Cantor Set

The Cantor set is a subset of the real line built by starting with the interval from 0 to 1 and repeatedly removing the open middle third of every remaining segment, infinitely many times. Georg Cantor described the construction in 1883 as an example of a set that is nowhere dense yet contains no isolated points. Despite being built by removing almost everything, the Cantor set is uncountably infinite, in one-to-one correspondence with the real numbers themselves, while its total length, or Lebesgue measure, is exactly zero. It is self-similar, consisting of two scaled copies of itself joined end to end, making it a foundational example of a fractal long before that word existed. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/