# The Infinite Hotel Paradox - Jeff Dekofsky

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**Published: 16 January 2014**- Sign up for our newsletter and never miss an animation: bit.ly/TEDEdNewsletter

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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.

One day I fell from the roof of the infinite hotel and to this day I am still falling !!!

I also lost my son in the infinity hotel :v

The hotel is infinite because it has no reality distinction therefore is just an ilusion

its infinite duh

Or just let them all go in a new room you have infinet rooms anyways

Narrator: everyone was happy

Me: tell that to the room-cleaning lady, GIVE HER A VACATION

The elevator broke, sorry guys...

What????

Imagine guest ∞ waiting for the elevator to get to floor 1,

One Like for the Night Manager, He is an Infinite amount of energy...

If it was infinite then it would never be full

That poor manager though

So, the night manager is a mathematician

Yep this is a riddle

Are they currently hiring?

Thank you

This makes no sense since the narrator said all the infinite rooms are occupied. So all the infinite room vacancies are already occupied so there's no way to move to the next room just to accommodate the visitor. 🤔🤔🤔🤔🤔

wooow quel travail !!!! et moi qui n'aime pas les math ! bravo ! j'ai adoré ! :)

You lost me at, "The infinite hotel is full"

The hotels booming more than ever . . . Well actually it’s booming the exact same as ever

https://www.youtube.com/watch?v=i31Zf-rCXK8&t=365s

Wow I actually understood🥶🥶

Not being funny but I wouldn't be going to a hotel where I have to move rooms everyday

MURGH!

I am wondering what kind of lifts would be there to take them at those rooms ?

🧐😕😕😕

If everything is infinite , why not infinite numbers of workers like him

I think that if we admitted the Universe space is infinite in size and take the space as if it was the hotel and the stars as the guests, then all the operations would be possible, or at least not contradictory. For example, if all the galaxies were getting apart from each other, then soon there would be room for more galaxies.

Imagine, you slept peacefully, having a good dream, relaxed from a hard day until someone wakes you up and tells you to go to room 100,357,028,482,938,282,482,475,213,093,825 at 2am

Infinite Rooms cannot be occupied by infinite people since its Infinite

And saying next room is n+1 is wrong since n=infinity

And 1+infinity=infinity

This.is.absurd

Night manager : go to room 156735968803937593742

Doctor strange : 😑

Ok back then it has to be maid so we could understand the concept of infinity but how is the hotel full ?Was it just for the lil paradoxe or does it mean that infinite may actually be a number? Sigh... I'm outta here

I lost it on the prime numbers, what about you?

Letting the infinite numbers of rooms are full of infinite numbers of guests is impossible; because subtracting infinity from infinity is not zero.

I'm surprised that I understood everything he said. Does that mean my mind is able quantify infinity. Does that mean my mind is greater than infinity?!?!?!?

看沒懂...為什麼要這麼麻煩

Wait what happens to the people already occupying the rooms like 3^7 or 5^11? Where do they go?

Nayomika Shashidhar people already there go to two to the power of their room number.

If an infinite amount of people come in then you can never sleep because you are just moving to another room for an infinite amount of time

So there’s always and never room at the same time?

Wait... but that means he would have to ask an infinite number of people...

ok bt why just the manager don't just

put the next guest

in the room ∞+1???

this room EXISTS, for is an infinit hotel

I don't really think applying math and numbers and formula to an abstract concept like infinity, which is otherwise easily understood, is the play.

I do however, super dig the concept of Hilbert's Infinite Hotel as a Hitchhiker's Guide to the Galaxy location.

شيء عظيم👌👌👌

If there are infinite rooms and infinite guests there are no problems with the rooms because its infinity!? I dont check it

♾

Night Manager at 2 AM: Sorry ma'am we're gonna have to ask you to switch rooms

I'm surprised that I got most of it, even the part with the prime numbers

Wait i thought 3 was a prime number though?

Surely it is a logistical nightmare.

that poor night manager should unionize