• SkyezOpen@lemmy.world
    8·
    2 months ago

    The heck is the grand Gilbert hotel?

    Rephrased, for any countably infinite set, there exists a bijective function which maps the countably infinite set to the set of natural numbers, even if the countably infinite set contains the natural numbers.

    Ah, but of course.

    • Dem Bosain@midwest.socialEnglish
      4·
      2 months ago

      It’s a thought experiment on infinity. If you have a hotel with infinite rooms, and an infinite number of guests, can you fit another guest? You can’t just put them in any random room, because that room already has a guest. But if you shift all the existing guests to the next room in line (guest 1 to room 2, guest 2 to room 3, etc.) all the way to infinity, now you have an empty room 1.

      If a bus with an infinite number of passengers shows up, you can fit them too. Guest 1 goes to room 2, guest 2 to room 4, guest 3 to room 6, etc. Now you have an infinite number of empty rooms.

  • yetAnotherUser@discuss.tchncs.de
    6·
    2 months ago

    Just put the boulder in the first room and tell the guest to deal with it. What are they gonna do? Sisyphus has a massive boulder and plenty of muscle mass to deal with an unfriendly hotel roommate.