The Infinite Hotel Paradox - Jeff Dekofsky
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- Опубликовано: 1 фев 2025
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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.
"Everyone's happy. and the hotel's business is booming more than ever."
*Angry maid walks by*
This hotel has infinity maids
@@arnold8248 who work an infinite number of shifts for an infinite amount of time.
Also no retirement.
I’m feeling like the maid being like 🤬🤯👺👹💩
Infinite maids!
Imagine the elevator in that place.
"Hey man, where are you staying?"
"Room 1.949213 x 10^77789"
Maybe they all stay on an infinite 1st floor.
"Oh, you're lucky. I'm staying in room 8.369304720x10^4830382075."
The lift control panel is basically a scientific calculator
@@MrSRMatthews 😂😂😂
They only need a number close to infinity to contain infinity passengers because they will die in their finite life on the infinity long way to their infinity room number.
"One night, the infinite hotel is full"
Me: _"Infinite confusion"_
'One night, the infinite hotel is full with an infinite amount of people'
Brain: 💥
where is the numbers alabnole and Omega?
Asu howwwwwww
Who are those poor women birthing an infinite number of children?
@@LegacyCrono the mothers of the wicked
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 stairs..... 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.
underrated comment
bro. Who are you? Einstein the memer coz holy cow thats a great comment!
Eh, you got an infinite amount of time to get there.
Hey are u at your room yet?
@@fmjjjjn7510 Not yet, still stuck in the elevator
Bus driver: Are there rooms open for my passengers?
Manager: Yesn’t
well yes, but actually no.
Seagull i haven't even watched the video yet but funny
Some answer is yes and always yes. Bus driver may be driving a while to get to next open room but it is always there.
Clever :)
Stop I’m near to shedding actual tears 😭
"The hardworking night manager" looks like the cleaning lady has to work harder
nah, they hired an infinite number of cleaning works for their infinite cleaning crew
@@themanguy2110 Should've hired Infinite Managers
@Jean Llup I think we should hire half of infinity (before you say anything I know what that means)
@@clairdeloona how do you get half of something that isn't countable
@@ravelnavarro9625 half of infinity is also infinity
"One night, The Infinite Hotel is completely full"
*laughs in mathematics*
To the nth °
Then the infinite amount of passengers use an infinite amount of energy to walk up the infinite stairs in an infinite amount of time.
Then I think of when they need to go to the dining room to eat an infinite amount of food
LOL
Yeah that's my problem, too. If the hotel has got an endless number of rooms, it will never be full. So you can forget the whole experiment.
inifinite hotel cant be full right?
And the night manager is now in depression.
*CRIES IN MATHEMATICS*
Imagine being at floor 2194, needing to be at floor 8302, and then seeing that the elevator is currently at 29175, slowly ticking down
And then Buddy the Elf gets into your elevator and presses all of the buttons ...
It will have infinite elevators
@@AA-ni3km :trol:
@@AA-ni3km me whenI have to wait an infinite amount of time because an elf pressed all of the infinite amount of floors buttons, slowly ticking every number that exists
"Maybe there's super mega bombastic ultrasonic fast fantastic elavator that delivers you to any floor instantly" - summer, 2 weeks ago
“The infinite hotel is full”
Science: *breaks*
thats exactly what i was thinking but then i realized he was talking about alef 0 which is the countable infinite natural numbers.a weird concept
IT IS *ALEF NULL*
Pupper Playlist Night Manager: No it ain’t
XDDD
Infinity=infinity but infinity is also an infinite times more powerful
Now compare this to zero
A wild universe deletion appears!
I rated this Hilbert's hotel 1 star
They kept making me change my room
No matter how you rate the hotel, it will always be a 3-star hotel because average
@@rhamzellibay4098 That's not true, everyone could rate it 1 and it would have an average of 1. Just because there's infinite people doesn't mean that there's infinite possibilities of ratings.
@@ctleans6326 probability assumes infinitely many samples, such as in a dice with 6 faces that has a probability of ⅙ for each face if rolled infinitely many times. It means that in a hotel with a 1/5 chance of choosing numbers from 1-5, all numbers appear infinitely many times. Therefore, all 5's and 1's average to 3, and 4's and 2's average to 3. There's no way you can make infinitely many samples follow the same probability of 1/5 of choosing 1 since (1/5)^∞ = 0.
@@rhamzellibay4098 People rating a hotel isn't exclusively random, some may rate it 5, and some may rate it 1, but every rating isn't equally likely to occur, unless you treat people as dice.
