Interval Notation

Interval notation specifies an interval of the real line by writing its endpoints between symbols that indicate whether they are included. A square bracket means that the adjoining endpoint is included, while a parenthesis means that it is excluded. Thus, for , the notations , , , and denote a closed interval, an open interval, and the two possible half-closed intervals, respectively.

For example, iff , so interval notation is an abbreviation for the corresponding set-builder notation. A bound equal to is always written with a parenthesis, as in , , and , since is not a real endpoint. The degenerate interval denotes the singleton set , whereas , , and denote the empty set.