What are Numbers?
Understanding numbers, number systems, and their properties
Interactive What Are Numbers Visualization
Introduction
Numbers are the foundation of mathematics. They can be classified into different sets based on their properties. Understanding these number sets helps us work with the right type of numbers for each situation.
Number Hierarchy:
ℕ ⊂ W ⊂ ℤ ⊂ ℚ ⊂ ℝ ⊂ ℂ
Natural ⊂ Whole ⊂ Integer ⊂ Rational ⊂ Real ⊂ Complex
How to Use
- Enter any number in the input field to see which number sets it belongs to
- Try different numbers: integers (5, -3), fractions (1/2), decimals (0.5), irrationals (√2, π), or complex (3+4i)
- Select a number set from the dropdown to learn about its properties and examples
- Toggle the number line to visualize where real numbers are located
- Observe the hierarchy: Natural ⊂ Whole ⊂ Integer ⊂ Rational ⊂ Real ⊂ Complex
- Notice that each number belongs to multiple sets (e.g., 5 is natural, whole, integer, rational, real, and complex)
Try: 5, -3, 0, 1/2, 0.5, √2, π, 3+4i
Classification of "5"
ℝ Real Numbersℂ Complex Numbersℚ Rational Numbersℤ IntegersW Whole Numbersℕ Natural Numbers
This number belongs to: Real Numbers, Complex Numbers, Rational Numbers, Integers, Whole Numbers, Natural Numbers
ℕ Natural Numbers
Counting numbers starting from 1
Examples:
Includes:
- • Positive integers starting from 1
Number Line
The number line shows real numbers. Your number is marked in blue (if it's a real number).
Number Set Hierarchy
ℕNatural Numbers: 1, 2, 3, ...
WWhole Numbers: 0, 1, 2, 3, ... (includes 0)
ℤIntegers: ..., -2, -1, 0, 1, 2, ... (includes negatives)
ℚRational Numbers: All fractions and terminating/repeating decimals
ℝ\ℚIrrational Numbers: Non-repeating, non-terminating decimals (π, √2, etc.)
ℝReal Numbers: All rational and irrational numbers
ℂComplex Numbers: a + bi (includes all real numbers)
ℕ ⊂ W ⊂ ℤ ⊂ ℚ ⊂ ℝ ⊂ ℂ
Each set contains all previous sets
Lessons
Individual learning units
Lessons coming soon