@@ctleans6326 There's no way you can predict how will people rate a hotel because that's their personal preference. There are infinitely many guests so all numbers 1 2 3 4 and 5 rating will also appear infinitely many times, making them equally likely. I'm assuming a more probabilistic scenario lol.
"Everyone is happy"
Except the cleaning lady 😂
There's an countable infinite amount of cleaning ladies.
The lady is the 🤖
Infinity Fawlty Towers 😳
...
Guests at 3,141,592,653rd floor:
"We are not satisfied!"
Basil Fawlty shouting very loudly: "Well, people like you never are, are youuu?" 😂
The poor plumber is not very happy either 😂
But she gets infinite money for her job
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.
And an infinite amount of debris
Breaking news: A second infinite plane has hit the infinite hotel
@@JoseMedina-xq8mf ♾️/♾️
@@JoseMedina-xq8mf breaking news infinite planes are hitting infinite skycraper causing infinite deaths and infinite 9/11
@@ygotsvlog3762 Infinite jet fuel cant melt infinite steel beams
Manager: Sir, we'd like to request that you move from Room 1 to Room 2
Guy: No
Manager: Oh
**entire hotel implodes**
A Thanos move no doubt
You could just start from room 2 and ignore room 1
Haha! It is like...imagine that in SW: The Phantom Menace Anakin asks his mother if he can go with Qui Gon Jinn and mother says no.
(Closing music starts immediately) &
THE END..
*entire hotel implodes* infinitely
@@yechankim7713 You could also start from room n+1 and leave everyone where they are
Can we just respect the one maid who cleans all the rooms
What if there are infinite maids that look the same
@@TheSewDew Oi!
That's jokes aside a good theory!
No
There's actually an infinite amount of maids
She does get an infinite number of tips though
Imagine how annoying it is to constantly get kicked out of your room
Thank you! I couldn't believe nobody else was mentioning this. It would have terrible online reviews. Infinitely bad.
It's okay, they have infinite complimentary mints as well. Totally makes up for having to move yourself and all your stuff over 2,000,000 floors a few times a night.
@@morallyconflictedtortoise6494 😀😆😂🤣
And all that because one mathematic smoked too little weed and thought only infinityth guy can go to infinityth+1 room. Just send newcomer there. You only need infinity of weed as without it he will not find his way.
you actually never get a room you move to room 3? well they actually need you in room 7. And so on
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 💀
Swag in ohio 😩🤘
lmaooooo
down in ohio
50?
@@thanhtamnguyenthi7073 ?
"Everyone is happy"
Probably not, who would want to constantly be asked to switch rooms?
they switched rooms infinity amounts of times
Even worse, they have to walk infinite amount of stairs
they tell different people to switch rooms
Its an Infinite hotel. Not a five star infinte hotel. You get what you pay for
@@Noah-Runge Sounds like a hotel with negative infinite stars.
everyone gangsta until the manager calls to fix the roof
Impossible.
There is no roof since there are infinite rooms
lol!!!😂😂😂
@@ajaymahajan3890 the roof is still there just infinitely high
Oooooooooo fluck
Builder: how many floors do you want?
Manager: *yes*
Underrated
~infinity~
Wait wouldint it get destroyed by the sun or it will stop at the max build high
Back Huat Lee lol I never thought of that
@@someguywithahecktonofcomme9154it will take a infinite amount of time
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.
wow same haha. this video is my childhood, it always feels nostalgic to be here again
Bosses: **Creates an infinite hotel**
“His bosses weren’t very good in math”
That and the, "guest at Pi expecting a Pi". -_-
Like seriously??
You cannot joke in between someone else's joke! That too on Infinity!
maybe this hotel wasn't created by his boss
How did they even manage to build a hotel with an infinite number of rooms in the first place? Wouldn't that take forever? 😅
He might have infinite bosses
Daniel Makhlouf *Smol laugh of joy*
“Everyone is happy”
The janitor: *Are you sure about that?*
At least the boss is happy
2:51 I am Jealous of her melons
The hotel hires an infinite number of janitors, one for each of the infinite floors.
Yeah
@@casanova7635 you didn’t contribute anything to the conversation
"HE MIGHT LOSE HIS JOB"
Isn't he already gonna lose his job because hes constantly kicking guests out of their room?
But he makes infinity dollars a night who cares if he loses his job
@@Selfish_Mango no job means no profit means no money means no infinitu dollars
@M. Woller have you read the fault in our stars, "Some infinites as bigger than other infinites" #)
He's just on an infinite amount of weed
After one paycheck he can retire
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.
I agree
Nobody gonna give props to the cleaning lady at this hotel ? /:
Who said the cleaner's a lady?
