Interval notation

Definition

Interval notation is a mathematical shorthand used to represent subsets of the real number line. It uses parentheses and brackets to describe the set's endpoints and whether those endpoints are included or excluded.

5 Must Know Facts For Your Next Test

1. Parentheses, $(a, b)$, indicate that the endpoints $a$ and $b$ are not included in the interval.
2. Brackets, $[a, b]$, indicate that the endpoints $a$ and $b$ are included in the interval.
3. A combination of parentheses and brackets can be used, for example, $(a, b]$, where $a$ is excluded and $b$ is included.
4. Infinity symbols, $\infty$ or $-\infty$, are always paired with parentheses because infinity is not a specific number that can be reached.
5. Interval notation can represent solutions to inequalities and the domain of functions efficiently.

Review Questions

• How do you denote an interval where both endpoints are included?
• What does it mean if an interval uses a parenthesis on one side and a bracket on the other?
• Why can't infinity be represented with a bracket in interval notation?

Related terms

Inequality:

An inequality expresses the relationship between two expressions that may not be equal, using signs like $<$, $\leq$, $>$, or $\geq$.

Domain:

The set of all possible input values (usually x-values) for which a function is defined.

Absolute Value Inequalities: Inequalities that involve the absolute value function, often requiring special techniques to solve.