Cantor's set

Cantor’s set is a mathematical construction created by repeatedly removing the middle third of a line segment, starting with a single interval. Despite removing parts, the remaining set is uncountably infinite—meaning it has as many points as the original segment—and has no intervals of length. It’s a perfect example of a fractal: highly structured, self-similar, and nowhere dense. The set highlights counterintuitive properties in mathematics, such as being both uncountably infinite and nowhere continuous, illustrating complex behaviors in real analysis and topology.