For an example of just how counter-intuitive infinity is, consider Hilbert's Grand Hotel. If a hotel has a countably infinite number of rooms, all of which are

For an example of just how counter-intuitive infinity is, consider Hilbert's Grand Hotel. If a hotel has a countably infinite number of rooms, all of which are full, the hotel can still house new guests. In fact, it can accept a countably infinite number of new guests. That is why you can't simply divide infinity by infinity. http://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel http://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Gran...