Difference between revisions of "Interval, open"
From Encyclopedia of Mathematics
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| − | The set of points contained in between two given constants | + | 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 $x$, $a\leq x\leq b$. |
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See also [[Interval, closed|Interval, closed]]; [[Interval and segment|Interval and segment]]. | See also [[Interval, closed|Interval, closed]]; [[Interval and segment|Interval and segment]]. | ||
| − | Many authors use the (increasingly popular) alternative | + | Many authors use the (increasingly popular) alternative $]a,b[$ to denote the open interval $a<x<b$. |
Latest revision as of 13:30, 9 April 2014
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 $x$, $a\leq x\leq b$.
Comments
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: http://encyclopediaofmath.org/index.php?title=Interval,_open&oldid=31443
Interval, open. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Interval,_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