Can an Infinite Hotel Run Out of Rooms?
David Leshem
What if I told you that I would pay for your trip to a dream destination? You have the location picked out, the activities planned, and the flights booked. Lastly, you need a place to stay. You choose the fanciest hotel in town. Unfortunately, this hotel has a finite number of rooms, and due to some procrastination, they are fully booked. What a shame. Luckily, you hear about an “infinite hotel” that is just a few doors down from where you wanted to stay. The name of this hotel is Hilbert’s Hotel, named after the findings of famous mathematician David Hilbert.
Hilbert’s Hotel
Hilbert’s Hotel has an infinite capacity, and the management promises that it can find space for anyone. Let’s investigate if this is true. Each room is assigned a Natural number starting from 1, 2, 3, and extending to infinity. Imagine the hotel is full. There are an infinite number of people staying in the hotel with an infinite number of rooms. However, they can accommodate you. The manager of the hotel will simply ask the person in room 1 to move to room 2, the person in room 2 to move to room 3, and so on.… Read the rest