How An Infinite Hotel Ran Out Of Room
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.
References: Ewald, W., & Sieg, W. (2013). David Hilbert's Lectures on the Foundations of Arithmetic and Logic 1917-1933. Springer Berlin Heidelberg. --
Gamow, G. (1988). One, two, three--infinity: facts and speculations of science. Courier Corporation. --
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
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

  • An ordinary fish
    An ordinary fish

    Make a rip off from ted ed, get~5,5 million views

  • Whiteling 299
    Whiteling 299

    2:00 well that’s still just infinity so you what you did with one infinite buss

  • MrCombat

    Ah yes, this will help me a lot next time I’m in charge of an infinite hotel and giving a room to “ABBABABABABAAAABABABAABBBAAABAAAABABBBBAABAAAA…”

  • Return31

    You just broke my brain

  • Sad Sadif
    Sad Sadif

    No... if there are infinite rooms and infinite people and an infinite;y long bus shows up with infinity more people - there's *nothing* you can do. There's no much mass that you're in a singularity. Game over.

  • Petra Solano
    Petra Solano

    what about cleaning the rooms though

  • 1w

    How tf can u make a infinite numbered spread sheet ITS INFINITE

  • Kevin Ghandour
    Kevin Ghandour

    What if I arrive tired and he goes like 'your room is room 36,003


    I give up thinking at 2:00

  • Holy Yoghurt Man
    Holy Yoghurt Man

    I dont get how that diagonal rule works. Does anyone know where I can find an explanation for this?

  • Joe Garza
    Joe Garza

    A bus with an infinite number of hookers shows up , where do you put them .. hotel attendant ... meet me in my office

  • kanak sharma
    kanak sharma

    Well will you even be able to call all the customer to move rooms ahead

  • Tangetpine



    Sir you’ll be in room 9000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

  • Furkan Baysal
    Furkan Baysal

    veritasium: everybody can fit into the hotel as long as they don't identify themselves with some weird name me: that sounds familiar

  • Ashierkun

    The word infinite has lost all meaning

  • TCRG

    All they needed to do is move every customers to a room twice the original number. (eg. I was in room 5, so i’ll move to move to room 10) wait nvm

  • Marco FD
    Marco FD

    Doesn't make sense to me? 😅It says infinite

  • G-360

    2:42 .... Wait I've seen this somewhere... Highschool chemistry flashbacks,

  • Student

    This somehow reminds me of P.M.I. in discrete mathematics.

  • Mooie Steen van Henk
    Mooie Steen van Henk

    I say like: WAIT, WHAT

  • Peter Ruiz
    Peter Ruiz

    This is why math never made any sence to me. I don't mean basic adding, and decimals, ect. I mean, the way math is taught, and there is no real objective or project. Just exersizes in who knows what. Yes, math relates to everything. But not the way it is taught. Now, folks are going to write and try ro explane things... Ir ,or ,be insulting....Forget it. I do fine without silliness.

    • eggynack

      I'd argue the opposite is actually true. Math education tends to be very... utilitarian. You learn these rules and techniques so you know what to plug into a spreadsheet, or at the top end what to plug into a big physics computer. It's all about climbing this weird math ladder that will ideally lead you to some lucrative job if you're interested in the right field. And, y'know, it's boring as all hell. Rote memorization and drilled repetition of steps. But real math, the topic in its most essential form, it's more like this video. Taking a set of facts and using them to prove something with endless possibilities of approach. It is, at its core, an art. Ignore for a minute what it relates to, whether you can find use for endless hotels in some job. Isn't it kinda, I dunno, pretty? The way all these ideas combine into this elegant and perfected whole, giving rise to unanticipated results. It can be a thing of beauty if you get deep into it, and education frequently alienates us from that beauty. Math can absolutely be plugged into any variety of materially useful things, rocket ships and GPS and cellphones, but often it's pursued on its own terms. Cause it's weird and beautiful.

