I'm gunna have to be one of those people that says "really? O_o" when presumably everyone else clearly grasps the concept.
I get that if you had an infinite number of rooms, and an infinite number of guests staying, you still have room for an infinite number more guests.
But in your example, surely "occupied" is, more than just an indicator of another guest, a state of the room. You have an infinite number of occupied rooms, but zero unoccupied rooms, so no space for more guests.
I get that if you had an infinite number of rooms, and an infinite number of guests staying, you still have room for an infinite number more guests.
But in your example, surely "occupied" is, more than just an indicator of another guest, a state of the room. You have an infinite number of occupied rooms, but zero unoccupied rooms, so no space for more guests.