How An Infinite Hotel Ran Out Of Room

324 000 Көрүүлөр 6 млн

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., \u0026 Sieg, W. (2013). David Hilbert's Lectures on the Foundations of Arithmetic and Logic 1917-1933. Springer Berlin Heidelberg. -- ve42.co/Ewald2013

Gamow, G. (1988). One, two, three--infinity: facts and speculations of science. Courier Corporation. -- 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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Жорумдар

  1. Lowraith
    Lowraith
    15 мүнөт мурун

    I call no on this one. Convert all As to 0s, and Bs to 1s, then shift them from binary to decimal base. You now have an infinite number of unique positive integers, EXACTLY like when you had a single, infinite bus show up. Each person's binary-converted name equates to their seat assignment in the bus. Then you just use the same solution you used on the bus. If that can't work because of the unique diagonal, THEN THE BUS COULDN'T HAVE WORKED EITHER, FOR THE SAME EXACT REASON. This is a logical error, ultimately. You see, the string of characters formed by the diagonal is itself infinitely long. Which means you can never resolve it in the first place. It's meaningless. The name/number will never be on the list, because it is, itself, one of the forms of infinity. And infinity is not a number. It's a concept. This fails to prove that you can't house all the guests, because there will never be any particular guest with an infinitely long name.

  2. Sumit Kumar
    Sumit Kumar
    36 мүнөт мурун

    You would need an infinite amount of money funded by infinite number of owners and an infinite number of workers to make a hotel with infinite number of rooms and an infinite number of staff to run the hotel and infinite amount of mathematicians to deal with infinite amount of money . Find the mistake and you'll get the infinite amount of profit made by the hotel with..... "repeats again" 😂😂

  3. yan wu
    yan wu
    Саат мурун

    Bruh, I spent 6 minutes of my life watching a video, hoping I would understand so I can teach my friends but I didn’t

  4. Jaewon Cheon
    Jaewon Cheon
    Саат мурун

    카운터에 한글이 있네

  5. Eleanor Conway 2!
    Eleanor Conway 2!
    2 саат мурун

    Ababbabaabaababababbababababababababaabbababababababababbababababababababababaabba

  6. Vung Muan Ching
    Vung Muan Ching
    3 саат мурун

    wtf ;_;

  7. Jaime L
    Jaime L
    3 саат мурун

    Welcome to The Hotel California!🤪

  8. Speed Junkie
    Speed Junkie
    4 саат мурун

    I understood the logic, but I still don't understand the logic

  9. Jyoti Prakash Das - 08
    Jyoti Prakash Das - 08
    4 саат мурун

    U could again assign the name of all the people with the seats infinitly and give them the room

  10. Harshita gupta
    Harshita gupta
    6 саат мурун

    Wait will someone tell me what purpose this vdo serves..... P.S- I'm here for the frst tym

  11. Stifler2277
    Stifler2277
    7 саат мурун

    Look "infinity" is a concept and not a number. For instance, how many numbers is between 1 and 2, you get 1.0000000......infinity...1 up to the number 2 ( 1.0000001, 1.0000002, 1.0000003.........) So are there more numbers between 1 and 3, than between 1 and 2? It makes sense that there must be more numbers between 1 and 3 than between 1 and 2, but theoretically there is not, since infinity is a concept and not a number since: n+1> 1 So in conclusion infinity + infinity is not > than infinity, you cant count infinity and you can neither assign a character (x) in it.

    1. Brien831
      Brien831
      3 саат мурун

      We are not talking about numbers, but sets and their sizes. You can determine, if two sets are the same size if you can find a bijection between them. A bijection is a map, that maps one element of one set to exactly one element of the other set and vice versa. For example there is a bijection between the natural numbers, and the rational numbers, wich means they have the same size. However for every open interval in the real numbers, for example (0,1) there exists no bijection to the natural numbers. In mathematics we say the set of all real numbers in (0,1) is uncountable, and for the rational numbers we say they are countable. Now in fact the set of all numbers in (0,1) has the same size as the real numbers as there exists a bijection even though the real numbers cover (0,1). If you want a more intuitive definition about set sizes, you may want to look into measure theory.

