NUM020 · Numbers & number systems · Classes 9–12
Interval notation
Interval notation writes a set of real numbers between two ends. A square bracket includes the end point; a round bracket leaves it out.
[−2, 3)Interval notation
📐 Formula
[a, b] : a ≤ x ≤ b; (a, b) : a < x < b; [a, b) : a ≤ x < b
✏️ Worked example
[−2, 3) means −2 ≤ x < 3: −2 is included, 3 is not. Its length is 5.
🌍 Where it is used
Domains of functions, ranges of safe values (e.g. temperature limits).
❓ Quick check
Which interval means 1 < x ≤ 4?
🏋️ Practice
EasyWrite 0 ≤ x ≤ 5 in interval notation.
Answer: [0, 5]
MediumIs 3 in (3, 7)?
Answer: No
ChallengeWrite x > 2 as an interval.
Answer: (2, ∞)