Numbers are one of the most important things which one needs to perform daily calculations. Numbers are those inventions by humans which have made life easy and simple. People have now become very familiar with different types of numbers. Different types of numbers have been taught to students in their primary classes and even in secondary classes too. There is a large variety of numbers that are discovered in mathematics like __whole number__, rational numbers, irrational numbers, natural numbers, etc.

This article deals with different types of numbers and also discusses the necessary details and the difference which arises between the numbers that are due to differences in the properties.

- Whole numbers: These sets of numbers can also be considered as sets of all-
__natural numbers__including zero. This set does not include the numbers which are not positive, that is the negative numbers and it also doesn’t include the numbers which are in decimal values or fractional values. The set of these numbers can easily be remembered by the symbol “W”.

## Listed below are some of the properties of whole numbers.

- These sets of numbers are closed in multiplicative and additive properties.
- The number which can be concluded as the additive identity of the whole number is zero.
- The multiplicative identity is number one.
- The commutative and associative laws can be applied during the addition and multiplication of these numbers.
- This set of numbers satisfies the distributive property of multiplication.

- Integers: It can be defined as the set of those numbers which include all the set of whole numbers and it also includes the negative numbers set too. The integer set is represented by the letter “Z”.

## Listed below are the properties of integers.

- These are closed under additive, subtractive and multiplicative properties.
- All the properties are applicable and used for the addition and multiplication of integer numbers.
- The property of associativity is approved in the addition and subtraction of numbers.
- The additive identity of the integers is the number zero.
- Multiplication of the integers can obey the distributive property.

- Natural numbers: These numbers can also be referred to as counting numbers. The set of these types consists of all the numbers starting from one to infinity. The set of this number is known by the symbol “N”.

## Some properties of natural numbers:

- If we add two natural numbers, the process can be carried out easily because they are additive, commutative, and associative.
- The multiplicative nature of these numbers is also additive, commutative and associative.
- The additive identity of the natural number is zero.
- The identity of these types of numbers under multiplication is equal to one.

- Real numbers: Any set of numbers let it be positive or negative, whole or natural, or fractional all are termed under real numbers. These are represented by the letter “R”.

## Listed below are some properties of real numbers:

- The inverse property can be satisfied with real numbers.
- The identity of these numbers let them be additive or multiplicative are 0 and 1 respectively.

- Rational number: The numbers which are seen in p by q form or fractional form are termed as rational numbers. These numbers are recognized and symbolized by “Q”.

## Listed below are some of the basic properties of rational numbers.

- These numbers also satisfy all the basic properties like associativity, commutative and distributive.
- Although the distributive property is applicable in addition and subtraction only.

- Irrational number: The number which cannot be expressed as p by q ratio that is it cannot be expressed in the ratio are termed as irrational numbers

For example π,√5, etc.

These were some of the basic numbers which we __study in mathematics__. If a student gets stuck in any problem or wants to brush up his weak concepts then this can be cleared with the help of the google website known as Cuemath. This website is a great initiative to help students.