Interval Notation Calculator

Interval Notation Calculator

Exclusive (Open / Parenthesis) Inclusive (Closed / Bracket)

Exclusive (Open / Parenthesis) Inclusive (Closed / Bracket)

What is Interval Notation?

Interval notation is a simplified way of representing a range of numbers on a number line. It uses specific symbols—parentheses and brackets—to indicate whether the endpoints of the range are included or excluded. This system is widely used in algebra, calculus, and set theory to define domains, ranges, and solution sets for inequalities.

The Rules of Brackets and Parentheses

Understanding the symbols is the most critical part of reading interval notation:

• Parentheses ( ): These are used for "exclusive" boundaries. This means the number itself is not part of the set. In inequalities, this corresponds to "greater than" (>) or "less than" (<).
• Brackets [ ]: These are used for "inclusive" boundaries. This means the number is included in the set. In inequalities, this corresponds to "greater than or equal to" (≥) or "less than or equal to" (≤).
• Infinity (∞): Infinity is not a specific number, so you can never "reach" it. Therefore, negative infinity (-∞) and positive infinity (∞) are ALWAYS paired with parentheses, never brackets.

Common Interval Examples

Bounded Interval: [2, 10)
This means the set starts at 2 (included) and goes up to 10 (not included). In inequality terms: 2 ≤ x < 10.

Unbounded Interval: (-∞, 5]
This means all numbers less than or equal to 5. In inequality terms: x ≤ 5.

All Real Numbers: (-∞, ∞)
This represents every possible number on the number line.

How to Use This Calculator

1. Enter your lower bound (the starting number) and your upper bound (the ending number). If the range goes on forever, use "inf" or "-inf".

2. Select the boundary type. Choose "Inclusive" if the endpoint is part of the set (≤ or ≥) or "Exclusive" if it is not ().

3. Click "Generate" to see the mathematical notation and the corresponding inequality expression.