  12. Andrew Ye
    Andrew Ye
    7 саат мурун

    infinite can not be "complete"

  13. Andrew Ye
    Andrew Ye
    7 саат мурун

    One thing I am confused on. When describing infinity, we are still giving it a finite set amount, not an infinite. This still doesn't work. Infinite isn't something we can do/explain.

  14. Rishabh Raj XB 39
    Rishabh Raj XB 39
    7 саат мурун

    Our mathematics teacher once tried to explain the concept of infinity to us, but he ended confused himself.😂 I'm gonna share this video to him.

  15. Anakin Skywalker
    Anakin Skywalker
    9 саат мурун

    After watching this video, you made me believe that infinity is finite ☹️

  16. MONEYBOY512
    MONEYBOY512
    10 саат мурун

    This is not even a realistic situation

  17. MONEYBOY512
    MONEYBOY512
    10 саат мурун

    How does this help me

  18. Hm
    Hm
    10 саат мурун

    "Just go in an empty room"

  19. Steve Newcombe
    Steve Newcombe
    11 саат мурун

    I just got my head around the hotel then these freekin huge busses start rocking up; loads of em. Just how big is the car park?!

  20. A S
    A S
    11 саат мурун

    We all know "Uvuvwevwevwe Onyetenyevwe Ugwemuhwem OSAS" aint getting a chance at this hotel.

  21. Balaji MD
    Balaji MD
    12 саат мурун

    This is really entertaining but conceptually wrong.. We can better understand the concept of infinity by the Indian word 'Purnam'.. Below is a famous verse which can make you realize the absolute.. Term 'Infinity' is a cheap version and has lost the value overtime.. FYI: 'OM Purnamadah Purnamidam Purnat Purnamudachyate Purnasya Purnamadaya Purnamevavashishyate'

  22. Chip Vos
    Chip Vos
    12 саат мурун

    "You pull out an infinite spreadsheet of course" - of course 😅

  23. olgierd ogden
    olgierd ogden
    13 саат мурун

    I’d like to comment but my answer is to long)))..

  24. Archie Areopex
    Archie Areopex
    18 саат мурун

    This is... mind blowing..

  25. Derek Nereida
    Derek Nereida
    19 саат мурун

    The good meat byerly scold because list demographically obey till a equal work. accidental, last encyclopedia

  26. Rob Gibson
    Rob Gibson
    19 саат мурун

    When you have infinity + 2 guests. Duh.

  27. Zander Leslie
    Zander Leslie
    20 саат мурун

    Its infinite cause they break there legs on the way there

  28. Chloe Chong
    Chloe Chong
    21 саат мурун

    I lost all my braincells when watching this entire video

  29. Nico Pauly
    Nico Pauly
    21 саат мурун

    I’m glad I now know what to do if I’m ever put in this situation. Thanks!

  30. Jada Lydia
    Jada Lydia
    22 саат мурун

    I think people aren’t going to like to be moved

  31. Global warming is hot
    Global warming is hot
    23 саат мурун

    Could they not just accept everyone and have them walk until they find an empty room?

  32. Hannah K. V.
    Hannah K. V.
    23 саат мурун

    I know the KGshows comments section is a stupid place to ask a question like this, but I'm going to ask it here in case anybody knows: At the very end, there is 1 creature that has a different sequence of A's and B's than the infinite amount of other creatures. It can't be more than 1, since there are only 2 letters to choose from, and you've already switched 1 of those in each other creatures' to come up with this one that is different. But since this is only infinity + 1 + infinity (those already at the hotel), couldn't you put the 1 first, and then arrange the rest according to even and odd numbers? I've seen the ABBA thing done with decimals in other videos, so let's do it with those as well. For numbers, you could add 1, or 2, or 3, or subtract 1, 2, 3, etc. as well. Let's say you could subtract/add/whatever to these numbers to produce an infinite amount of decimals that are different from the original infinity. Well, in this case, you'd have infinity (original) + infinity (those you just found that are different from the original) + infinity (those at the hotel). So couldn't you just put each person in a room in multiples of 3? There are infinite number of them, just like the multiples of 2. Wouldn't that mean that all infinities are the same, and countable/uncountable infinities don't exist? Obviously there are different infinities, so why wouldn't these work? Please help, I've had this question for months now and I still haven't found an answer.

