The Infinite Hotel Paradox - Jeff Dekofsky

  • Published on: 16 January 2014
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    The Infinite Hotel, a thought experiment created by German mathematician David Hilbert, is a hotel with an infinite number of rooms. Easy to comprehend, right? Wrong. What if it's completely booked but one person wants to check in? What about 40? Or an infinitely full bus of people? Jeff Dekofsky solves these heady lodging issues using Hilbert's paradox.

    Lesson by Jeff Dekofsky, animation by The Moving Company Animation Studio.
  • Runtime : 6:
  • Jeff Dekofsky Nadav Arbel Moving Company Animation Studio Infinite Hotel Infinity Hotel Infinite Hotel Paradox Infinity Hotel Paradox Hilbert's Hotel Grand Hotel Hilbert's Grand Hotel infinity what is infinity how big is infinity how to understand infinity TED TED-Ed TED Ed TEDEducation math paradox math problem mathematics thought experiment


  • Enrique Guzman
    Enrique Guzman   5 hours ago

    wouldn't room number 6 be filled because there was already a person in there from the 2N movement. basically 2 times (room 3) would be placed inside room 6. Also theoretically no one would have to move they new people would simply have to go up the elevator for a time of infinity to get to their respective rooms

  • Stefano M
    Stefano M   5 hours ago

    Infinite rooms, infinite busses, infinite floors, infinite money but just 2 employee in this hotel!

  • Mankala Saipavan
    Mankala Saipavan   16 hours ago

    I need infinite amount of time to understand about this infinite hotel

  • Luisa
    Luisa   18 hours ago

    excuse me, can you explain that again

  • Concepcion Ponce
    Concepcion Ponce   1 days ago

    Someone count how many times he said "infinity" and "finite"

  • V W
    V W   1 days ago

    why is no one talking about how pissed the cleaning lady looks

  • Charlie Clapp
    Charlie Clapp   1 days ago

    Theoretically, infinite buses of infinite people is infinity², which is infinity, so they can do the same tactic as before (doubling room number)

  • Tedwin Tansan
    Tedwin Tansan   1 days ago

    Imagine being the last passenger to step out of the infinite bus

  • 주노
    주노   1 days ago

    4:00 And he handed out the keys to his guest forever because of the infinite keys.

  • Basic ASMR
    Basic ASMR   1 days ago

    You lost me at infinite hotel being full. There is no full, just ever increasing.

  • Connor Lapping
    Connor Lapping   1 days ago

    Just assign them a room number of π after the decimal so room 1 is 3. 1, 4, 1, 5 ,9 etc all the digits of pi since pi is infinite. You'd never run out of rooms.

  • Feez17
    Feez17   2 days ago

    Just gonna enjoyed this animation

  • Tabarik Ahmed
    Tabarik Ahmed   2 days ago

    Is Donald trump owner of this hotel….¿😂😂😂😂😂😂

  • S C
    S C   2 days ago

    Man wtf

  • James Cook
    James Cook   2 days ago

    I’m going to stop you at 3:42 so infinity means infinity ♾ numberless or more so number overness if there is an infinite amount of rooms there is infinite rooms no matter if the people are infinity times 2 you still have infinity there is no problem with more people because there is infinite places to stay the only problem is there is no infinite time to be had so I’m posting this and peace out for forever

  • Scott Warren
    Scott Warren   2 days ago

    @TED-Ed If a hotel has an infinite number of guests, is it even possible to say that the hotel is completely full? My mind can't think out the answer.

  • Scott Warren
    Scott Warren   2 days ago

    @TED-Ed At 2:33, if the hotel already has an infinite amount of money, it won't lose any money by unwelcoming all new guests.So, ur wrong, the hotel simply won't lose any money.

  • Meister Van
    Meister Van   2 days ago

    how would an infinite number of rooms in a hotel be full if its never ending?

  • kymani fenton
    kymani fenton   3 days ago

    A perfect reason of why you should go to Heaven

  • Omar Sawtari
    Omar Sawtari   3 days ago

    My dumnass really thought i can understand this

  • Brian Scott
    Brian Scott   3 days ago

    Did anyone else see the glitch at the start?

  • TAB00
    TAB00   3 days ago

    why cant the new customers just go to room 1203897123091723012731231759375930572+1 and so on?

  • Unotch
    Unotch   3 days ago

    The problem is that one of the guest will now know exactly, how big infinity +1 is.The nightmanager just has to call that guy to solve any problem involving infinity.I am sure he is willing to help for halve of an infinite sallary.