Interval

Definition

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

5 Must Know Facts For Your Next Test

1. Intervals can be represented using inequality notation or interval notation.
2. A closed interval includes its endpoints and is denoted by square brackets: $[a, b]$.
3. An open interval does not include its endpoints and is denoted by parentheses: $(a, b)$.
4. A half-open (or half-closed) interval includes one endpoint but not the other, e.g., $[a, b)$ or $(a, b]$.
5. The union and intersection of intervals can also form new intervals, depending on their overlap.

Review Questions

• How do you denote an interval that includes both endpoints?
• What is the difference between an open interval and a closed interval?
• Can two disjoint intervals have a non-empty intersection?

Related terms

Inequality: A mathematical statement that shows the relationship between two expressions that are not equal.

Absolute Value: The distance of a number from zero on the number line; denoted as $|x|$.

Union: \text{In set theory}, it is the set containing all elements of given sets; often denoted as $A \cup B$.