    1. eggynack
      eggynack
      20 саат мурун

      @Hannah K. V. It's not that they're infinite together. There's no need to combine anything with anything else. The set is simply uncountably infinite unto itself. The point of the proof isn't that you have this infinite list and then you can add one to it, or add infinity to it, or even add uncountable infinity to it. The point is that, no matter what list you produce, it will always be incomplete. It could be some specially designed list, or a completely arbitrary list, or anywhere in between, but it will always be missing something. A list of the evens, the odds, the naturals, the integers, all of these are very possible. Nothing missing. The reason why what I did above was interesting was because it demonstrates something we already knew, that an attempt to list an uncountably infinite set will always, always, be missing an uncountably infinite set's worth of elements.

    2. Hannah K. V.
      Hannah K. V.
      20 саат мурун

      @eggynack What I don't understand is why the second infinite list of numbers is the same as the first, but together they're uncountably infinite. Why doesn't infinity x 2 = infinity? Earlier in the video it was mentioned that when you have 2 infinite sets, you can match 1 with the evens and 2 with the odds. So why can't you do that with the original set of infinity and the new, different set of infinity? I hope this makes sense it's difficult to explain lol

    3. eggynack
      eggynack
      21 саат мурун

      The amount of numbers you're missing isn't simply one, or even infinite. It's uncountably infinite. What's left over is exactly as numerous as the set you started with. There's actually a pretty cool way to do create such a set of missing numbers via the diagonal argument, though I dunno how to do it offhand with the binary set presented here. Just with the base 10 representation. But check it. Consider a list of the reals between 0 and 1. .4987891234... .1972304802... .7171717171... .9999199999... .3141592653... and so on. So you do the standard diagonal trick, adding one to each of the digits along the diagonal, getting you .50806... But, as you note, you can also add two to each digit, getting .61917... Or, y'know, you could alternate between 1's and 2's, getting .60907... Or, and here's the cool part, you could use literally any combination of 1's and 2's and you'd get a new number. And we can represent these as decimal numbers, with, for the sake of argument, the 1's replaced with 0's and the 2's replaced with 1's. So the ones so far are like .0000... .1111... .1010... and so on. Except what do ya got when you have literally any combination of 0's and 1's after a decimal point? You got the set of all real numbers between 0 and 1 in binary. Which, y'know, that's just the set of all real numbers. In other words, in attempting to list the set of all real numbers, you missed literally all of them. 100%. And you can't do any better than that. Any attempted list will miss as many numbers as were in the original set. It is a far greater infinity than the infinity of the list, or the hotel.

  33. Trexy Lemur
    Trexy Lemur
    23 саат мурун

    is anybody gonna talk about how ted-ed did a video similar to this also im not saying he copied their video but it was a really good ted-ed video

  34. Daniel Röder
    Daniel Röder
    Күн мурун

    But there is a way to fit all guests into unique rooms. Just tell them to treat their name as binary instructions to find their room, A = 0 and B = 1. For example, if their name starts ABBA... then they add 1 ( as offset because first room is called 1) + 0*1 + 1*2 + 1*4 + 0*8 ..... so after the first 4 letters that guest would stand before room 7 and then calculate his next step. Everyone is guranteed to have a unique room this way. The guest at room 1 would have all As in his name, the guest in room 2 would be named B followed by infinite As. Every guest would have a unique room to himself after infinite calucations for the room number (which might be slightly annoying for the guests but gives you enough time to write the guestlist...). If there is another person at that room, that guest would have the exact name so that can't happen as we know. Your room list would look something like this: AAAAAAA.... BAAAAAA.... ABAAAAA.... BBAAAAA.... AABAAAA.... and so on. The argument with the name that doesn't appear on the list: If you start writing out the first letters of the first names of the list you will see that the technique of switching the letters on the diagonal will generate a string consisting out of all Bs. Because on the diagonal there will only be As going down the list. Otherwise it would mean that the two graphs Y=f(2 to the power of X) and Y=f(X) )intersect for a number X > 0. "All Bs" happens to be in the last room and at the end of that infinite list, because by definition it is on the opposite end of "All A", the guest who has to add every 2 to the power of X term.

