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 $x$, $a\leq x\leq b$.
Many authors use the (increasingly popular) alternative $]a,b[$ to denote the open interval $a<x<b$.
Interval, open. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Interval,_open&oldid=31443