Interval Notation Calculator
Convert between interval notation and inequalities instantly
Convert Interval Notation
Examples: (-∞, 5), [2, 8], (3, ∞)
Frequently Asked Questions
What is interval notation?
Interval notation is a way to represent a set of numbers between two endpoints. It uses brackets [ ] for inclusive endpoints and parentheses ( ) for exclusive endpoints. For example, [2, 5) means 2 ≤ x < 5.
What's the difference between ( ) and [ ]?
Parentheses ( ) mean the endpoint is NOT included (open interval). Brackets [ ] mean the endpoint IS included (closed interval). For example, (3, 7] means 3 < x ≤ 7.
How do you write infinity?
Infinity (∞) and negative infinity (-∞) always use parentheses, never brackets, because infinity is not a real number you can reach. For example: (-∞, 5) or [3, ∞).
What is union notation?
The union symbol ∪ combines multiple intervals. For example, (-∞, 2) ∪ (5, ∞) represents all numbers less than 2 OR greater than 5, but not between 2 and 5.
How do you convert from inequality?
For x < 5, write (-∞, 5). For x ≥ 3, write [3, ∞). For 2 < x ≤ 7, write (2, 7]. Use < or > with parentheses, ≤ or ≥ with brackets.
Can an interval include just one number?
Yes! [5, 5] represents the single point x = 5. However, (5, 5) is empty because there are no numbers strictly between 5 and 5.