Who says there's not infinite of her?
@@Cuzjudd even an infinite amount of cleaning ladys is not enough to clean an infinite number of rooms. Partially because they all exist in overlapping space and cant move because of that.
Edit: There is actually an infinite amount of cleaning ladys on any mm^3 but there is still infinite space without any cleaning lady at all. Welcome to infinity ;)
@@derfzgrld but if we have infinite cleaning ladies, we can just assign a cleaning lady for every floor, now each lady only has one floor to worry about.
JeraJera01 they show her
Teacher: "The homework isn't that complicated"
The homework:
underrated
i'd rather drop out
This is not complicated 😅
No caps, this is actually my homework.
@@mish4272 Same, BA1 MT at EPFL and this is part of my Computer Science homework
Mathematician: "All the math works out."
Hotel Company: "Ok sounds good, let do it!"
The Architect: *Visible terror*
omg this comment is gold why doesn’t it have 10k likes sksksksskskk
@@axlychee3113 shut up
The engineer : had a stroke and died
@@CJ-ow2ld Imagine the elevators!
Elevator: I can get you to your room in 3-5 business days
Imagine walking in at 3:00 AM and realizing you have to go to room 12237863891763892787652
"The infinite hotel got full"
Me: Hold up, somethin ain't right
Something's wrong, I can feel it.
Infinite confusion
this theory is wrong the hotel is already FULL with infinite numbers of guest which are = to infinite numbers of rooms he said
@@arslanakram043 Yes, but just if you are considering only the countable infinity. But according to absolute infinity, not.
@@moisesggomes Ahhhhhh right, just clicked, of course, should have spotted it *frantically googles 'countable infinity'*
Everyone's chillin' until karen refuses to move to the next room
Profits: *crashes* in a second
The hotel still has room, having infinite space, there will always be more room. So it can’t be full
@@ChrisHinners008 you don’t seem to understand the concept of the paradox. The hotel isn’t generating new rooms or anything like that, an infinite of rooms exist there aren’t new ones when there are new people, so when there are an infinite amount of people they fit in the infinite amount of rooms. You can run out of room if you are working with multiple infinities.
@@zackschaefer my brain is kinda crashing now
imagine infinite amount of karens
Job: night manager in a hotel
Requirements: PhD in applied mathematics
@@TJYuh32 Additional requirements: Must be capable of sorting out an infinite number of people within 24 hrs.
@@jasonchiu272 8-12*
seriously suggested:: ability to complete supertasks
Lmao
@@TJYuh32 per nano sec
@@jasonchiu272 other additional requirements: must be able to solve calculus math questions in seconds.
The most insane part to me is after all that effort, the hotel makes the same amount of money as before all that troubles
Its actually infinite amount of money not same but the term "Infinity" remains same.
What i mean is he made Infinity amount of money before the guests came, infinite amount after the guests came
@@jasinsworld3095 Initial infinity and final infinity are the same, otherwise either the former or both of them weren't infinite.
In reality, the whole "thought experiment" is flawed at the start, because by saying that the infinite hotel is full with infinite people, it tricks your mind into associating infinite to a finite quantity, but an infinite container can never be full in the way we intend it.
We associate room 1 to guest 1, room 2 to guest 2, and so on, but numbers lose meaning when they're infinite; you can always add any amount of guests, and infinite + N (where N can also be infinite) still equals infinite, and at the same time, if the rooms are infinite, it means they are already equal to infinite + N.
"Creating" free rooms by moving people is the demonstration that it's all based on an illusion of human minds thinking about infinite as if it was finite: "there was" already more (infinite) space for additional guests, because the reality is that the "new" guest aren't additional, they were already part of infinite.
The buffet must be a nightmare
Yea but then again there is infinite food.
Dániel Deák and most likely infinitely large
Only problem is the dining room must be infinitely large, so it takes for an infinite amount of guests an infinite amount of time to find their table
Poor staff
@@ucnguyenanh9414 there would probably be infinite staff
_"The Infinite Hotel Room is full"_
*Task failed successfully*
:)
:)
:)
:)
:)
The real paradox is how there’s still some sort of economy after this single man gained infinite money
Because everyone works for the manager .
Donovan Reynolds whatever country this is both has a GDP of infinity, a GDP per capita of infinity, and a GINI of 100.
Because he has cheats on
Manager
@@abrahampowell6792 HESOYAM
“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….
