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Mathematics-Online course: Basic Mathematics - Real Numbers

Interval

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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 $ a$ and $ b$, 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)
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  automatically generated 10/31/2008