Half-Open Interval
High School
Definition
An interval that only has one endpoint. It is represented as [a, b) or (a, b] with the square bracket [] on the end that is closed and the parentheses () on the end that isn't. It is also sometimes called a half-open interval.
Worked examples
\([2, 5)\) includes 2, 3, 4 but not 5
The square bracket means 2 is in; the parenthesis means 5 is out.
\((0, 3]\) includes 1, 2, 3 but not 0
The parenthesis excludes 0; the square bracket includes 3.
Common mistakes
- \([2, 5)\) includes 5 → \([2, 5)\) does not include 5 The parenthesis means that endpoint is excluded, not included.
- writing \([2, 5]\) when you mean \([2, 5)\) → \([2, 5)\) has a parenthesis on the open end Square brackets on both ends make it a closed interval, not half-open.
- \((0, 3]\) is the same as \([0, 3)\) → \((0, 3]\) excludes 0 and includes 3; \([0, 3)\) does the opposite Which endpoint is open or closed changes which numbers belong to the interval.
Where you'll use it next
Half-open intervals appear when writing domain and range in functions, solving inequalities, describing continuity in calculus, and working with sequences and series where one boundary behaves differently.
Found in 1 StudyPug lesson
Mastering Interval Notation Brackets: Your Complete Guide
KindergartenKindergartenAlgebra
Unlock the power of interval notations! Learn to represent number ranges on a line, express inequality solutions, and define function domains. Perfect for enhancing your math skills and problem-solving abilities.
See also
Reviewed by Pat Cheng, M.Ed. — StudyPug Curriculum Lead · Last updated June 6, 2026