How Does The Infinite Hotel Paradox - Jeff Dekofsky Work?

The Infinite Hotel is like a hotel that never runs out of rooms, even when it’s completely full!

Imagine you’re staying at this hotel, and every room has someone in it. That means the hotel is full, right? But then a new guest shows up, and there's still space for them! How? Well, everyone just moves to the next room: the person in Room 1 goes to Room 2, the one in Room 2 goes to Room 3, and so on. Since the hotel is infinite, there’s always a new room at the end, even when it seems like there's no more space!

What happens with a bus full of people?

Now imagine a whole bus of guests arrives, let’s say 100 people! The hotel is still full, but again, there's room. Everyone just moves to the next room, the person in Room 1 goes to Room 101, the one in Room 2 goes to Room 102, and so on. That way, Rooms 1 through 100 are free for the new guests!

It’s like having an endless line of rooms that just keeps going, no matter how many people come, there’s always a place for them! The Infinite Hotel is like a hotel that never runs out of rooms, even when it’s completely full!

Imagine you’re staying at this hotel, and every room has someone in it. That means the hotel is full, right? But then a new guest shows up, and there's still space for them! How? Well, everyone just moves to the next room: the person in Room 1 goes to Room 2, the one in Room 2 goes to Room 3, and so on. Since the hotel is infinite, there’s always a new room at the end, even when it seems like there's no more space!

What happens with a bus full of people?

Now imagine a whole bus of guests arrives, let’s say 100 people! The hotel is still full, but again, there's room. Everyone just moves to the next room, the person in Room 1 goes to Room 101, the one in Room 2 goes to Room 102, and so on. That way, Rooms 1 through 100 are free for the new guests!

It’s like having an endless line of rooms that just keeps going, no matter how many people come, there’s always a place for them!

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Examples

  1. A hotel with infinite rooms can always make space for one more guest by shifting everyone to the next room.
  2. Even if every room is full, there's still room for a new guest because there are infinitely many rooms.
  3. If an infinite number of new guests arrive, each current guest just moves to the room number doubled.

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