Cantor dust

Cantor dust is a mathematical concept derived from the Cantor set, a classic example in topology and set theory. It starts with a line segment, which is repeatedly divided into thirds, removing the middle third each time. As this process continues infinitely, what remains is a fractal set known as Cantor dust. This set is uncountably infinite, meaning there are infinitely many points in it, yet it has a measure of zero, meaning it occupies no space in the traditional sense. Cantor dust illustrates the intriguing nature of infinity and the counterintuitive properties of sets in mathematics.