This is something I was thinking about. Note that I am not a mathematician, so don't get mad if the answer to this is really obvious. Ok, so define x as the set of all real positive integers. Clearly, this is an infinite set. Now define y as the set of all real positive even integers (or odd, it doesn't really matter). Since y is contained by x, it would seem that x has to be greater then y. But they are both infinite, so they would also seem to be equal. What gives?