The Cantor set is a subset of real numbers with certain properties that are interesting to mathematicians. These properties relate to topology, measurement, geometry, as well as set theory. Some of them are:

• When represented geometrically, the set is a fractal, it has a Hausdorff dimension which is not an integer
• It has the same cardinality as the set of real numbers
• It is self-similar

The set is named after Georg Cantor. Henry John Stephen Smith discovered it in 1875, and Cantor first described it in 1883.