The Infinite Hotel Paradox - Jeff Dekofsky

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.

[Asu]

"One night, the infinite hotel is full"

Me: _"Infinite confusion"_

[azryxthefolf]

Imagine the elevator in that place.

"Hey man, where are you staying?"
"Room 1.949213 x 10^77789"

[RobloxKid]

As someone who has visited this hotel before, I really enjoyed the experience. When I came in, the night manager asked everyone to move to the next room and I went to room 1. There were a lot of complaints cuz it was 4 AM. And then, a million people came in at 3 AM and I had to move to room 1, 000, 001. The room was in floor 4000, so I wanted to take the elevator. I was trying to find an elevator out of the infinitely many that was at least close to floor 1, but after looking for like 2 hours, the closest one I could find was at floor 5.63 octillion, and the one I was standing next to was at floor 5.68 x 10^178, which was actually relatively close. The hotel tried to fix this problem by making the elevators go at the speed of light, the highest possible speed, but even that won't get you that one elevator that's stuck at 5.63 octillion. So, of course I had to take the and as I get there, the manager told me to move to two to the power of my room number which was uh.... room number 1.98 x 10^301030 (according to wolfram alpha). This is going to be a fun journey!

Update: It has been 19 years and I am still at floor 189.23 quadrillion. Help.

[pinballed]

Imagine being at floor 2194, needing to be at floor 8302, and then seeing that the elevator is currently at 29175, slowly ticking down

[Dev_Toast]

“The infinite hotel is full”
Science: *breaks*

[RK-jbrq]

"Everyone is happy"

Except the cleaning lady 😂

[InterestingFactTime]

One night, the unthinkable happens. The night manager walks outside, and sees an infinitely long plane with an infinite amount of passengers crash into the infinite hotel. The hotel collapses into flames, causing an infinite amount of deaths.

[downwitthe]

imagine chilling at room no.12 and suddenly you have to move to room 4096 because there are infinite amount of buses with infinite amount of customers outside.. cant even have a hotel room peacefully in ohio 💀

[seagull]

Bus driver: Are there rooms open for my passengers?

Manager: Yesn’t

[ilovecats]

everyone gangsta until the manager calls to fix the roof

[hasanicahyadi]

The most insane part to me is after all that effort, the hotel makes the same amount of money as before all that troubles

[RavenStarMedia]

I keep coming back to this because I love the animation, I love the concept, and I think an animated series comedy series involving concepts of infinity would be cool.

[lukadjordjevic]

Can we just respect the one maid who cleans all the rooms

[stephenhofmann]

I believe it’s fair to say that in this paradox, we need not worry for the night manager’s predicament because there are infinite ways that he can free up more space giving his seemingly infinitely high level of intelligence and problem solving. One must imagine Sisyphus happy, even if his stone was actually finding vacancy in an infinitely booked hotel.

[Neonlaserz]

I watched this video all the way 9 years ago, back when I was seven. Over the years I'd keep coming back to this video just because of how well presented it is. Here I am today, in my junior year of high school, having just about finished Calculus BC and having invariably dealt with infinity numerous times, watching this video once more. It's a good video.

[segul]

"The infinite hotel got full"
Me: Hold up, somethin ain't right

[hahanamegobrrr]

"One night, The Infinite Hotel is completely full"

*laughs in mathematics*

[gilthenrill]

“The person on the first bus who is sitting on seat number 7 will go to room no. 3^7 AKA room no.2187”
The guy: Hello, are there any available rooms?
Receptionist: Yes, you’re going to room no. 2187. It’s on the 219th floor.
The guy: Uhh…. How long does it take to get there on elevator?
Receptionist: About 38 minutes and 9 seconds.
The guy: Wait… so I have to wait over half an hour in the elevator just to get to my room?
Receptionist: Yes. Oh and we are expecting another infinitely long bus so at 8pm expect to have to go to room no.4374.
The guy: Oh god….

[thienhuynh]

Imagine walking in at 3:00 AM and realizing you have to go to room 12237863891763892787652

[Swift-Prime]

Imagine how annoying it is to constantly get kicked out of your room