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 analysis method used to calculate rounding error.

The concept of interval can also be extended to any subset S of totally ordered set T, so that if both X and Y belong to S, and X

In France and some other European countries, "and" is used instead of "and". Like writing, writing. This article was originally included in ISO 31-1compiled by the International Organization for Standardization. Υ o 31-1is a set of specifications about mathematical symbols used in physical science and technology. In 2009, it has been replaced by the newly formulated ISO 80000-2, which no longer includes the use of and.

In the set language, we define various intervals as:

Note that all represent empty sets, and single element sets cannot be represented by intervals. For example, the collection {0} cannot be represented as. When a>b, the above four symbols are generally considered to represent an empty set. When the interval is not an empty set, a and b are called the endpoints of the interval. B-a is generally defined as the length of the interval. The midpoint of the interval is (a+b)/2.

The interval [a, b] is sometimes called a line segment. (If it is not an empty set or a single element set)

Parentheses and square brackets have other uses besides indicating intervals, depending on the context. For example, it can also represent the coordinates of the midpoint in the analytic geometry of ordered pairs in set theory, the coordinates of vectors in linear algebra, sometimes a complex number, and sometimes the greatest common divisor of integers in number theory. Occasionally used to indicate ordered pairs, especially in the field of computer science. Also in number theory, the least common multiple of integers is used.

Some authors use real number set to represent the complement set of interval, that is, it contains real numbers less than or equal to A and real numbers greater than or equal to B.