An interval can be used to represent a set of values that lies between two numbers. It can also represent a set of values that are greater than or less than a specific number. They are often represented by using inequalities. An interval on a number line, consisting of the real numbers, contains an infinite amount of numbers. In the interval 1≤x≤4, all numbers between the x-values 1 and 4 are a part of the set. For example, 1, 2.7, 3.5, 3.61 and 4. To visually represent an interval, a number line is often used. This is done by marking the end points of the interval and drawing between them.

An interval does not have to be limited between two ends. For example, the inequality x≥0 is a set of all positive real numbers larger than or equal to 0.

Interval Notation

An interval can be denoted in different ways. One way is the interval notation, using [] and ().

The interval above can be described with an inequality as where ≤ indicates that the endpoint is included and $<$ that it's not. The inequality can be translated to interval notation where [ indicates that the endpoint is included and ) that it's not. The interval can then be read as all numbers greater and equal to -1 and less than 2. For more examples see the table below.

Inequality	Interval Notation
$0<x<24$	(0,24)
0.1≤y≤2.7	[0.1,2.7]
3≤x	$[3,\infty )$
$z<899$	$(\text{-}\infty ,899)$

Note that if the variable only has one limit, the other is infinity and is not included in the interval.