Hotel Infinity

The Hotel Infinity paradox is used to explain the concept of infinity. Picture a hotel in your mind. Try to imagine that this room has an infinite number of rooms with an infinite number of guests staying in them. Now, imagine you walked up to the reception and asked for a room. Unfortunately, the infinite rooms are full of infinite guests, meaning there is no room at the inn for you. Luckily, the desk manager has a brainwave. He says: “I’ve got it. I’ll just move the guest in Room 1 to Room 2!” And he does. He moves the guest that was in Room 2 to Room 3, and Room 3 to Room 4, and so on—an infinite number of guests getting bumped deeper into the infinite number of rooms. This seems perfectly reasonable. However, the hotel originally had an infinite number of guests and now it has infinity plus one. So which number is really infinity?