TITLE: What are the ways of proving that the Cantor set is uncountable apart from Cantor diagonalization?
QUESTION [22 upvotes]: What are the ways of proving that the Cantor set is uncountable apart from Cantor diagonalization? Are there any based on dynamical systems?

REPLY [6 votes]: Use a fat Cantor set, and show that it has positive Lebesgue measure. Then, remember that all countable sets are null.