In mathematics, an interval usually refers to a set of real numbers: if X and Y are two numbers in a set, then any number between X and Y also belongs to the set. For example, a set consisting of real numbers that conform to 0 ≤ x ≤ 1 is an interval, which includes 0, 1 and all real numbers between 0 and 1. Other examples are: real number set, negative real number set, etc.

Interval plays an important role in integral theory, because as the simplest set of real numbers, they can be easily defined as "length" or "measure". Then, we can extend the concept of "measure" and introduce Borel measure and Lebesgue measure.

Interval is also the core concept of interval arithmetic. Interval arithmetic is a numerical value.