Hey person on the first bus in seat 7, another infinite set of infinite busses has arrived. Please move to room 22521666186739810716017129863546474247925813985186306383480395759255528226899398031271474259176472311138130302909797370563984143657840869015723623128208458564711932390036470899999940399003451938771468124775412134017692556582989981820657376622292117781429636251681663364133246565240603802421309871873386179061056683850002592550658912005406539073633368208169912295100765107813056035892005304712416817301893705332191267615274619407764899319819287315641053762034009508858938727147166108668063720886082155921552955435591503022900749768195878181491707144967461286550140023171580051111358071521188926359524314904062599527129957121490685127011258936786658012354838528. It's on the 2252166618673981071601712986354647424792581398518630638348039575925552822689939803127147425917647231113813030290979737056398414365784086901572362312820845856471193239003647089999994039900345193877146812477541213401769255658298998182065737662229211778142963625168166336413324656524060380242130987187338617906105668385000259255065891200540653907363336820816991229510076510781305603589200530471241681730189370533219126761527461940776489931981928731564105376203400950885893872714716610866806372088608215592155295543559150302290074976819587818149170714496746128655014002317158005111135807152118892635952431490406259952712995712149068512701125893678665801235483853rd floor.
FAX 🤣🤣
"And then, he named hotel "inn-finity""
That is clever.
Underrated.
Ah, I see what you did there.
Watch this comment be the first one with the most likes
I don't get it :(
legends says the guests are still moving to the next room
HAHAHAAHA
Just add infinite amount of newcomers. It will result in making +1 operation every time new guest arrives, but due to newcomers being infinite number of operations would be infinite.
Math says so to
Yes R, they r
they need to be
Infinite hotel? *_Trivag∞_*
@DaFragileTomato yes it is
@DaFragileTomato its infinitely underrated
Best comment ever
You got me there 😂
bendydick cumonmyback best username ever
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.
oh wait.. but what if there are infinite nights with infinite buses of infinite people? or what if there are:
infinite nights, infinite buses of infinite people, infinite rooms, and infinite elevators that only go up to floor n.
2:55 imagine being in room 50 and suddenly having to move to the quadrillionth room
That would be horrible
Same imagine being in room 100
how would the elevator work if it had infinie buttons
@@felixjaphygaming9115 You would just go to your room. 🙄
with an elevator, of course
"The Infinite Hotel Room is full"
Brain.exe has stopped working.
Every room has a guest, so it' s full.
Its funny how the "infinite" hotel only has one employee
Hidde Lekanne Deprez but then they move to the next room, which apparently didn’t exist
@@epicgaming7813 I admit that this video does a terrible job at explaining the problem and is basically one big inside math joke for the people who already know the problem.
It's a mapping problem, if you map person 1 to room 1, aka n to n then you know every room will be full. but if you map person 1 to room 2, aka n to n + 1 you know that room 1 will be empty (since there is no person 0). Intuitively you would eventually run into a problem: since both sets are infinite, thus equally large, that when the mapping is unequal (n+1) you run out of rooms before you run out of people. But that's where infinity comes in, both sets don't have an ending so this problem can't occur. Thus as long as you can find a mapping which assigns each person an unique room number you're allowed to fill whatever rooms you know won't be mapped to with whatever you want :p
To give an advanced example: I can say person 1 gets room 2, aka n to n * 2, and I have 1 free room for ever empty room, but the set is still infinite, meaning I have both infinite amount of full rooms and infinite amount of empty rooms. Intuitively I just created a "bigger" infinity with this mapping but mathematicians didn't find this distinction useful so we use other methods to compare infinities in size.
Hidde Lekanne Deprez I’m sorry I’m too lazy to read all that oof
This video should be called "how to lose an infinite amount of brain cells "
😂😂😂😂
I only have 2 though so that’s impossible
@@Lyenati you saying that actually makes me believe you.
Your Kyckling No, it makes sense. You can’t loose an infinite amount if there’s a finite amount.
@@Lyenati Then why did you specify that you had 2 IQ?
“Banking an infinite amount of dollars”
Inflation: “Do I look like a joke to you”
TED-Ed : The infinity hotel is full
Me:
Excuse me, wtf
Ahahahaha true
because it's countably Infinite
淼淼 8 Billion is countable
Yes, i really don't understand the first problem
it's one-to-one and onto, so that's why an infinity hotel can be full, one person for one room each
“One night the infinite hotel is full”
Logic: adios
Infinite - infinite = 0 :)
@@remainincognito6303 no infinite-infinite = infinite
Duhh Trueee
The hotel with the infinite rooms and infinite stories can't be full you're right 👌👍
Cause then it will not be actual infinite, it'll br finite if it's full, right??
