The Cantor set

The Cantor set is a mathematical construction created by repeatedly removing the middle thirds of a line segment, beginning with a whole line. Starting with a single segment, you remove the middle third, then do the same for each remaining segment, continuing infinitely. This process results in a complex, dust-like set of points that is uncountably infinite yet has no length—meaning it takes up no space on the line. The Cantor set is important in understanding concepts of infinity, measure, and fractal geometry, illustrating how something can be infinitely intricate without occupying any measurable length.