The Infinite Hotel Paradox - Jeff Dekofsky

View full lesson: 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.

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Comments

Can I get infinite likes?
Y don't u just move the people the normal way
This is the only hotel that travels through infinite universes. Just saying we could use hotel floors as celestial measurements.
You forgot about the infinite number of guests checking out of the hotel everyday! No guest stays for an infinite amount of nights so the rooms will be emptying themselves. Technically it’ll work out just fine without using the prime numbers just yet.
If he had infinite money in the first place why does he want more money? Weird! If he gets fired he will still have infinite money that will probably never go to zero
If there are an infinite number of rooms, just keep handing out keys in order.
Forget the infinite hotel create a matrioshka brain and simulate as many people as you want
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Why not just pile them up?
Do they have free calculators?
The one whom created this had too much time on his hands, or no life.
Why would he Loa an infinite amount money when he has an infinite amount money?
*Is infinity a prime or a composite?*
How the heck is the hotel full in the first place?
What does it mean when you do a number to the power of another number? Like how is 2 to the power of 7 128? O.O
Gosh, can you imagine being a maid of the Infinite Hotel?
That Night Manager is a genius.
AHHHHHHHHHHHHHHHHHHH, ITS TOO MUCH!!!!! AHHHHHHHHHHHHHHHHHHH! I THOUGHT I COULD UNDERSTAND THIS!!!!! AHHHHHHHHHHHHHHHHHHH!!
I really don't.see the problem or paradox just know that there os an infinite nu.ber of rooms means that therw will always be a room for more...period.
It is contradictory : how can an infinite hotel be full??..GUYS THAT IS WHY IT HAS BEEN NAMED PARADOX, RYT????
Imagine all the guests of a hotel having to change rooms because of a new arrival.
Lets play a game, take a drink every time you hear "Infinite"...
I think i got it. imagine 40 infinity room and 40 infinity people come in after the 40 infinity people came in, the hotel should be full but then 2 other infinity people came in the hotel and the hotel manager tells to the old guests to go in the next room so the 2 other infinity people can come in but if the hotel is already full with the infinity people in the infinity rooms how can there be other space for the 2 infinity? This is the paradox for the people who did not get it. This is just an explanation of what i think.
This hotel manager is way too smart to be a hotel manager.
If the hotel has infinite number of rooms, and the existing guests can have new rooms, WHY TF NEW PEOPLE CAN'T GET NEW ROOMS AS WELL
This is too confusing.
Theory: Infinity is just a concept and there is not infinity in the physical world.
A crisis when all the arriving guests are gonna stay they for an infinite number of years.
Where do they keep all those keys
How the infinity hotel could be full with infinity customers
There's a very simple solution to any problem for the night manager. First of all, he's a genius, but he has an infinite salary, so he can leave once receiving his first paycheck.
Or, just send them to the top floor if you filled it from the bottom..........
This is physically impossible not in the way of the infinite hotel but he can’t finish one bus
So that's when I'll use math outside of school
I feel sorry for the maid
Nothing is infinite. Except my suffering.
I think higher orders of infinity described by hotel rooms is impossible. there could be a room 0 and there could be a 0.00000... it doesnt make sense
Imagine the day the elevator breaks
Or just add rooms to the top as it is infinite, solving all this mindless confusing math
Using "full" with Infinity, then increase its capacity later on doesnt make sense.
Ahh, reminds me of my discrete math course in my freshman year
So much moving..... OH! I'm tired.😥
Why isn't this video infinitely long then?
Imagine getting a phone call at 3am from the night manager "hey umm we need you to move '2n' rooms away"
But if it's infinite can't the new guests just go to the next room???
Really though, nobody has to change rooms. An infinite number of guests, just keep loading them into unused rooms. I don't understand why you have to move everyone to a new room.
My brain would still be intact if the manger just said, "we're full. Go away"
I'd hate to be on the top floor...
So if Room 1/2 contains half the room of Room 1, that means Room 1/1000000 is a million times smaller than Room 1. I guess bacteria is allowed to book in the hotel too
Why is it necessary to move people if there is an infinite number of rooms?
I hope they use teleporters for delivery. And next year a machine that changes digital hotel numbers without having to switch
There's an infinite amount of girls there None of them like me
Send everybody to the next empty floor.
I don't want to be staying in that hotel. If more guests just keep on arriving and I have to change my room every single time, then...
Find me in room 999,999,232,425,242,342,532,442,985,656,554,324,253,531,433,100 in level 999,999,000,000,000,000,000,000-999,999,999,999,999,999,999,999,999,999,999.
It took an english explanation for me, a german, to understand this... Props to you
I kind of don't really understand, if it is full in the first place, then the last number of the room will go for room 1. dont usually hotel got list of occupied room and not. and i do not understand why should the guests got room number counted that way when they could just gave the room number that's not taken, because it is infinate... please tell me... i'm confused... if it's infinate, then it will not have limited number of room, if it's not infinate then then person occupied the last room number will be kicked out or occupied room 1.... explaination please... ??