@@remainincognito6303 lmao no infinite is a concept, not a predictable number. That is false by so many aspects.
@@sciencedoneright infinite - infinite isn't defined actually
Imagine waiting for the elevator of this hotel...
Infinity time
No tension! The hotel has infinite numbers of elevators 😉
There should be infinite number of elevators
Its fast as light
@Chim Chim Genie maybe it's not a button for each floor but rather one keypad where you input floor numbers?
I rewatch this video from time to time only bc i like the animations, and hurting my brain
forget about the manager
THE CLEANER HAS TO CLEAN AN INFINITE AMOUNT OF ROOMS
Omg
A maids Nightmare for sure :) Peace
There are infinite cleaners
Naw it’s cool, they got an infinite wait staff
@@jimiplayscobo5877 I can imagine smile ✌️
So basically the hotel guests are simply getting kicked out for an infinite amount of times ( ͠° ͟ʖ ͡°)
Yeah, this hotel deserves a rating of 1/∞
Ali Raza why not Negative Infinity?
@@raynerfr How to losing your braincell
Ice Pumpkin I’m sorry, what?
@@raynerfr can u count negative in finity to infinity?
Ice Pumpkin uhhhh, no? It’s literally impossible to count to negative/infinity
Ya know what is the meaning of infinity?
Manager’s IQ
first reply
@@mariafe7050 my god I completely forgot about this comment
I remember watching this video like 4-5 years ago, I had no background in math... Today when I was trying to show Q is countable, I used one of the ideas from the video! Never really realized or understood how important this video was and what kinda technicalities it had!
Imagine having to change rooms everyday and some dude telling you to go to room 2^7 id just give a bad review and leave
Imagine if you made a friend on your trip.
"Hello Mr Manager, this is my friend and we'd like to have neighboring rooms"
"Oh, I'm afraid it isn't possible Ma'am, you'll have to take the room number 7^14 = 678223072849 and your friend here will have to take the room 7^15 = 4747561509943".
Exactly!!!
@@CodecrafterArtemis OMG this made me laugh so hard
@@j5803 Me too xD
@@CodecrafterArtemis just ask the person next door to 7^14 to move the room 7^15 since they're always moving rooms it seems
Legend has it, He works for TRIVAGO now.
Hotel?
Trivago
😁
Hotel? Trivago.
😂😂😂😂😂
You start off understanding and following the video, and then eventually trail off and end up in the comments
Damn! You a mind reader?
It doesn't make any sense. If it was an infinite hotel it couldn't be full
Infinity isn’t a measurable quantity, it’s only a hypothetical idea. To put it simply, infinity does not exist in real life, as everything can be quantified and infinity by definition cannot be quantified. There are extremely large numbers, like the number of atoms in the universe, but no infinity, it only exists in our heads.
literally
Sheepy. Exactly what I done! 😂
Note to myself: Always book room number 0. So I won't get kicked out.
Except it doesn't exist in that hotel because all the rooms are natural numbers, therefore integers 1 and up.
Wouldn’t Room 0 just be the lobby
u would get kicked out at the n+1 and the cycle continues
That’s the lobby!
Its the lobby!
”So your room will be 2n+6^8-46^n”
Me: visible confusion
your*
Me: *∞ confusion*
if n = 3, then it will be
2 * 3 + 6 ^ 8 - 46 ^ 3
now shrink it until you find the answer
6 + 1679616 - 97336
1679622 - 97336
1582286
so, if someone is on room 3, he'll be on room 1,582,286
BonesYT whoa-
@@BonesRUclips Damn my legs are gonna hurt by the time I go to sleep
The hotel is full, with infinite guests.
Manager: *STONKS*
redditor
EPICO !!!
*Infinite stonks*
Don't you mean *ST∞NKS*
@@goodestboi7692 lmao😂🤣😂
Manager: hi ur gonna have to move to room 42069
Me: nice
More like: You'll need to move to room 345,748,838,889,226,728,826,528,282,828,282,629,529,772,628,738,538,729,628,728,827,419,319,420,026,001,519,520,001,510,528,000,000,000,000,729,620,729 to the 639,729,820,829,829,000,629,729th power
Othoniel Molina Argueta You really dont get the joke do you
@@Ke.442 I cringe reading your comment.
@@othonielmolinaargueta3442 dude
Nice
Relax and unwind with this soothing lofi track. Perfect for studying, reading, or just chilling out. 📚🎶
Me: gets settled in room 49
Manager: move to room 50
Me: ok no problem
Manager: now move to room 100
Me: well this is a bit frustrating, but will do
Manager: ma'am I'm going to need you to move to room 1,267,650,600,228,229,401,496,703,205,376
Lmao me in the infinite hotel
Lmao
I like that you actually calculated the numbers instead of putting in random numbers.
