Mathematics-Online lexicon: Cantor Set

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	Mathematics-Online lexicon:
	Cantor Set

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We divide the unit interval

into three equals parts and remove the middle subinterval

. Then, we repeat the procedure with the two remaining subintervals, i.e., we split each of them into three parts and remove the middle subintervals

and

, respectively.

$\includegraphics[width=.8\linewidth]{a_cantormenge_bild.eps}$

Continuing the subdivision process indefinitely, we arrive in the limit at an uncountable set with measure

$\displaystyle 1-\frac{1}{3} - \frac{1}{3}\cdot\frac{2}{3} - \frac{1}{3}\cdot \left(\frac{2}{3} \right)^2 - \ldots = 0\,.$

It is referred to as Cantor Set.

(Authors: Höllig/Kopf/Abele)

see also:

automatically generated 6/11/2007