The Infinite Hotel Paradox [5:59]


The Infinite Hotel Paradox, created by German mathematician David Hilbert, is one of the most famous thought experiments in philosophy and mathematics.  In short, imagine an infinite hotel with all its rooms filled.  But then, the next day, a couple comes looking for a room.  Before turning them away the manager gets an idea: the people in room #1 will move to room #2, thus opening up the room for the new couple.  But what about the people in room #2?  Well they’ll go to room #3, and so on.  That way every single guest with a room has a new room to go to and the couple that just arrived will have a room too.  The same happens when you have an infinite number of new guests arriving!

Discussion Questions

  • Thus this paradox about infinity mean that the concept is meaningless?  Or is it just beyond our understanding?
  • What other paradoxes about infinity can you think of?
  • What did the video mean by “the lowest level of infinity”?

Keywords: philosophy, thought experiment, Hilbert, math, mathematics, infinity,


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