Interval

Definition

An interval is a range of numbers between two given values. It can be either closed, open, or half-open depending on whether the endpoints are included.

5 Must Know Facts For Your Next Test

1. A closed interval $[a, b]$ includes both endpoints: $a$ and $b$.
2. An open interval $(a, b)$ excludes both endpoints: $a$ and $b$.
3. A half-open (or half-closed) interval can include one endpoint but not the other, such as $[a, b)$ or $(a, b]$.
4. Intervals are often used to express solutions to inequalities.
5. Graphically, intervals can be represented on a number line with solid dots for included endpoints and open circles for excluded ones.

Review Questions

• What is the difference between a closed interval and an open interval?
• How would you graphically represent the interval $(2, 5]$?
• If you have the inequality $3 < x \leq 7$, how would you write this as an interval?

Related terms

Inequality: A mathematical statement that compares two expressions using symbols like <, >, ≤, or ≥.

Absolute Value: The distance of a number from zero on the number line; always non-negative.

Number Line: A visual representation of numbers arranged in order along a straight line.