Hilbert imagines a hypothetical hotel with rooms numbered 1, 2, 3, and so on. The hotel is full and new guest arrives wanting a room. I can not move any guest. So i say to new guest wait 1 sec a new room must become available as Infinite guests one must leaving at any time.
is this good answer?
Why not ask them to move to room 2N+1? Then you could accommodate an infinite number of new guests (all the rooms 2N are now empty) before having to ask anyone to move again.
As I understand, that works too, and leads down that path to exploring the multiple ‘levels’ of infinity.
That’s how you handle an infinite number of people showing up and needing rooms.
It was probably 50 years ago but I loved Hotel Infinity movie.