a number $3$.

There are some puppies and count them. Therefore, the total number of puppies are four and the quantity is denoted by a number $4$.


The natural numbers are also used for labelling the quantities.

labelling numbers

For example, there are several chairs in the picture. All the chairs are the same. So, it is so difficult to talk about a particular chair. The natural numbers are used to identify every chair by labeling each chair with a natural number.


According to the set theory, the natural numbers are collected as a set to express the natural numbers in simple form. The set of natural numbers is denoted by a letter N in mathematics.

$N \,=\, \Big\{1, 2, 3, 4,\cdots\Big\}$

Natural numbers are infinite. So, the set of natural numbers is an example for an infinite set.

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