    1. Tom Svoboda
      Tom Svoboda
      13 саат мурун

      which room does BBBBB... get?

  35. Mechros
    Mechros
    Күн мурун

    There's so much that doesn't make sense. For example there are an infinite amount of people on an infinite amount of buses. It could also mean you could fit an infinite amount of people in one infinitely long bus. This would create another "Hilbert's hotel" but on a bus. If all values are not finitely set but are infinite (including the rooms), it would quite literally never end. Though I do understand that this video's point was to try and prove different sized infinities.

    1. Brien831
      Brien831
      2 саат мурун

      Yes his explanation is a bit sloppy there. If you want some further explanation look into countable and uncountable sets. Sometimes abstraction is easier to understand than simplification.

  36. Isaac Rock
    Isaac Rock
    Күн мурун

    Anybody else's brain full after 2 min

  37. TheRealRB3902
    TheRealRB3902
    Күн мурун

    5:56 anyone know where I can get a wallpaper like this? This looks so nice. Even if I can't get a premade one, could anyone at least tell me how to make something like this if they know? thanks so much in advance edit: by wallpaper i mean like a wallpaper for my macbook

    1. TheRealRB3902
      TheRealRB3902
      7 саат мурун

      @Red Panda ohhh yeah that looks amazing ty :D

    2. Red Panda
      Red Panda
      21 саат мурун

      I don't know where to find a wallpaper that look exactly like that but maybe you will like vaporwave grid wallpaper. You can search it on google.

  38. Liam -
    Liam -
    Күн мурун

    I just lost thousands of brain cells by watching this one video 👁👄👁

  39. Petru-Mihai Petrenchi
    Petru-Mihai Petrenchi
    Күн мурун

    I think I saw this first on vsauce a couple of years ago

  40. Rexanious
    Rexanious
    Күн мурун

    the problem isnt infinity or sth its how they will walk to their room lmao, "yes sir your room is 7252846 please walk $down the hall"

  41. Puar XI
    Puar XI
    Күн мурун

    Instead of making everyone goes to the next room. Why don't just let the new guest taking the room that the last person would take anyway?

  42. flare
    flare
    Күн мурун

    This is called The Banach-Tarski Paradox. It was the topic of a VSAUSE Video a while back which used the Hilbert Hotel example.

    1. flare
      flare
      11 саат мурун

      @Tom Svoboda I KNOW

    2. Tom Svoboda
      Tom Svoboda
      13 саат мурун

      @flare banach tarski paradox is the theorem about reassembling a ball into two balls. this video is way more basic stuff (different sizes of infinite sets), but it's a needed ingredient for banach tarski, so it was covered in the vsauce video. but the banach tarski paradox itself is something different. pythagorean theorem is about triangles, but not everything involving triangles is the pythagorean theorem.

    3. flare
      flare
      Күн мурун

      @Tom Svoboda oh wait it isn’t?

    4. Tom Svoboda
      Tom Svoboda
      Күн мурун

      this is unrelated to the banach tarski paradox (even though it was mentioned in that vsauce video)

  43. Ayush Patil
    Ayush Patil
    Күн мурун

    This video is already there on Ted channel uploaded 2014.he just told the same

  44. Lordlouckster
    Lordlouckster
    Күн мурун

    Ted-Ed used powers of primes. bus-th prime ^ seat

    1. eggynack
      eggynack
      Күн мурун

      This way is better, cause it actually fills all the rooms. The power of primes thing leaves infinite rooms empty.

