Hilbert's paradox of the Grand Hotel
Hilbert's paradox of the Grand Hotel (colloquially the Infinite Hotel Paradox or Hilbert's Hotel) is a thought experiment which illustrates a counterintuitive property of infinite sets. It shows that a fully occupied hotel with infinitely many rooms may still accommodate additional guests, even infinitely many of them, and this process may be repeated infinitely often.
Source: Wikipedia — Hilbert's paradox of the Grand Hotel (CC BY-SA 4.0)