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. Intervals are usually represented algebraically with inequalities and graphically with a number line. This is done by marking the endpoints of the interval and drawing a line segment between them.

An interval consisting of real numbers contains an infinite amount of numbers. In the interval 1 ≤ x ≤ 4, all numbers between 1 and 4 are 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 ≥ 0 is the set of all positive real numbers greater than or equal to 0.

Interval Notation

Interval notation is a way to denote an interval. In this notation, a square bracket, [ or ], is used when the end value is included, and a round bracket, ( or ), is used when the end value is not included. When using interval notation, the left value is less than the right value.

Interval Notation	Description	Type of Interval
(a,b)	Both ends are not included	Open interval
[a,b]	Both ends are included	Closed interval
[a,b) or (a,b]	One end is not included	Half-open interval

The following applet shows some more examples of intervals. Note that if the variable only has one limit, the other is infinity, ∞ or -∞, and is not included in the interval.