  45. Flávio
    Flávio
    Күн мурун

    Me watching: Hey, that's not allowed ✋🏼

  46. Atapd
    Atapd
    Күн мурун

    COPY FROM TED-ED

  47. Muazzam Hazmi
    Muazzam Hazmi
    Күн мурун

    I don't understand this but I agree

  48. HyperBlade 93
    HyperBlade 93
    Күн мурун

    the most interesting part of this whole thing is wondering how much money is being raked in from all those guests.

    1. Bitfire31337
      Bitfire31337
      11 саат мурун

      That's easy: An infinite amount. Depending on the net profit per guest and night it might be a bigger or lesser infinity though 😅.

  49. MegaMrblackguy
    MegaMrblackguy
    Күн мурун

    This is dumb.

  50. Jiri Valek
    Jiri Valek
    Күн мурун

    you can compare the amount of members of an infinite group only if you simplify it by using a finite group...but than you are comparing our number systems rather than the actual number of members.

  51. Tomor Inferno
    Tomor Inferno
    Күн мурун

    wouldn't infinity mean that no matter how many Infinity are filling that infinity it would never be full? Due to Infinity not being like 1+1 but more like everything+everything+everything=everything

  52. D. Dillon Duffield
    D. Dillon Duffield
    Күн мурун

    Surreal! No I mean, do a long video on Surreal Numbers! 👌😸

  53. Guhan SEN
    Guhan SEN
    Күн мурун

    Thats y i took Biology over maths

  54. MisterSaur
    MisterSaur
    Күн мурун

    She: How much you love me? He: Infinite.. She: Will you buy that dress for me? He: Infinite also has limits.

  55. schotte
    schotte
    Күн мурун

    Infinite number of rooms, maybe - but I’d hate to imagine the breakfast buffet.

  56. Barty
    Barty
    Күн мурун

    What did I just watch

  57. Surekha Veer
    Surekha Veer
    Күн мурун

    This is hard as dark season 3😂😂got it

  58. Madilynn Coit
    Madilynn Coit
    Күн мурун

    Just go to the next open room lol

  59. Alex Ramin
    Alex Ramin
    Күн мурун

    There is more than one infinity, there is Aleph Null, Omega, Omega Squared….

  60. His Dudeness
    His Dudeness
    Күн мурун

    i know this must be a stupid doubt but why dont the newcomers just move to the room next to last... why does the manager has to bother everyone

  61. G0tch0c0late
    G0tch0c0late
    Күн мурун

    WTF

  62. Grubhub Dad
    Grubhub Dad
    Күн мурун

    Veritasium: "Have you ever had a stroke?" Me: "No." Veritasium: "Would you like to?"

    1. Bitfire31337
      Bitfire31337
      11 саат мурун

      Underrated comment 🤣

  63. MemerMcMemer
    MemerMcMemer
    Күн мурун

    I am slime

  64. jamesonknott
    jamesonknott
    Күн мурун

    This is why everyone hates mathematicians. This is so stupid. If there aren't enough rooms for infinite guests then obviously there are not "infinite" rooms. You're describing infinity and not infinity.

    1. jamesonknott
      jamesonknott
      Күн мурун

      @Tom Svoboda You don't. Because the bus doesn't exist and neither does the hotel.

    2. Tom Svoboda
      Tom Svoboda
      Күн мурун

      how do you sort the people of the last bus into the hotel then?

  65. Brian
    Brian
    Күн мурун

    who cleans the rooms?

  66. Cindy Nguyen
    Cindy Nguyen
    Күн мурун

    Scp-182737362821818273364646328929181827374664646467721819191928373746-hotel

  67. Saibot XV
    Saibot XV
    2 күн мурун

    1:26 some people are still going to their room... literally it took years to the poor guy in the room 4673480886491. Poor Marvin

  68. Oz Ramos
    Oz Ramos
    2 күн мурун

    wow, that's a good cliffhanger! subscribed!

