Mathematics-Online lexicon: interval

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	Mathematics-Online lexicon:
	interval

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

With real numbers $a\le b$ the notation

$\displaystyle [a,b] = \{x\in\mathbb{R}:\ a\le x\le b\}$

refers to a closed interval. Leaving out the end points

and

, one obtains the open interval

$\displaystyle (a,b)\, .$

Analogously, half-open intervals

$\displaystyle [a,b),\quad (a,b]$

are defined.

Moreover, $\pm\infty$ are also used as boundaries of intervals. So, for example,

$\displaystyle [a,\infty) = \{x\in\mathbb{R}:\ a\le x\}$

and $(-\infty,\infty)=\mathbb{R}$ .

(Authors: Höllig/Kopf/Abele)

automatically generated 6/11/2007