Suppose you have a hotel with an infinite number of rooms. You're booked solid. A new guest shows up. Can you fit him in? Of course: Just have all of your guests move down one room. This leaves Room 1 open and your guest can take that room. For any finite number of guests, you just have them move that number of rooms down.
You can even add an infinite number of people. Just have every guest move to the room twice as large as they are currently in: 1 moves to 2, 2 moves to 4, 3 moves to 6, etc. This leaves all the odd-numbered rooms empty (of which there are an infinite number), and you can fit them in.
That sounds familiar, is it something to do with Hilbert space?
TTFN,
WK