  69. The Presence
    The Presence
    2 күн мурун

    If the infinite names has just two letters, doesn't that mean that their is going to have the name that formed throught flipped diagonally picked letters? I mean their is no end to number of combinations so we can computer it, but no matter how you pick and flip the letter, its still going to be someones name

    1. eggynack
      eggynack
      Күн мурун

      The new name is indeed present on the bus, as it follows the rules for name creation. However, it provably does not show up on the list that was supposed to have all the names. Such is the problem.

  70. sufie mohd
    sufie mohd
    2 күн мурун

    I want to show this video to my math teacher

  71. Gunnar Kulak
    Gunnar Kulak
    2 күн мурун

    Infinite Hilbert Hotel's

  72. TheRandomNoob
    TheRandomNoob
    2 күн мурун

    *my roblox character named infinite is satisfied.*

  73. Imqrove
    Imqrove
    2 күн мурун

    I like the part where he said infinite

  74. alewender
    alewender
    2 күн мурун

    make everyone (including the party bus) go up one

  75. David Hyland
    David Hyland
    2 күн мурун

    I don't get it, surely the diagonally formed naming would also eventually appear in the ordinary course of listing. Seems like they are all double booking to me. But if all the names never ends it's like an infinite number of possible irrational numbers which is kinda cheating, give them a room number of pi, they'll spend so long reading their room number they'll never leave the bus.

    1. Brien831
      Brien831
      2 саат мурун

      No infact, if you only had all the irrational numbers as guests, you could fit them into you hotel. The rationals and the natural numbers have the same magnitude.

  76. Aarick Zook
    Aarick Zook
    2 күн мурун

    Simple solution: rename the rooms the same way that the people are named. Each person goes into the room with their name.

  77. Frank Hayden
    Frank Hayden
    2 күн мурун

    The problem with the uncountable infinite fitting with a countable infinite is simply a problem on paper. This is a theoretical problem for the person who wants to plan ahead and make this graph before they arrive… this is not a problem in real life, because in this scenario, this uncountable infinite is in fact countable one by one. We can’t plan ahead for every room, but if they all line up and keep coming in, we will always have another room for them and we will always have another row to fill out on the spreadsheet. You didn’t plan for the opposite letter person showing up, because you couldn’t count him? Well you demonstrated how this is not a problem as you explained it… you wrote it down. If it can be written down, it exists it is tangible it can be counted. The problem isn’t in getting them rooms, the problem is in counting the hypothetical.

  78. Hubert Gran
    Hubert Gran
    2 күн мурун

    Infinite is not a number

  79. Vanguard Of the revolution
    Vanguard Of the revolution
    2 күн мурун

    “Your mother arrives”

  80. Nicholas Cooper
    Nicholas Cooper
    2 күн мурун

    There is a solution for the person without a room to get a room; that’s the manager’s name! The hallway with infinite rooms is the room!

  81. Hydros92
    Hydros92
    2 күн мурун

    The problem I have with the "differently sized infinities" concept in math is that it doesn't make sense to me. You start with the premise that there are an infinite number of passengers with an infinitely long, unique name consisting on the letters A and B. and you write down all the rooms in this infinite hotel and all the names of the passengers, which is part of the premise so we assume that this impossibility is possible. if you were then to flip the letters along the diagonal to make a new name and don't find it on the list, what you have discovered is that you haven't written down all the names not that the list of passengers must exceed the list of rooms as both are, by premise and definition, without limit. The only way to have this problem is to impose a limit on one of the factors, in which case, it's no longer infinite and the whole thought experiment just kind of falls over. I know there was a whole math civil war over this very discussion but I've not yet had anyone explain how the problem doesn't violate it's own rules. I can see it as a way to illustrate how to deal with problems of incredibly large numbers that would be almost impossible to work with practically, but not as a proof of the logical existence of the childhood taunt "Yeah well... mine is infinity plus one!" which is how I've seen it presented.

