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:
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COMMENTS: 40

Stefano M 5 hours ago
Infinite rooms, infinite busses, infinite floors, infinite money but just 2 employee in this hotel!

Mankala Saipavan 16 hours ago
I need infinite amount of time to understand about this infinite hotel

Fogs • Lucas Fogaça 1 days ago
well, some infinities are bigger than other infinities, righ @john green?

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)

Basic ASMR 1 days ago
You lost me at infinite hotel being full. There is no full, just ever increasing.

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.

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 2 days ago
@TEDEd 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 2 days ago
@TEDEd 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 2 days ago
how would an infinite number of rooms in a hotel be full if its never ending?

New Kingston Sports Association 3 days ago
The infinity hotel is still under construction, it can never be finished.

TAB00 3 days ago
why cant the new customers just go to room 1203897123091723012731231759375930572+1 and so on?

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.
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