We will be working with sets of numbers in this chapter.

The interval notation is a useful way to represent sets of real numbers.

For example, $(-2,3]$ is used to represent the set of numbers described by ${-2 < x \leq 3.}$

Meanwhile, $(-\infty, -1)$ and $[1, \infty)$ represent the sets described by the inequalities ${x < -1}$ and $x \geq 1$ respectively.

Separate intervals can be combined by taking the union: ${(-\infty, -1) \cup [1, \infty)} = {\{x \in \mathbb{R}: x < -1 \textrm{ or } x \geq 1\}.}$

Examples

The diagram shows the visualization of various sets on a number line, as well as their representations in interval notation.