Cantor set

The Cantor set, introduced by German mathematician Georg Cantor, is a remarkable construction involving only the real numbers between zero and one.

Related Topics:
German - Mathematician - Georg Cantor - Real number

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The Cantor set is defined by repeatedly removing the middle thirds of line segments. One starts by removing the middle third from the unit interval , leaving ∪ . Next, the "middle thirds" of all of the remaining intervals are removed. This process is continued ad infinitum. The Cantor set consists of all points in the interval that are not removed at any step in this infinite process.

Related Topics:
Interval - Ad infinitum

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The first six steps of this process are illustrated below.

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