    1. Hydros92
      Hydros92
      10 саат мурун

      @Tom Svoboda ​​@eggynack Thank you both for helping me understand this, I can see where I was going wrong in my logic with it now. I'm not a smart man, I'm more of a nuts and bolts type thinker than a theoretical one but you both genuinely helped get the concept through my thick skull so again, thank you for that. Also my apologies if the second @ doesn't work

    2. Tom Svoboda
      Tom Svoboda
      Күн мурун

      @Hydros92 The exact mathematical statement we're dealing with goes as follows: there doesn't exist a 1-1 correspondence (a pairing) between natural numbers and infinite binary strings. It's the same thing as trying to pair a 3-element set with a 5-element set, it's just not possible. The finite case is easily understood: the naive reason is that 5 is larger than 3. The latter set has more elements, so there will always be leftovers. We use this intuition to _interpret_ the infinite case as the set of binary strings being larger than the set of natural numbers. But it's just semantics. We're not arguing that it's "truly larger" in some metaphysical sense. It's more like giving a meaning to the word "larger" in this context. It doesn't matter what you call it, we don't need to use the words "larger" or "size" at all. The point is that the _fact itself_ holds, it won't go away, and it demonstrates itself throughout mathematics.

    3. eggynack
      eggynack
      Күн мурун

      @Hydros92 Time isn't part of this. You set the rule for how the new name is generated and there it is. Notably, we do not know what the new name is. Can't know, really. unless we contrive the list to take a certain shape. But the rule works. It takes in an input that makes sense and it has an output that we understand, so such a name must exist. We don't actually have to create the name for it to prove this reality. Notably, your assertion that an infinitely long list must contain all possibilities is trivial to disprove. I just have to give you an infinite list that doesn't do that. Check it: BAAAA... ABAAA... AABAAA... AAABAAA... and so on. Not only are we missing tons of possibilities, but we don't even have one with more than one B. As for differently sized infinities? There's no grand need for it. It's just true. If it weren't true then it wouldn't be true. Such is math.

    4. Hydros92
      Hydros92
      Күн мурун

      @eggynack Thank you for taking the time to address my confusion on this issue. I think perhaps my problem with the logic of this thought experiment is that the premise states that there are infinite passengers, so the list will be infinitely long, all the names are infinitely long but also unique, so all possible permutations must then exist in the list and to carry out the task of flipping a character in each name would take an infinite amount of time and would never complete, so to prove the name wasn't on the list would be an impossibility as you could never generate the name to prove that it wasn't there, without introducing a finite value. Maybe I would be able to gloss over that if I knew the need to have one infinite to be larger than another infinite as it doesn't sit right in my head on why we would ever need to make such a logical loophole.

    5. eggynack
      eggynack
      Күн мурун

      @Hydros92 Infinite does not mean all. An infinite list can be missing stuff. It can have limits. The only thing an infinite thing is not allowed to be is finite, and this list is definitely not finite.

  82. playless Namer
    playless Namer
    2 күн мурун

    a infinte amount of guests is the same like a infinite amount of busses with infinite guests.

  83. Adrian B
    Adrian B
    2 күн мурун

    I see a problem with "an infinite number of buses with an infinite number of people"...isn't that equal to ONE buss with an infinite number of people? How can u use plural on infinite?

  84. bac phan
    bac phan
    2 күн мурун

    I feel bad for any developer who has to write the software for this hotel

  85. Jesse
    Jesse
    2 күн мурун

    Explain why this is irrelevant & dumb af, there's no hotel this big you donut

  86. Joop Meijer
    Joop Meijer
    2 күн мурун

    This is flawed. A hotel with infinite rooms, all occupied, by an infinite number of people. Then a new person is invoked that is not part of the infinite number of people. If invoking a person is allowed, why not invoke an empty room?

    1. Tom Svoboda
      Tom Svoboda
      2 күн мурун

      @Joop Meijer that depends. "infinity + 1" equals infinity if you're concerned only about size (adding an extra element to an infinite set doesn't change its size). it doesn't necessarily equal to infinity if you care also about an ordering. for example the natural numbers are implicitly ordered into an infinite line 1 < 2 < 3 < 4 < .. adding +1 corresponds to adding an extra element to the end of this line, which changes properties of the ordering: the new line now has a last element which wasn't true before. so "infinity" and "infinity+1" are different objects now. the amount of elements stays the same though, it's only the ordering that got change. look up cardinal numbers and ordinal numbers.

