Standard Cantor set

The standard Cantor set is a mathematical construction created by repeatedly removing the middle third of a line segment. Starting with a single line, remove the middle third, leaving two segments; then remove the middle third from each remaining segment, and repeat infinitely. The result is a fractal set composed of infinitely many points that’s uncountably infinite in size but has no length or intervals—meaning it’s "thin" yet densely packed with points. Despite its seemingly sparse nature, it exhibits complex, self-similar structure at every scale, making it a fundamental example in understanding fractals and concepts of size and continuity in math.