Mathematical definition of Numbers & Types of Numbers

Numbers are the backbone of Mathematics. This is the widest area in the mathematics field. In order to explain mathematical definition of numbers and Types of numbers, we initially understand the need for the existence of them, we may have go to the years past. In ancient times, not only to measure something but also define the quantity, there’s nothing which could fulfill the requirement. For instance, we could say a dozen of Mangoes, one Kg of Sugar, etc.. This was the basic necessity behind the origin of the number system. Firstly, Let us now define the Numbers in am mathematical way, furthermore, we’ll move to types…

Mathematical Definition of Numbers:

In order to express mathematical definition of numbers, we say- ‘They are the quantity, amount or the arithmetic value basically and most generally used not only for the purpose of counting but also for calculation. This also provides access for every subject to use the fixed and unique measurements. As a result, the unique measuring system comes into use. Numbers are unique and fix all over the world’.

Types of Numbers:

As per the definition of Numbers, the numbers are unique. Also,the numbers in Mathematics are of various types. These types use the various conditions as the base for their classification. Since the definition of numbers is unique, but also this classification apart from the conditions do not interfere with the values of the numbers, as a result, their values remain unchanged. The classification not only arrange the numbers but also gives uniqueness to them. Furthermore, Let us now discuss about the conditions for the classification of numbers:

  • The  numbers classify on the basis of Sets-


  • The numbers classify on the basis of divisibility-

    • Prime
    • Composite
    • Even
    • Odd

Let us have a look at the mathematical definitions or conditions over which we classify numbers. Firstly, we start along the classification on the basis of Sets of numbers. later on we move towards the remaining.

Real Numbers:

This is one of the most biggest set in Maths. For Mathematical definition, we say- ‘These are the numbers with true value which have actual existence in other words, we can say, these can be represented along the number line. Also they have fixed true value’.

Rational Numbers:

The Mathematical definition of these numbers can be simply ‘the numbers that we write in the form of ratio, or say in the form of (p/q).

Irrational Numbers:

We can define them as the numbers which are not rational.


These are nothing but the pure numbers. In other words, these can be written without using fractional component. This set involve the negative, positive and the zero numbers and Integers belongs to the Set of Reals.

Whole Numbers:

The definition of this set is the set of positive integers starting from zero (0) onward. This set is the subset of the Integers.

Natural Numbers:

Mathematical definition of Naturals is that -‘The set of positive integers from 1 onward’.

The relation of all the sets is defined by the following Hierarchical diagram.

Types of Numbers


Here, we have discussed about the definition of numbers and their various types. Above are the classifications of the numbers due to which they have unique and probably the identical arrangement. We’ll discuss these types in details…