Overview
This lecture introduces interval notation, explaining how to write solutions for inequalities using brackets and parentheses on the number line.
Interval Notation Basics
- Interval notation is a way to write intervals on the number line.
- Parentheses ( ) are used for less than (<) and greater than (>) inequalities, not including endpoints.
- Brackets [ ] are used for less than or equal to (≤) and greater than or equal to (≥), including endpoints.
- Parentheses are always used with infinity (∞ or -∞) because infinity is not a specific value.
Examples
- For ( x > 3 ): the interval is written as ( (3, \infty) ).
- For ( x \leq 2 ): the interval is written as ( (-\infty, 2] ).
- For ( -2 \leq x < 3 ): the interval is written as ( -2, 3) ).
Key Terms & Definitions
- Interval Notation — A shorthand for describing subsets of the real number line using brackets and parentheses.
- Parentheses ( ) — Indicates endpoints are not included in the interval.
- Brackets [ ] — Indicates endpoints are included in the interval.
- Infinity (∞) — Represents unboundedness; always paired with parentheses.
Action Items / Next Steps
- Practice writing interval notation for different inequalities.
- Review number line representations of intervals with open and closed dots.