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A full infinite hotel can still make room

Imagine Hilbert's Hotel: infinitely many numbered rooms, every one occupied, and a new guest at reception. Moving each guest from room n to room n + 1 frees Room 1 because there is no last room. Explore why a different reassignment can even accommodate a countably infinite busload.

3–7 min

Questions you could explore

  • Why does moving everyone to the next room fail in an ordinary finite hotel?
  • How does reassigning rooms for one new guest differ from accommodating infinitely many new guests?

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3–5 min

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2–3 min

The leap years the Gregorian calendar skips

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