Cantor set

The Cantor set is a subset of the real numbers that exhibits a number of interesting and counter-intuitive properties. It is among the simplest examples of a fractal.

The Cantor set can be described recursively as follows: begin with the set [0,1] and then remove the ( open) middle third, dividing the interval into two intervals of length . Then remove the middle third of the two remaining segments, and remove the middle third of the four remaining segments, and so on ad infinitum.

Equivalently, we may define to be the set of real numbers between and with a base three expansion that contains only the digits and .

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