For anyone wondering how we know the Cantor set is uncountable, here is one way: Take any real in the interval [0,1) Express as a binary expansion

For anyone wondering how we know the Cantor set is uncountable, here is one way: Take any real in the interval [0,1) Express as a binary expansion Convert all the 1's to 2's Reinterpret as a ternary number That forms a bijection between [0,1) and the Cantor set.