Cantor Set
The Cantor Set is a unique mathematical construct created by removing the middle third of a line segment repeatedly. Starting with the interval from 0 to 1, the first step removes the segment from 1/3 to 2/3, leaving two segments: [0, 1/3] and [2/3, 1]. This process continues infinitely, removing the middle third of each remaining segment.
Despite removing many points, the Cantor Set contains an uncountably infinite number of points. It is an example of a set that is closed and perfect, yet has a total length of zero. This paradoxical nature makes it a fascinating topic in set theory and fractal geometry.