Can someone explain how the Cantor set can be uncountable but also contain no intervals? I am assuming that as k goes to infinity, we are left with 0 and 1 in the final interation so the set is finite with those elements. The set of natural numbers is countable so I can bijectively map every Cantor interval to an element in N, right? So it seems countable to me with no intervals. But my notes say the opposite.