Trolley Memes

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I can't keep up with the new philosophy meta (lemmy.world)

submitted 1 month ago by [email protected] to c/[email protected]

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[–] SkyezOpen 9 points 1 month ago (1 children)

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.

[–] [email protected] 5 points 1 month 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.