    2. Joop Meijer
      Joop Meijer
      2 күн мурун

      @Tom Svoboda Hi Tom, would you say that infinity + 1 is greater than infinity? Is this allowed?

    3. Tom Svoboda
      Tom Svoboda
      2 күн мурун

      Your argument doesn't make any sense. Consider a hotel for 20 people which is full. Then a new person is invoked that is not part of the 20 people. If invoking a person is allowed, why not invoke an empty room? Have I shown that the concept of hotel for 20 people is flawed?

  87. Łogan
    Łogan
    2 күн мурун

    To get this job your qualifications must be insane

  88. Devarsh Dey
    Devarsh Dey
    2 күн мурун

    Your favourite element is molybdenum since your profile is atomic no. 42 and molybdenum matches this atomic number so I predicted that your favourite element is molybdenum.

  89. Devarsh Dey
    Devarsh Dey
    2 күн мурун

    It's name is "the infinite hotel Paradox"

  90. Seventhsage
    Seventhsage
    2 күн мурун

    Think about this... There are an infinite set of positive integers. There are also an infinite set of positive even integers (and odd), but wouldn't, by their definition, the even numbers be a smaller set of infinite numbers? a 1/2 infinity? While both are infinite, if you had a set of them, the infinite positive integers would contain the infinite even and odd numbers set, so wouldn't the first (by definition) have to be bigger by at least a factor of two? It's a very fun thought experiment. The original problem that is referenced here is "are there more integers between one and infinity then there are numbers between 0 and 1, where instead of flipping the A's and B's, you just take the digit and tick it up one, creating a whole new number that wasn't on the list before. Different interpretation, but same principle, (and yes, there are, for the same reason.)

  91. Hafiz Razali
    Hafiz Razali
    2 күн мурун

    I am confusion

  92. JK
    JK
    2 күн мурун

    There is a great way of understanding different infinities Imagine the infinite amount of numbers in between 0 and 1, you can take an unlimited amount of decimal numbers. Now take every single number between 0 and 2, here it is near double of all numbers between 0 and 1, which is infinite, but there are still infinite numbers between 0 and 2.

  93. Rbx Mod
    Rbx Mod
    2 күн мурун

    literally just put the next guy to show up in the next room...

  94. manas satam
    manas satam
    2 күн мурун

    That's over thinking

  95. Gelatin72
    Gelatin72
    2 күн мурун

    This in no way makes sense to me. Infinite number of rooms=infinite amount of guests. There should be at least on room left

  96. jpablo700
    jpablo700
    2 күн мурун

    Some infinities are bigger than other infinities. Boom! Problem solved.

  97. TheMadHatt
    TheMadHatt
    2 күн мурун

    What if you tell ABBA and the rest of the party bus to treat the A’s and B’s in their names like 1’s and 0’s and convert from binary to decimal to get their room number? I think they would also need to put a 1 in front of every name so that names starting with 0’s are still unique

    1. Tom Svoboda
      Tom Svoboda
      Күн мурун

      @TheMadHatt no, the rooms are explicitly indexed by natural numbers, and natural numbers have only finitely many digits.

    2. TheMadHatt
      TheMadHatt
      2 күн мурун

      On second thought they don’t need to bother converting, just send ABBAAAAAA… into room 1100111111… send BABABABA… into room 10101010… by telling them to use the simple strategy of changing A’s to 1’s and B’s to 0’s and popping a 1 in front. If they have infinitely long names I’m sure they don’t mind having infinitely long room numbers, no?

  98. Yee Wood
    Yee Wood
    2 күн мурун

    Just imagine being in room 938749837413058145 and being told to go to a room with double that number :(

  99. sleepy
    sleepy
    2 күн мурун

    "infinite hotel infinite rooms infinite people infinite buses infinite spreadsheet" very realistic stuff you see.

  100. mobiusevalon
    mobiusevalon
    2 күн мурун

    This seems like something hotel managers have nightmares about and wake up in a cold sweat