An interval is a set of real numbers located between two other real numbers. The two numbers at each end are called endpoints. Interval notations are used to express an interval using a pair of numbers and a parenthesis or bracket. Parentheses are used for open intervals and infinities while brackets are used for closed intervals.
An interval can either be an open or closed interval, depending on whether or not the endpoints are finite and included in the set. Open intervals, denoted by (a, b), have endpoints that are not included in the number set. Closed intervals, denoted by [a, b], have finite and included endpoints. If one of the endpoints involves infinity, it still has all of its limit points; thus, it is still considered a closed interval. Intervals can also be half closed or half open if one of the endpoints is included and the other endpoint is not. There is also a degenerate interval, a number set that contains only a single real number. Empty sets can also be considered as degenerate. Line segments are a form of a closed interval with two finite endpoints. A ray is an interval with one finite endpoint and the other one is infinity.
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