Mathematical
Hilbert's Hotel
A fully booked infinite hotel can still accommodate new guests
Overview
A thought experiment illustrating the counterintuitive properties of infinite sets.
A hotel with infinitely many rooms, all occupied, receives a new guest. The hotel can accommodate them by moving the guest in room 1 to room 2, room 2 to room 3, etc. This frees up room 1, despite the hotel being 'full'.