Well the thing is only if there is infinite people in the hotel
Omicron Force who cares
Not sure the guest in room 0.5 should be worried about his "neighbour" in room 1 when there is infinite rooms between them.
This got me thinking, is there the same amount of space between room 1/2 and room 1, as there is between room 100 and room 1?
@@edwardbrandon3170 There are both infinite rooms between them if you meant that. That is why there is a very big difference if you have n ∈ ℕ or n ∈ ℝ
@@edwardbrandon3170 You would be correct, there is infinite space between rooms 1/2 and room 1, just as there is infinite space between 100 and 1. Hence the reasoning of the paradox. Infinite just means "to much or to big for our measly human brains to understand"
@@edwardbrandon3170 It is possible to mathematically prove that there is the exact same "distance" (amount of numbers) in the intervals [1/2; 1](A) and [1; 100](B). Simply assign one number from interval A to each number from interval B through a bijective function
and 0.1928 reccuring would have to go to room 0.3856 recurring
things taught in class: a+b whole square
things asked in exams: infinity hotel paradox
Vishal Thale lmaoooo
wait is the term for (a+b)^2 really 'whole' square and not like 'quantity' squared? Maybe it's an american vs british thing?
-Hello! So the hotel is completely full?
-yes
-may be room 7 available?
-nope!
-room 1876544?
-occupied!
-room 7262545277272722727?
-no luck!
-room n?
-you wish!
-room n to the n power
-nope.
-THAN WHAT IS ALL THAN NONCENCE ABOUT MOVING PEOPLE INTO THOSE OCCUPIED ROOMS?
Congratulations. That is why this thought experiment is for people who can't tie the shoelaces on both of their shoes.
So this is the only hotel that TRIVAGO can’t show us.
Trivago be like:
I fear no man
But that thing...
*Infinite Hotel*
It scares me
But TRIVAG♾ can
@@theconfusedguywhogotthespi9889 😂
@@theconfusedguywhogotthespi9889 hahahah
🤣🤣🤣🤣
The infinite hotel is completely full.
Me : Wtf am i doing with my life
JellyGames Mostly looking for an alternative hotel. One where they dont keep waking you up to change rooms.
JellyGames
U R learning alchemist which makes single stone into the gold
YOUR DR T
GET HIM
HES DR T
"The hotel manager decides to find a room for him. How?"
7th grade me: infinity plus one.
@@flammableflame5056 hootel
I don't know why i found this cute😅
Infinity plus one is actually a legitimate answer
im in 7grade
Actually infinity + 1 makes sense!
"Square root rooms, like room radical 2, and room pi, where the guests expect free desert"
Best line.
Can somebody tell the manager that room sqrt(42) is being noisy? I don't want to climb down an infinite set of stairs to go tell him. Also, as expected this hotel is no exception to the norm and does not have infinite free wifi.
Lol wtf are you doing here
Cyranek Its in the 20's so.....
WHAT ARE YOU DOING HERE `?
Cyranek hail
666 likes omg
The Infinite hotel: *Exist*
The Infinite IKEA Store: *Fnally, a worthy opponent. Our battle will be legendary*
SCP foundation: oooooo a new SCP to contain!
Infinite IKEA store: you better put it right next to my containment
SCP foundation: no, they're in a different continent
Could the stand arrow count as an scp
Then some guest opens room #θ-prime and the hotel collapses.
The kung fu panda line
but it was me dio
Imagine staying at a hotel and the guys asks you to move to room 2 to 36 power
Wyatt you would move to room 68.719.476.736
maybe the elevator is infinitely fast
@@caiooctavio yes, but with infinite floor you could never reach anywhere
*You could never reach the truth**
@@thebookless3381 ohshitthat'sdeep
Imagine being in room 1 sleeping at 3 am and some guy tells you to move to room 192838377374747474736366383892829919
Hard working night manager?!What abaut the only cleaner in an INFINITE HOTEL???!!
Let's say it has infinite staff too
infinite cleaners o
so right
@@f4d4 But on the animation there is only one old maid, who is probably never gonna see her grandchildren, because of the infinite work at the hotel
ShowStopper there are not that many Hispanics chill
It’s funny how I thought i might be able to understand this
DJ Stone Productions Hahahaha sameeeee
Jessica Suchy freal 😂😂😂💀😭
Im So Smart so i dont know what is there hard to understand So probably you still understood more than me
😂
Same
Worker: Sir, you have to go to room 1,605,546,491,106,999,545,694,136,742,623,645,786,434,205,316,1405,000,000,000,000.
