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A collection of points on a Line Segment. If the endpoints $a$ and $b$ are Finite and are included, the interval is called Closed and is denoted $[a,b]$. If one of the endpoints is $\pm\infty$, then the interval still contains all of its Limit Points, so $[a,\infty)$ and $(-\infty, b]$ are also closed intervals. If the endpoints are not included, the interval is called Open and denoted $(a,b)$. If one endpoint is included but not the other, the interval is denoted $[a,b)$ or $(a,b]$ and is called a Half-Closed (or Half-Open) interval.

See also Closed Interval, Half-Closed Interval, Limit Point, Open Interval, Pencil

© 1996-9 Eric W. Weisstein