Number Systems Visualizer
This interactive visualization shows the hierarchy and key differences between fundamental number systems in mathematics, from the basic Natural Numbers to the comprehensive Real Numbers.
Number Systems Hierarchy
Natural (ℕ)
1, 2, 3, …
Integers (ℤ)
…, -1, 0, 1, …
Rational (ℚ)
1/2, 0.75, -4/3
Real (ℝ)
π, √2, e
Number Systems Overview
Click on any number system above to see detailed information about it.
Number Systems Comparison
| Property | Natural (ℕ) | Integers (ℤ) | Rational (ℚ) | Real (ℝ) |
|---|---|---|---|---|
| Definition | Counting numbers (1, 2, 3…) | ℕ plus negatives and zero | Fractions p/q (q≠0) | ℚ plus irrational numbers |
| Cardinality | Countably infinite | Countably infinite | Countably infinite | Uncountably infinite |
| Closure Under +,× | Yes | Yes | Yes | Yes |
| Closure Under – | No | Yes | Yes | Yes |
| Closure Under ÷ | No | No | Yes (except ÷0) | Yes (except ÷0) |
| Density | Discrete | Discrete | Dense | Dense and Complete |
| Examples | 5, 42, 100 | -3, 0, 7 | 1/2, -4/7, 0.3̄ | π, √2, e, 0.101001… |
