If there's a hotel with infinite rooms, could it ever be completely full? Could you run out of space to put everyone? The surprising answer is yes -- this is important to know if you're the manager of the Hilbert Hotel.
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References: Ewald, W., & Sieg, W. (2013). David Hilbert's Lectures on the Foundations of Arithmetic and Logic 1917-1933. Springer Berlin Heidelberg. -- https://ve42.co/Ewald2013
Gamow, G. (1988). One, two, three--infinity: facts and speculations of science. Courier Corporation. -- https://ve42.co/Gamow1947
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Special thanks to Patreon supporters: Paul Peijzel, Crated Comments, Anna, Mac Malkawi, Michael Schneider, Oleksii Leonov, Jim Osmun, Tyson McDowell, Ludovic Robillard, jim buckmaster, fanime96, Juan Benet, Ruslan Khroma, Robert Blum, Richard Sundvall, Lee Redden, Vincent, Marinus Kuivenhoven, Alfred Wallace, Arjun Chakroborty, Joar Wandborg, Clayton Greenwell, Pindex, Michael Krugman, Cy 'kkm' K'Nelson, Sam Lutfi, Ron Neal
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Animation by JD Pounds and Jonny Hyman
Thumbnail by Iván Tello
Music by Jonny Hyman and from Epidemic Sound and E's Jammy Jams (Hotel Lavish - Radio Nights, Steps in Time - Golden Age Radio, What Now - Golden Age Radio, Book Bag - E's Jammy Jams, Arabian Sand - E's Jammy Jams, Firefly in a Fairytale - Gareth Coker)
Written By Derek Muller and Alex Kontorovich
Sound Design by Jonny Hyman
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I like to come back to this video every once in a while. It's well animated and discusses things in an impressively simple and easy to understand manner.
@Bigboy-dan Says:
The thing is if there is a infinite amount of people the planet would collapse into a supermassive black hole
@vinfinityguy Says:
what if you name the rooms after the infinite sequences of As and Bs, therefore there will always be another room for each person, just like there'll always be another name in the infinite sequence of As and Bs? Then it can absolutely fit a countable infinity, and would probably spin an argument online on whether theres more people than rooms, if you pit Vincent's Hotel against the Bus of As and Bs
@Abdeena Says:
Oh well
@ScottMStolz Says:
Just put the infinite AB people in a queue, and assign them a number, incrementing by one each time. Then use that number to assign the rooms.
@mouleeshwaran5776 Says:
What if the blue guy opened Infinite Hotels with Infinite rooms!
@CodyBarr-m2l Says:
Infinite is not possible
@peemiguesssecondary Says:
Just bring infinite busses with infinite people, problem solved
@HerricktheMildlyPerturbed Says:
"but that's a video for another time" 5 years later and the video that's referencing either isn't up or isn't linked in the descripiton. wtf.
@zunerashahid949 Says:
Gilbert Hotel
@Ilikelores Says:
Infinity is really just the opposite end of 0. It keeps getting larger depending on the context, as everything kinda approaches 0 but never reaches absolute 0
@neildavidson6360 Says:
Imagine the queue for coffee at breakfast.
@pontuseuxinus1958 Says:
If the hotel get full then is not infinite anymore and infinite hotel to be rly infinite should work like this: every time a person move in another room is being built,like this the hotel never run out of rooms.
O.T. The question should be ,if all the infinity of the living ppl stay in the hotel,the hotel get full??
@lolski13 Says:
A bit late, but I have a few questions.
If you have infinite rooms filled with infinate guests.
And ask everyone to go 1 room to the right, isnt that infinity -1?
And if you have all odd numbers free, isnt that half of infinity?
@Wallace_1123 Says:
"Different sized infinities"
Then why are they even called infinite? 💀💀💀
@heytherehowdy Says:
What if you designated each Abba person on the party bus a number? Then they would fit, right?
@Niiiiiiian Says:
It is an infinite hotel though, ppl will leave after the second time they have to move
@Niiiiiiian Says:
The manager can write down infinite numbers but can’t keep track of the occupied rooms so ppl wouldn’t have to move every time a single person arrives?
@sukanyavodapelli Says:
1:19 we need money more than beast jimmy to build that big bus 😂😂
@aaronliu230 Says:
Hotel owner with infinite numbers in the bank account😊
@MuhammadShahbaz-xl2vk Says:
It can work . let's say A=1 and B=2 . The hotel manager will tell all guests in any room that has 1 or 2 to go to the next room that doesn't have 1 or 2 . Room number 1 will go to 3 and 2 will go to 4 and 3 will go to 5 and 4 will go to 6 and so on. Now we have all rooms that contain 1 or 2 empty. Now everyone will go into the room number according to their name . We will translate AA to 11 and BB to 22 and AB to 12 and so on. Every number imaginable in the list will have a room according to it.
@LandonLord-o1z4k Says:
however a infinite amount of people means their is a infinite amount of math so the people lowkey collapse into an infinite blackhole
@Shister_gd Says:
2:03 just say no goddamnit
@latifasidelkhier6943 Says:
What if you had 3 .5 billion infinite rooms
@sparks3894 Says:
If an infinite hotel has all rooms filled up then its just PR. They are scamming you or maybe their space character in ads is tiny "Come In finite hotel" 😂
@4xd7 Says:
Nga what are you talking about😂😂😂
@aHMeDaLi-ig2hb Says:
The fact that he made the long form video 5 years ago is insane
@AnshSingh-h3h Says:
5:10 when bro said "countably infinite" my brain blasted
@fantastikkabak Says:
i didnt understand
@arbitrarynumberz Says:
"Suddenly, to Hilbert's dismay, a bus of infinite Karens pulls up."
@patakdaca428 Says:
Istg this was more then 5 yrs ago
@peizhang3040 Says:
“Why not just construct infinite infinite hotels”
@Sneedle23 Says:
Took the words right out of my mouth
@FahimAmsyar1209 Says:
Respect to the person who made it
@feeniedefenseattorney Says:
i watched this when it first came out and the graphics traumatised me
@Giorgees1 Says:
Why I Am Watching This
@Yappa-u1b7n Says:
Why?
@TheColdRain777 Says:
The energy required to keep all the lights on in this hotel is an infinite amount of universes each second worth of energy 😂
@Nigel_B Says:
Is there an infinite number of cockroaches or blocked toilets?
@JacobAndHisChannel Says:
I finally got it after 5 years 😭✌️
@Plethorial Says:
5:33 I don't it's so mind blowing to get to know that infinite factorial is bigger than infinity
@vi0let831 Says:
The characters look so silly I love them. Altho they're a bit eerily realistic lol
@hutmitfrosch3030 Says:
Ok, we fit everyone from the infinit number of infinit busses in - but what about those, that are already in?
@mkay6089 Says:
IF it is infinite then there is no limit...
@noahkirkpatrick8912 Says:
If you can put a number on infinity, then it's not infinity. It's only a number when you observe it.
@TheJes8p Says:
i know this is an old video, but everytime i think of it im like "who came up with this??"😂😂
@0011peace Says:
your mistake is thinking infinity is number its not. what you have is artifact infinities for something to be truely infinite it has infinite in an infinite number of ways
@michaelbjorck8112 Says:
Great video! ❤
@abhisek-chatterjee Says:
So that's why The Eagles wrote "You can check out any time you like, but you can never leave."
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