How An Infinite Hotel Ran Out Of Room?

The infinite hotel had endless rooms, but one day, it ran out of space because of a special trick with numbers.

Imagine you're playing with blocks, each block is a room in the hotel, and every time someone arrives, you give them a new block. But this hotel has infinitely many blocks, like having a never-ending line of toy boxes.

One day, every single room was full, there were people in all the blocks. But then, a new person arrived! How could they get a room?

The hotel manager had a clever idea: he asked everyone to move just one block over, the person in room 1 went to room 2, the person in room 2 went to room 3, and so on. Because there are infinitely many rooms, no one ran out of space! The new person could take room 1.

But then, infinitely many more people arrived all at once, like a never-ending line of friends coming for a playdate! The manager smiled again: he told everyone to move to the next even-numbered room, room 1 went to room 2, room 2 went to room 4, and so on. That freed up all the odd-numbered rooms, giving space for all the new friends.

Even with infinite people, there was always a way to make more room!