NUMBER SYSTEM

 NUMBER SYSTEM 

The number system is a way of classifying and representing numbers used for counting, measuring, and calculations.

Types of Numbers

Natural Numbers (ℕ)

Counting numbers starting from 1

Ex:1, 2, 3, 4, …

Whole Numbers (𝕎)

Natural numbers including zero

Ex:0, 1, 2, 3, …

Integers (ℤ)

All positive numbers, negative numbers, and zero

Ex:… −3, −2, −1, 0, 1, 2, 3, …

Rational Numbers (ℚ)

Numbers that can be written in the form p/q, where q ≠ 0

Ex: 1/2, −3/4, 5, 0.25

Irrational Numbers

Numbers that cannot be written as p/q and have non-terminating, non-repeating decimals

Ex:√2, √3, π

Real Numbers (ℝ)

All rational and irrational numbers together

Ex:Includes every number on the number line

Hierarchy of Number System

Natural ⊂ Whole ⊂ Integers ⊂ Rational ⊂ Real

Importance of Number System

Helps in counting and measuring

Used in daily life calculations

Forms the foundation of mathematics

Important for algebra, geometry, and higher maths