An interval is used to represent a set of values that lies between two numbers, or a set of values that are greater than or less than a specific number. They are often represented by using inequalities. To visually represent an interval, a number line is often used. This is done by marking the end points of the interval and drawing a line segment between them.

An interval on a number line, consisting of the real numbers, contains an infinite amount of numbers. In the interval $1\le x\le 4$, all numbers between the $x\text{-}$values $1$ and $4$ are a part of the set. For example, $1$, $2.7$, $3.5$, $3.61$ and $4$. An interval does not have to be limited between two ends. For example, the inequality $x\ge 0$ is a set of all positive real numbers larger than or equal to 0.

Interval Notation

Interval notation is a way to denote an interval. In this notation, a square bracket $[]$ is used when the end value is included and a round bracket $()$ is used when the end value is not included.

The interval above can be described with an inequality where $\le$ indicates that the end point is included and $<$ that it is not. The inequality can be translated to interval notation where $[$ indicates that the end point is included and $)$ that it is not. The interval can then be read as all numbers greater and equal to $\text{-}1$ and less than $2$. More examples of intervals are provided below with interval notation along with number line and inequality representations. Note that if the variable only has one limit, the other is infinity and is not included in the interval.