Cantor Sets

A Cantor set is a mathematical construction created by repeatedly removing the middle thirds of a line segment, starting with a whole segment. Despite removing parts at each step, the remaining set is uncountably infinite and has no simple length—it’s a fractal, meaning it’s complex and endlessly detailed at every scale. The Cantor set is a fundamental example in mathematics demonstrating how a set can be infinitely detailed, yet have a total length of zero, illustrating surprising properties of infinity and measure in analysis.