interval notation

Interval notation is a compact shorthand for “every real number between here and there.” Instead of writing 2 ≤ x ≤ 7 or shading a number line, you just record the two endpoints and signal, with the bracket shape, whether each endpoint is included.

A square bracket means the endpoint is part of the set (it goes with ≤ or ≥); a round parenthesis means the endpoint is excluded (it goes with < or >). So [2, 7] includes both ends, (2, 7) excludes both, and [2, 7) includes 2 but not 7. The smaller number is always written first.

Infinity gets a parenthesis every time, because infinity is not a number you can ever reach — write (−∞, 5] or (3, ∞), never with a square bracket against the ∞ symbol. To express an “or” range with a gap, join two intervals with the union symbol ∪, as in (−∞, −1) ∪ (4, ∞).