  • Some guy who pays Roblox
    Some guy who pays Roblox

    I’m surprised I understand the video and not kill my brain cells.

  • Muhammed Yaseen
    Muhammed Yaseen

    Infinity can't exist in a finite world

  • Michael Frikke
    Michael Frikke

    Why move everyone 1 room ahead ? The new person takes the next number ?

  • Asbrayn

    Cant you just "create" a new room for every new guest ? If there are no limitations in the number of rooms you can possibly just always add a room more. Maybe im just stupid but if there really are no limits in terms of room numbers then I dont get the problem here

  • Will That3dPrintguy
    Will That3dPrintguy

    Infinity is infinity….it’s the same size infinity……stupid

  • Giriraj Kr Saikia
    Giriraj Kr Saikia

    He also got infinite money😂making him/her the most rich creature in the infinite universe😁

  • Dominik Tősér
    Dominik Tősér

    infinity my phone: 1e309, TAKE IT OR LEAVE IT

  • Jessie Michael
    Jessie Michael

    This is exactly one of the things my lecturer tried to explain to us and I just didn’t understand it AT ALL Especially the ABBBAABBABA part, so thank you so much for explaining it! Hopefully this will help me enough to pass my test this week :,)

  • FMJ

    Just tell them to find their own rooms

  • Zoheyra Bent BoRouis
    Zoheyra Bent BoRouis

    What happens when it's time to change the bed sheets?

  • Imposter

    I’ve lost some brain cells how infinity is not infinite

  • Ashley ♡
    Ashley ♡

    the thing is, this is a impossible problem to begin with. sure "some infinities may be more dense than others" but it shouldn't matter the density if the amount of time will still be.. infinite. a infinity the same density as the infinity of the hotel would still never fill the hotel because it would take infinite time to do so, the same would apply no matter the density of the infinity. you are expecting an end on something that by definition has none.

    • eggynack

      Density has nothing to do with it. Neither does time. The big bus simply has more guests than the hotel has rooms. Not at a certain point in time that gets resolved later, just always.


    At least you would make an infinite amount of money

  • Florence lea
    Florence lea

    I don’t get it… even after watching the video and paying such close attention it makes no sense :|

  • S t u c k a t 1 6
    S t u c k a t 1 6

    Im not settled with the list naming problem, Why the time is not factored in ? since the list is infinite which means its ever going and while you're taking letters from each row creating your non-existing guest's name what are the chances that whatever you come up with (If you come up with it in the first place since the names are infinite as well you'd never get to the end of finishing your name) is yet to be written on your on going names list.

    • eggynack

      Time isn't really a part of this. You say what the rules of the list are and then there just is the list. It's a math object, not a material one. For example, 1, 2, 3, 4, 5, 6... is a list of the natural numbers. All of them. You get how the pattern works, so it's completely done. Similarly, when we assume some list of the names on that last bus, it's a completed list. And the new name is provably not on it.

  • sergio menicucci
    sergio menicucci

    After this video I've got infinite headache

  • Kian G
    Kian G

    how about you tell everyone to double the room numbers (2->4 ; 3->6 ; 4->8 and so on) then you have an infinte amount of rooms? An other option would: room Nr. 1 takes the first prime number (2), the second room takes the 2nd prime number (3) and so on. Since there are infinite prime numbers, there are no problems with it. In the end you would have even more free rooms then with the first soloution right? I dont realy get the differnce between your "problem-case" and the version with the "normal" infinite bus version.

    • Kian G
      Kian G

      hmm I still dont get it all but I think I understand it better now. Thanks for the response

    • eggynack

      The problem is that the last bus simply has more guests. The previous busses are akin to the natural numbers. The integers. The rationals. The last set though, that's structured like the real numbers. Infinitely long strings of digits, or letters as the case may be. And the proof that it's a larger set is what is being presented at the end of the video. You could empty the entire hotel and you still wouldn't have enough room for that bus. Hell, you could empty the hotel, fill it with passengers, empty it again, refill it with passengers, and just keep doing that infinitely many times, and still you wouldn't be able to accommodate the big bus.

