Interval, open

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open segment

The set of points contained in between two given constants $a$ and $b$, i.e. satisfying the condition $a<x<b$. An open interval does not contain the end points, and is denoted by $(a,b)$, as distinct from the (closed) segment $[a,b]$ (a closed interval), which contains the end points, i.e. consists of the points $x$, $a\leq x\leq b$.


See also Interval, closed; Interval and segment.

Many authors use the (increasingly popular) alternative $]a,b[$ to denote the open interval $a<x<b$.

How to Cite This Entry:
Interval, open. Encyclopedia of Mathematics. URL:,_open&oldid=31443
This article was adapted from an original article by BSE-3 (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article