Me: *say sike right now*
SIKE THATS THE WRONG NUMBER
Renewin Celestian 😂
Or 1.6055465e+61
How do I read this?😂
Technically it could still be way worse
After this extraordinary performance, the night manager was given a raise and now makes 7.50/hr from 7.25
I remember watching this video a few years ago and by the end of it, I hadn’t understood a single second of the solutions. I remember simply dazing on the video even after it was done - perplexed by how complex it felt. Over the years I have learnt more, explored more and applied more. Though I won’t go as far as saying this video has been haunting me through these years, I will say that the thought of its existence would occasionally spring up in mind, puzzle it and eventually disappear, only to come back later. But today this video finally appeared in my suggestion page and well I understood it this time. I know it’s trivial but it’s another something that I have learnt, and I am happy about it, especially because how simple I found it as compared to the first time I was faced with it. Well I guess now that all is said for no absolute reason, I’ll just tell you - have a good day.
I feel you. Sometimes we just don't understand somethings no matter how we try... But then one day, out of nowhere, we clearly see through it... It is amazing...
BTW, I still haven't figuted out this video yet.. But I am so happy for you 😊
well suggest us, the confused viewers something about how will we understand
Wholesome 100
Gotta respect taking the patience and humility to understand unlike half the comments being like " this is wrong, i know better after a 10 minutes RUclips video, than a 100 years of mathematicians. My intuitions are just that good" lol
What grade are you in?
"room pi, where the guests expect free desert"
ok I see what you did there
Pi is also 3.14 which backwards is 41.3 or pie
Room pi-e
Who doesn't like to get a hotel room to eat pie?
@@jyotisrivastava1122 ROFL
@@prerakgames4668 it works better with other font
I feel that the hotel manager is a tad overqualified for this job.
Doesn't matter, the pay's good.
just a tad 😂😁😂
True, but most anyone else would be terribly under qualified I think...
Actually, he's infinitely qualified.
Arbitrary Renaissance actually, the pay is infinite
Imagine checking in at 5am and you have to go to room 9 quadrillion.
Imaging being settled in a room and then the manager is like: “you need to move oops”
And that too will happen Infinitly
Nice onee
"we need you to go to room 1943937^1837 "
Actually happened to me once, except we were kicked out cuz they had overbooked the entire place and didn't realise until it was too late 😂 Still loved New Zealand tho
I'll say "ok, I'm going home and never coming again."
*Room 6 is empty*
*The cleaning lady:* “This, does put a smile on my face...”
It doesn't matter how many rooms are empty since there are still infinite rooms to clean up! ^^
Don't worry. There's infinite number of cleaning people in this building
At the end of the video the word “infinite” doesn’t sound like a word anymore
jamai vu
That's called semantic satiation!
Take a shot every time
It’s a way of life the people live at the hotel
Daja vu
"the infinite hotel is full"
math: moye moye
I think that it’s only relatively full. From that initial perspective. When there comes more than one infinite of people that are already booked the space is automatically generated to fit the people that arrived. If that infinity that is full cannot fit more people it wouldn’t be infinite.
(I will contradict myself: if you have an infinite big water bottle that is filled, can there be added more water to it? Can that water bottle be stretched to be able to contain more water? If it’s full then that means that there shouldn’t be more space without deforming the first reference system……) This is how I’d imagine a closed infinity system…..
😭😭😭I can't
No matter how big the number is, it's always closer to Zero than Infinity!
Deep
Yes
Love that.
ah well it will also be close to its successive and previous number, if thats a whole number. If its a real number well, its infinitely close to the preceding and succeeding number.
Wow ! I'll remember this dude. Also, is God Infinity ?
Builder: how many floors would you like manager: yes
Yes
Builder : how many floors would you like ?
Manager : how many bread did you eat in your life
666 likes
Legend says they are still building to this day
minus 111 likes please
I was OK til’ 2n, but then everything changed when the fire nation attacked.
this is a genius joke that u should be getting more credit for honestly
Laughing infinitely hard at the comments xD but this was one of my favorite ones 😂 well done hehe
Only a few understands this. Made my day
watch my maths tricks videos.
When the winged hussars arrived
nice lesson, but the poor night manager. ever since that one dude came in when the hotel was full, he's been asking the next and next guest to move to the next and next room. there's no stopping -- he's going to be asking the next guest to move to the next room for eternity and never see his family again. this is his life now.
