Formula:
Interval notation is a concise way to represent subsets of real numbers. It uses parentheses `()` for exclusive (open) bounds and square brackets `[]` for inclusive (closed) bounds.
Let a be the lower bound and b be the upper bound.
- Open Interval: `(a, b)` implies `a < x < b` (exclusive of `a` and `b`)
- Closed Interval: `[a, b]` implies `a ≤ x ≤ b` (inclusive of `a` and `b`)
- Half-Open/Closed Interval: `(a, b]` implies `a < x ≤ b`; `[a, b)` implies `a ≤ x < b`
- Unbounded Intervals: Use `−∞` for negative infinity and `∞` for positive infinity. Always use parentheses `()` with infinity. For example, `[a, ∞)` implies `x ≥ a` and `(−∞, b)` implies `x < b`.