A while ago a math teacher of mine told a little story about a demon that's being chased by an angel. The demon goes into a hotel with an infinite number of rooms, and randomly picks a room to hide in. The point of the story was that if the angel only gets to look behind one door, there is no possible way that he could ever find the demon. Since the odds of the demon being in the room that the angel randomly selected are 1 over infinity, the chances of the angel finding the demon on the first try are exactly zero. I thought about this for a while, and it seems like there's a problem with the concept of the scenario. Specifically, it seems like this argument could also be used to prove that the angel couldn't look behind any door, since before the angel selects a door you could prove that the odds of any given door being selected are zero - and how could the angel ever pick a door if every potential door that might be picked has zero chance of being selected? But on the other hand, there are an infinite number of doors to choose from, so it seems like the angel should be able to pick one. So is the concept of randomly picking one choice from an infinite set of choices even mathematically meaningful? Does the very statement of the scenario violate the rules of math by assuming that the angel can randomly pick one room to look in from the infinitely many rooms available?