The number system in Mathematics is an important topic for JEE Main and Advance Exam, because it is the foundation of all mathematical concepts.

It is essential to have a good understanding of the number system to solve complex problems in algebra, geometry, trigonometry, and calculus.

The number system for JEE includes real numbers, complex numbers, rational numbers, irrational numbers, integers, and natural numbers.

It is important to understand the properties of these numbers and how they relate to each other. For example, the properties of real numbers are used extensively in calculus to solve problems related to limits, derivatives, and integrals.

In addition, the number system is used in many other fields such as physics, Chemistry, and Mathematics. So, having a good understanding of the number system can help you in many areas of Mathematics for JEE.

## List of Numbers in Number System for JEE Math

There are many types of numbers in the number system which are important for JEE Main and JEE Advance Exam, but some of the most common types are:

1. ### Natural numbers:

Natural Numbers are the numbers that are used for counting, ordering, and are represented by the set of positive integers {1, 2, 3, 4, …}. in other word, combination of cardinal and ordinal numbers is called natural numbers.

1. ### Whole numbers:

Whole Numbers are the numbers that include zero along with the natural numbers {0, 1, 2, 3, 4, …}. in other word, non-negative integers are called whole numbers.

1. ### Integers:

Integers are the set of whole numbers, their negatives, and zero {…, -3, -2, -1, 0, 1, 2, 3, …}. in other word, if we exclude decimal numbers from the set of real numbers then remaining real numbers will be Integers.

1. ### Rational numbers:

Rational Numbers are the numbers that can be expressed as a ratio of two integers (Can expressed in the form of p/q). For example, 2/3, -4/5, 0.75, and -1.25 are all rational numbers. They are terminating, non-terminating and repeating type of decimal numbers.

1. ### Irrational numbers:

Irrational Numbers are the numbers that cannot be expressed as a ratio of two integers (Can not expressed in the form of p/q) . They are non-repeating and non-terminating decimals such as pi (π) or the square root of 2.

1. ### Real numbers:

Real Numbers are the set of all rational and irrational numbers. They include all the numbers that can be plotted on a number line.

In other word, Set of Real Number is the union of Set of Decimal Numbers and Integers.

1. ### Imaginary Numbers:

Square root of Negative Numbers gives Imaginary numbers. Set of Imaginary Number is the Subset of Complex Numbers.

1. ### Complex numbers:

Numbers that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit, which is defined as the square root of -1. Set of Complex Numbers include both Imaginary and real Numbers.

## Venn diagram representation of set of numbers in Number System

In Venn diagram representation of number system, we will learn the following,

• Set of Complex Numbers includes real numbers, imaginary numbers, and complex numbers themselves.
• All real numbers can be considered as complex number.
• Set of Real numbers is the Subset of Complex Numbers.
• All Imaginary numbers can be considered as Complex number.
• Set of Imaginary Numbers is the subset of Complex Numbers.
• Real numbers can be represented in the form of complex number.
• Imaginary numbers can be represented in the form of complex numbers.
• Real Numbers includes both rational numbers and Irrational Numbers,
• Set of Real Numbers is the union of sets of decimal numbers and Integers.
• Natural numbers are subset of whole numbers or in other word, all natural numbers are whole numbers.
• Set of Whole numbers is the subset of Integers or in other word, all whole numbers are integers.
• All Integers are Rational Numbers or in other word, Set of Integers is the subset of Rational numbers.

## YouTube Video of Complete Number System in JEE Math

### YouTube Video of Number System Part 1

Youtube Video Number System Part 1, Contains Definition of Number System, Introduction of Decimal Number, Binary number system, Octal Numbers System, Hexadecimal Number System and About Complex Numbers Imaginary Numbers, Real Numbers, History Of evolution of Imaginary numbers and Complex Numbers and Venn diagram representation of Complex Numbers and Imaginary Numbers

### Video Lecture of Number System Part 2

Youtube Video of Number System Part 2, Contains Definition of Real Numbers, Decimal Numbers, Rational Numbers Irrational Numbers and Integers.

In this Part, you also learn venn diagram representation of Real Numbers system.

### YouTube Video of Number System Part 3

Youtube Video of Number System Part 3, Contains Integers, Definition of Integers,  representation of Set of Integers, Positive Integers, Negative Integers, Natural Numbers, Whole Numbers and their venn diagram representation.