Say it's 11:00 and you throw 100 rocks in a hole and at the exact same second a rabbit throws one rock out of the hole. Then at 11:30 you throw a 100 rocks in and the rabbit throws one rock out. At 11:45 you throw 100 rocks in and the rabbit throws one rock out and so on, with the time increments halving each time. How many rocks will be in the hole at 12:00? Well one thought is that you've thrown a countably infinite number of rocks in and the rabbit has thrown countably infinite number out so the answer is 0, but say you threw 99 rocks in the hole each time and there was no rabbit then obviously the answer is infinity. Where is the contradiction?