Basically if you’re in room pi you can’t move anywhere else.
You can always go to 2 pi... but after that you'll probably start running between those 2 rooms for infinity, as well as other guest, who were asked to go to room pi... so... everyone would be on corridor- switching rooms
First of all, you can, like you would with any number. And why pi, specificly? There is a number of real numbers equal to Aleph 1, which can all be used in normal operations. Yes, pi has infinite digits, but even 1 has (1,0000000000000000000000000...), so I don't see the problem.
Man u r right. Pi is having an infinite numbers of digits after decimal, which means that pi will never end and you will never be able to go to the next room but one thing u missed my boy is that all the rooms in hotel are having natural number as their room number.
Also it's shaped like a circle.
2:36 why worry about ur job when you have an infinite salary??
That manager has infinite brain cells
And infindently smart!
@@findystonerush9339 infidelity
@@aryaankhan3725 Maybe you could use your visual prowess to put the infinite guests under genjutsu with your infinite chakra and make them feel accommodated.
@Sister Supersonic launch the infinite tsukuyomi, problem solved
But to be real it is not possible...
I'm just over here trying to have a nice sleep and the manager keeps telling me to move rooms. Had to give them 0 stars
watch my useful mathematics videos.
I give the hotel infinite bad ratings.
*infinity stars
Or the manager could simply change the number plates of the rooms assigned.
me throughout the video:
experiencing extremely high confusion ever
I feel bad for the people walking on the infinite staircase to get to the infinite room
well since everything is infinite, they could get there in 0 seconds.
And all so the maiden
And the cleaning lady
Infinitely tiring.
SCP
I got stuck at "imagine a hotel"
M.woller im confused
hahhahhahah
Trivago.
Lol
So was i
Someone give that room service maid a raise.
I think her normal paycheck may already cover that raise, what she needs is a vacation
She have א0 $ and she need א1 $
@@CinnamonRolz240 The hotel gets infinite amount of money so she probably gets a lot
Maid be like: don't talk to me my brain hurts UwU
If every guest tipped her, if so only a single cent she would have an infinite amount of money.
There is some unintentional horror fuel to this. The larger the room number an infinite hotel-stayer got relocated to, the less chance they'd have of ever being able to find their way to the hotel exit when they were ready to leave, both in terms of knowing where to go and also the sheer distance involved. It's the hotel equivalent of the backrooms.
"One night, the infinite hotel is FULL"
Wait what
Adelmund Oppo yeah, this doesn’t make any sense
@@cuongnguyenviet3417 no, an infinite amount of person came
It can be infinitely filling up, but not full.
Or at least I don't get it
@@omniscientomnipresent5500 it doesn't matter, the amount of rooms never end, therefore you can't ever run out of rooms or be full. This entire video makes zero sense.
@@alfrednaccarato2359 a 40 peoples hotel can be filled by 40 peoples so why a ∞ peoples hotel couldn't be filled by ∞ peoples ?
“A hotel with an infinite number of rooms is full”
Is it just me or does that not sound right
The infinite Hotel is full of Infinite amount of people
@Too Beautiful To Handle Ya but the Hotel concept was just a way of ''dumbing'' it down for us.
It means that in every room, someone is there. There is nothing illogical about that
@@SterusXN89 bro if it is infinity room and infinity people then or than how can u fill the unfiled people. I mean u can fill the people in romm cause it is infinity room u see that. Plz explain if u can
imagine that the hotel is empty and a bus with infinite people arrives at the hotel.
Then, the first person of the bus (suppose that the people and the rooms are numbered) goes in room 1, the 2nd in room 2, the 3rd in room 3 and so on: each room is assigned to a person, the hotel is full. There is not a single room not assigned to anyone
At this point, one can proceed the way shown in the video to liberate a room (or more rooms), if necessary
Wouldn’t it take the manager an infinite amount of time to ask everyone to move rooms?
Moge it would take every guest some time adding up to aleph noll
What about an intercom system?
N1cKyP4mH4zP0Pc0rnT0Eat electrical signal to play your voice over the intercom would take an infinite amount of time to reach every speaker
The maid does it, that's why she looks so angry all the time
No, because a computer scientist already created algorithms for a computer software which can tell the guests infinite times.
Imagine coming to this hotel with infinite rooms and still not getting a room
When you come in with an infinite amount of others, each with a infinitely long name consisting of a and b.
Binary: Allow me to introduce myself
AAAAAAAAAAAAAAAAAAA.................= 11111111111111111111111.............
BBBBBBBBBBBBBBBBBBBBB..............=0000000000000000000...........