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Interval Notation

Interval notation is a compact way to write ranges of numbers using parentheses and brackets. Learn what ( ), [ ], and combinations mean, and when to use each.

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Parentheses and brackets

An interval describes a set of numbers between two endpoints. (2, 5) is all numbers strictly between 2 and 5; [2, 5] includes 2 and 5 themselves.

Including vs excluding endpoints

A parenthesis excludes the endpoint, a bracket includes it. Infinity is never included, so it always takes a parenthesis: [0, ∞) means all numbers greater than or equal to 0.

Frequently asked questions

1

What is interval notation?

Interval notation is a way to write a range of numbers using parentheses and brackets. (a, b) means numbers strictly between a and b; [a, b] includes the endpoints.

2

When do you use brackets vs parentheses?

A parenthesis excludes the endpoint (strict inequality), while a square bracket includes it. Infinity always uses a parenthesis because it is not a number you can reach.

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