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A never-ending hotel, always full of guests, helps to explain the nature of infinity.

(Part 4 of 6)
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26 COMMENTS

  1. Steve Posted on July 21, 2020 at 6:38 pm

    What if I brought an infinite number of hookers to my room?

    Reply
  2. Owen Fitzgerald Posted on July 21, 2020 at 6:38 pm

    This must be what Trump thought he has when he got the number of floors wrong in his hotel HAHAHA!

    Reply
  3. Deepesh Bhatt Posted on July 21, 2020 at 6:38 pm

    Youtube recommended me this video after I solved Hilbert hotel question at codeforces.

    Reply
  4. Jithendra A B Posted on July 21, 2020 at 6:38 pm

    Actually I had a solution to this and trying to publish a paper written by me on this, for any queries and clarifications please feel free to contact :- 9741192212(India)

    Reply
  5. jamesk479 Posted on July 21, 2020 at 6:38 pm

    Gee…thanks for ruining the puzzle aspect about this for anyone new to it. Dumb asses.

    Reply
  6. Supply Unique Notes(SUN) Posted on July 21, 2020 at 6:38 pm

    what about the resident of the last room ??? !!!

    Reply
  7. Hamza Raja Posted on July 21, 2020 at 6:38 pm

    A big problem of the human mind is to think of what is totally irrelevant and futile, like Hilbert thought this.

    Reply
  8. Michael Sebastian Posted on July 21, 2020 at 6:38 pm

    Have to inform the infinite people on the bus that they are already in the infinitely large hotel with infinite people.

    Reply
  9. Peter Anderson Posted on July 21, 2020 at 6:38 pm

    Why bother with maths? If the manager took the infinite people out of the hotel at the same time as the infinite number of people got out of each bus as it arrived, he would have only one set of infinite people? He could then fit the infinite number of people outside the hotel comfortably into the infinite hotel. Check out http://www.psawa.com/The_7_Dimensions_of_Everything_and_Nothing.html

    Reply
  10. Paul Perlova Posted on July 21, 2020 at 6:38 pm

    I actually applied this paradox to my job in a stockroom in HomeGoods in order to keep up with the trash and it actually works really well.

    Reply
  11. Silus Posted on July 21, 2020 at 6:38 pm

    Why does anyone need to move if there are infinite rooms. The new people just move into a room, irrespective of what the current occupants of other rooms are doing.

    Reply
  12. Memerboi69 Posted on July 21, 2020 at 6:38 pm

    hi im in room tau of the real number infinite hotel
    and the guy in room root 42 is so annoying

    Reply
  13. Damsel Elysium Posted on July 21, 2020 at 6:38 pm

    I made a short film about this! The trailer is here! https://youtu.be/L1y4a4W_RVY

    Reply
  14. Roiben Blitz Posted on July 21, 2020 at 6:38 pm

    Infinity*2 = Infinity = Case closed Next please.

    Reply
  15. iannickCZ Posted on July 21, 2020 at 6:38 pm

    If the infinite does not have "end", so the "start" neither, there is no room #1

    Reply
  16. ed bell Posted on July 21, 2020 at 6:38 pm

    Sorry their is no vacancy at The Grand Hotel. No finite object can be infinite in number, because anything infinite would require an infinite amount space to exist in, thus leaving no room for anything else. The only thing that can be infinite is infinity itself. The all of the all is the only thing infinite. Everything else is a sub division of it. And that's it. There is nothing more because that is everything. No extra anything can exist because everything that can exist is contained in the all of the all and it is never ending and ever increasing in size if you were going to try and quantify it. You can't. Numbers are a way in which we compare one thing to another to determine length, width, height, volume, speed, velocity, etc, etc & etc. What could you possibly compare infinity too?

    Reply
  17. Loyal Honda Fan Posted on July 21, 2020 at 6:38 pm

    That germans should better find a way to fix their cheating emissions on their cars… booooy

    Reply
  18. skilliyay Posted on July 21, 2020 at 6:38 pm

    What is being described here is the difference between a one dimensional and two dimensional infinity.

    Everybody can grasp the idea of a one dimensional infinity. It is the endless string of numbers or in the this case the linear string of rooms in the infinite hotel.

    The infinite hotel described is like a row of chalets with infinite length. We don't even need to consider how many storeys the hotel has or it's width. The hotel is infinitely long in one dimension and thus can accommodate infinite guests. The supposed paradox arises when the new guests arrive………

    When we introduce the new guest(s) we add a second dimension to the concept. It is helpful to think of this second dimension as time, but we could just as easily be adding infinite storeys to the hotel.

    It would take time for each guest to move to the next room. We cannot fully describe this movement of guests using only one dimension, because it has now become a 2D concept. If you watch Carl Sagan's video on the 4th dimension, you can see the limitations of comprehending shapes from a higher dimensional space.

    In this 2D infinity, we can accommodate an infinite number of new guests in the second infinite plane.

    Reply
  19. hamza mezbo Posted on July 21, 2020 at 6:38 pm

    Hi
    Why david choose the hotel to explain his theory
    Why not a train or something ????

    Reply
  20. fauxmosmexual Posted on July 21, 2020 at 6:38 pm

    is that david mitchell?

    Reply
  21. Jonas Venture Jr. Posted on July 21, 2020 at 6:38 pm

    This one gets an instant subscription. TedED had an animation about this but they made a really shitty boring video. This channel did it even better and they did it way faster.

    Reply
  22. Debi K Baughman Posted on July 21, 2020 at 6:38 pm

    I can see this being a problem in regards to the hotel, but in regards to life itself, and time it isn't taking into account death. death itself, in this account, is not a non-existance, but the dead being also doesn't use space in the same way as does the living being. The reason for the mistake here is a non-understanding of space, which is what he is basing his theory and conjecture on; see space as both empty and full at the same time (that's infinity) ; and then, well, then we get go into the understanding of Time which is both space and no space equally.

    Reply
  23. Philip B Posted on July 21, 2020 at 6:38 pm

    Which infinity does this conundrum best address?

    Reply
  24. Cohcky Posted on July 21, 2020 at 6:38 pm

    Can some one explain to me. How in an infinite hotel, where every room is infinitely occupied by a set of infinite people. Can each person move one room to the right? .. There is never going to be a space available for them to shift!? It's infinitely occupied.. They would keep asking each person to the right to shift and no ones ever going to get the opportunity to actually move.

    You're assuming there's an infinite amount of space available which is contradicting. How can you have a hotel full with an infinite amount of people. Suddenly vacant with an infinite amount of space available.

    Reply
  25. ubiquity Posted on July 21, 2020 at 6:38 pm

    If there are 2 guests in the hotel and 3 more arrive the 5th guest will have to walk to room 5 which is the closest available room. If there were 4 in the hotel and 5 arrive, the 9th guest will have to walk to room 9, 3B guests and 3B + 1 arrive, guest number 3B+1 will have to walk to room 3B+1, etc. What's my point? If there are N guests in the hotel and more than N guests arrive, the last arriving guest will have to get a key to room that was not previously occupied. Bottom line is, the hotel cannot contain an infinite number of people

    Reply
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