For the third scenario you could just move every person to n×2 again as it opens up an infinite number of rooms so yeah don't see why you had to deal with all the prime numbers and stuff
Wait, so I have to move from room 9,999,999,999,999,999,999,999,999 to room 19,999,999,999,999,999,999,999,998? F U!!!!
4:15 i think if you're gonna own an infinite hotel, being good at math might be something you should know
Guys what's your room number in Infinite Hotel? Mines room 2,345,216,137,578,262,262,677,661,998
I think this hotel would be the famous hotel California
5:17 LMAO
Why is the manager still working there if he has an infinite amount of money?
Well this video is wrong, because if there are infinite people occupying infinite rooms, if you would add 1 more room it would be automatically occupied by the same infinite people. Infinite + 1 = infinite - 1. Inifinite is not a static number, its infinite because its ever expending. Adding, deviding, substracting, multiplying it by any number won't make a difference,
Anlamadım zaten aştı beni lol
Maybe I don't understand the thought experiment, but was is the point in saying the infinite hotel gets "full"? If it has an infinite amount of rooms, it will never be full.
Damn, Luigi's hella good at math.
If all the rooms are booked in a hotel with infinite floors then its not a hotel with infinite floors
Too much of infinity
That makes no sense! Because infinty is endless, or? If there's still place in the infinite hotel, there aren't infinite people and endless much people could come in. Or is this false?
If the hotel is infinite then doesn't it have infinite weight
Uhhh... What are we talking about again..?
American airline still was not able to manage 300 countable people
How about to fit the infinite amount of guest on the infinite amount of infinite busses, move each person to room number n+infinity? That probably makes a paradox though.
Well you can only store a finite amount of bits in an elevators logic for the programming in floors. 32 bits is the equivalent of 4.3 billion floors(including mezzanines, and possibly other doors).
Infinity is just a myth,everything has an end.
It s lik in acterix and obelix the 12
How can a person build an infinite levels of space
There is no paradox just assign the next room
At 4:44, room 7 is next to room 13. 7=Friday 13=Thirteenth Friday the Thirteenth. So the infinite hotel is a nightmare
Wat..
Well, first of all, Infinity is a number that can not be counted or guessed. So, how is it possible that there is an Infinite Hotel with Infinite rooms that is COMPLETELY FULL? Infinity is a number that can not be counted. So, I for once think that this a big disappointment coming from TedEd.
Pretty good
I dont understand anything😂😂😂😂
What
Why cant the person walk up to n1?
Or you could just put the new customer into the next empty room? You should keep track of the people in each room if it is a hotel? For example if the hotel rooms are taken up to room #1 - #348 just do x + 1, x = to the last room availible. It would be much easier to assign people to the next room up than using bus/seat numbers allocations and squaring the number.
What
But if their infinite how are u supposed to get all the buses in an infinite line and infinite passenger in each infinite bus
One*
Wut
What if a guest says no
The only problem with this is that when someone asked for a room, the night manager has give an infinite amount of keys. Which will take an infinite amount of time.
It's cheating when you add more to infinity... :P By common sense a hotel with infinite number of rooms, completely booked - with also infinite guests - is completely full, period. The person who wants to check in has (infinite) bad luck. You can't add one room or add one guest, because there's already infinite rooms AND infinite guests in it. In other words: the person can't become one of the infinite guests - if he's not already one of them - because they're already with an infinite number of guests. So the rest can't be a guest. Our mind tries to cheat with the concept of infinity, by smuggle in another guest with our imagination... Even with multiple infinities, with even numbers: 2, 4, 6, 8, 'until' ∞ and odd numbers: 1, 3, 5, 7, 'until' ∞ - then you have a twofold of infinite rooms and guests. But two times infinite is still infinite, nothing more. We see two infinities but it's part of one infinity. Even infinite infinities like 1,9999999999∞ never reaches 2, than 2,9999999999∞ never reaches 3 etc. But infinite times infinite is still infinite, nothing more. Infinity is not a number, when you use numbers you can play with it, so it looks even more. For instance, you put all infinite guests in the infinite even rooms, now you got all odd rooms empty for another infinite guests right? Wrong, because you don't have two times infinite even rooms. You have to put two guests in each even room... If a hotel with infinite rooms is completely booked, then it is just that, nothing else...
I would just take the infinite dollars and run. Just kidding! I would never finish taking out the money, because that cash register would literally be bigger than the universe. I'm not kidding, if it had infinite money, it would have an indefinite space. I think I'll take a staycation this year
I got the room 100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100,100
I think that in order to answer the paradox, you must first find the error with the dilemma. Infinite is not a number, so the night manager never had to do all that math since the hotel is never full. I think the math presented here is just to throw you off.
So are we just going to ignore the blatant overpopulation problem that accompanies an infinite number of guests?
How can you earn a PHD? Create a problem that never existed and pretend to provide a complex solution. Genius!

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The Infinite Hotel Paradox - Jeff Dekofsky