Yeh, U[0, 1] is different because it assigns non-zero probabilities to intervals, not points. In this case we're assuming that we live in an uncountable populat

Yeh, U[0, 1] is different because it assigns non-zero probabilities to intervals, not points. In this case we're assuming that we live in an uncountable population (each real in [0, 1] is a person), so you can't do things like assign a unique number to each person. There, even if the maniac goes on kidnapping forever, he will only kidnap a countable subset of the population. Thinking about this honestly makes my brain hurt a little.