Number System In Math for JEE Main and Advance

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.

2. 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.

3. 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.

4. 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.

5. 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.

6. 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.

7. Imaginary Numbers:

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

8. 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.