The Intuitive Idea of Rare and Common Is False

There is no such thing as a typical room number at infinity hotel. The intuitive idea that there must be typical or average members of any set of values is false for infinite sets. We might think that half of all natural numbers are odd and half even, so that odd and even numbers are equally common amongst the natural numbers. But consider the following rearrangement: One, two, four, three, six, eight, five, ten, 12, seven. And this would make it appear that the odd numbers are half as common as the even numbers. So every guest in the hotel is more privileged than almost all other guests the clechade politicians promise to favor. Every one can be