How Does Hilbert's Infinite Hotel - 60-Second Adventures in Thought (4/6) Work?

Hilbert’s Infinite Hotel is like a super special hotel that can always fit more guests, even when it's full.

Imagine you’re in a hotel where every room has a number, Room 1, Room 2, Room 3, and so on, forever. That’s the Infinite Hotel! Now, suppose it’s completely full, every single guest is in their own room.

But then a new guest arrives. What do we do? Well, we just ask everyone to move to the next room over. The person in Room 1 moves to Room 2, the one in Room 2 goes to Room 3, and so on. That way, Room 1 becomes free, and our new friend can have it!

Now imagine a bus arrives with infinite people. We just ask everyone to move to the room with twice their number. So the person in Room 1 moves to Room 2, Room 2 goes to Room 4, Room 3 goes to Room 6, and so on. That opens up all the odd-numbered rooms, where our infinite new guests can stay.

It’s like having a never-ending line of rooms that always makes space for more friends!