📐 Interval Notation Calculator
Convert between inequalities and interval notation
How to Use This Calculator
Enter Bounds
Type lower and upper bounds of your interval
Set Inclusivity
Check boxes for [inclusive] or leave unchecked for (exclusive)
Convert
See interval notation and equivalent inequality
Interval Notation Guide
Notation Symbols:
- [ ]: Square brackets = inclusive, includes endpoint
- ( ): Parentheses = exclusive, excludes endpoint
- -∞: Negative infinity
- ∞: Positive infinity
Examples:
[2, 5] → 2 ≤ x ≤ 5 (both inclusive)
(2, 5) → 2 < x < 5 (both exclusive)
[2, 5) → 2 ≤ x < 5 (lower inclusive, upper exclusive)
(-∞, 5] → x ≤ 5 (unbounded below)
[2, ∞) → x ≥ 2 (unbounded above)
About Interval Notation Calculator
The Interval Notation Calculator converts between inequality notation and interval notation. Interval notation is a compact way to represent sets of real numbers, commonly used in calculus and real analysis.
Key Features
- Compact: More concise than inequality notation
- Standard: Widely used in mathematics
- Flexible: Handles bounded and unbounded intervals
Uses
- Domain and range of functions
- Solution sets of inequalities
- Real analysis and topology
Frequently Asked Questions
What's the difference between [ and (?
Square brackets [ ] indicate the endpoint is included (≤ or ≥). Parentheses ( ) indicate the endpoint is not included (< or >).
Can I use interval notation for all real numbers?
Yes! (-∞, ∞) represents all real numbers.
Why is (-∞ always used with ( and ∞ with )?
Infinity is never actually reached, so it's always exclusive. Hence we always use parentheses with ±∞.