  • Jesperado

    The problems mathematicians make up are very interesting and weird.

  • That Mask
    That Mask

    Dumb no cleaners

  • The Urban Crystal Healer
    The Urban Crystal Healer

    No! How did the infinite numbers of room get full in the first place?

    • eggynack

      Take each room and put a person in it.

  • Harsh Sharma
    Harsh Sharma

    Just say "keep walking until you find an empty room :D"

  • lilsmile01

    This is a weird universe of infinite everythingf

  • Undesignated

    Why don't you just put the hotel corridor on an infinite electronic belt so it just moves a an empty room to the front advise them it's free and no names required no maths required just human what do ya call it.

  • איתי גולן
    איתי גולן

    infinity is not finite. it doesn't matter, I think that it will take infinite time to put them in a room,but I see the video trying to organize the people then to solve the problem, you can even put everyone in the end of occupied rooms (if they ever reach there lol) and it will be fine. I agree that there are infinities that are "bigger" than others, but it is not the right terminology to say that there isn't enough from the infinite to contain the other infinities I didn't learn about infinities,so maybe I don't get the point very well,but sharing my thinking 😁

  • Mick Marty
    Mick Marty


  • Xanderbear1155

    What I watch at 3:00 am

  • poison girl
    poison girl

    My mind is fucked up now

  • Nemo Sundry
    Nemo Sundry

    This is just a bunch of contradictions and nonsense that shows infinity can't be documented. Infinity is probability before it becomes reality.

    • allee

      Sure mathematician, I'm sure you know about infinity more than the people who spent years learning about it.

  • Syamil Mukhtar
    Syamil Mukhtar

    I wonder how much they need to pay electricity and water bills

  • Loving Life
    Loving Life


  • Iddar Adingad
    Iddar Adingad

    Infinite Hotel with infinite guests; that means the hotel is full!

  • Curtis Han
    Curtis Han

    so if there's no vacancy and a new person comes in, how would moving ppl to a different room help making a room vacant? The only way to give the new person a room would be to evict an occupant. And if there are infinite rooms, why would it not have vacancy? How would moving people to different rooms help make room for new people?

    • eggynack

      You do not have to evict an occupant to make room for a new one. That is precisely why moving occupants helps. Look, imagine the hotel had 100 rooms, yeah? You move everyone up a room and it works fine. Except then you get up to the hundredth guest and you have to chuck him off the roof to make way. With an infinite hotel though, there is no last guest. You can just move everyone up and there isn't even a roof to chuck someone off of. Y

  • TheEightyFith

    wtf is the animation lmao

  • Tracker Plaz
    Tracker Plaz

    I don’t get it but I watch it.



  • Pogchamp

    Everyone gangsta till you get the last room

  • Random Grass Patch
    Random Grass Patch

    The numbers, Mason! What do they mean?

  • Epic Muffin
    Epic Muffin

    my brain hurts

  • U Weird
    U Weird

    These characters got me dying 😂 😭

  • DatBigBoi

    My dumb selfs brain hurts so much that idk what pain is

  • Jaiven Wright
    Jaiven Wright

    I lost brain cells while watching this

  • justSTUMBLEDupon


  • Joaquín Gutiérrez
    Joaquín Gutiérrez

    Amazing video!!! Thank you

  • Void

    Wait what? Infinity can’t run out, even if it takes infinite time it still can’t run out...

  • Hello Person
    Hello Person

    thats a lot of walking

  • YeetGamer27

    Honestly, the only thing I was thinking about is how someone past 10000 rooms can even walk that far or find their room

  • Luka Benedičič
    Luka Benedičič

    just tell the new ones to find the first room thats free

  • Lit

    But is it possible to have infinite different keys of the same length? And if not, how likely is it that my key opens someone elses door when I try it on some random door?

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