The Infinite Hotel Paradox - Jeff Dekofsky

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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.

[@RK-jb6rq]

"Everyone is happy" Except the cleaning lady 😂

[@C4_Shaf]

There's an countable infinite amount of cleaning ladies.

[@zeeliang7828]

The lady is the 🤖

[@Bjowolf2]

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?" 😂

[@Bjowolf2]

The poor plumber is not very happy either 😂

[@davidvorano3904]

But she gets infinite money for her job

[@seagull1076]

Bus driver: Are there rooms open for my passengers? Manager: Yesn’t

[@sazidmohammad2374]

Thats the imbrogilo!!!

[@nuttskippy6293]

well yes, but actually no.

[@yarenkurtulus]

Seagull i haven't even watched the video yet but funny

[@scallywag1716]

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.

[@calik.5094]

Clever :)

[@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

[@AA-ni3km]

And then Buddy the Elf gets into your elevator and presses all of the buttons ...

[@mohakmotwani4427]

It will have infinite elevators

[@itzwindows]

@@AA-ni3km :trol:

[@spikepowir]

@@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

[@taskfailedsuccesfully738]

"Maybe there's super mega bombastic ultrasonic fast fantastic elavator that delivers you to any floor instantly" - summer, 2 weeks ago

[@RobloxKid123]

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.

[@thatmuffinguy3692]

underrated comment

[@abhyudaykaushik9669]

bro. Who are you? Einstein the memer coz holy cow thats a great comment!

[@benwills7343]

Eh, you got an infinite amount of time to get there.

[@fmjjjjn7510]

Hey are u at your room yet?

[@RobloxKid123]

@@fmjjjjn7510 Not yet, still stuck in the elevator

[@azryxthefolf6331]

Imagine the elevator in that place. "Hey man, where are you staying?" "Room 1.949213 x 10^77789"

[@inneropinion6572]

Maybe they all stay on an infinite 1st floor.

[@estebson]

"Oh, you're lucky. I'm staying in room 8.369304720x10^4830382075."

[@MrSRMatthews]

The lift control panel is basically a scientific calculator

[@venkatasriharsha5911]

@@MrSRMatthews 😂😂😂

[@Ken-vz1gl]

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.

[@Asu01]

"One night, the infinite hotel is full" Me: _"Infinite confusion"_

[@crystallava5002]

'One night, the infinite hotel is full with an infinite amount of people' Brain: 💥

[@andro.txt0]

where is the numbers alabnole and Omega?

[@jeank2323]

Asu howwwwwww

[@LegacyCrono]

Who are those poor women birthing an infinite number of children?

[@carloalbertopirastru9503]

@@LegacyCrono the mothers of the wicked

[@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.

[@dumbreon_plays2139]

And an infinite amount of debris

[@JoseMedina-xq8mf]

Breaking news: A second infinite plane has hit the infinite hotel

[@silverthewitchdoctor8262]

@@JoseMedina-xq8mf ♾️/♾️

[@ygotsvlog3762]

@@JoseMedina-xq8mf breaking news infinite planes are hitting infinite skycraper causing infinite deaths and infinite 9/11

[@JoseMedina-xq8mf]

@@ygotsvlog3762 Infinite jet fuel cant melt infinite steel beams

[@downwitthe1876]

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 💀

[@ofakind-qq7sz]

Swag in ohio 😩🤘

[@NetherFrog]

lmaooooo

[@core609]

down in ohio

[@thanhtamnguyenthi7073]

50?

[@NetherFrog]

@@thanhtamnguyenthi7073 ?

[@Dev_Toast]

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

[@averagesoul8256]

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

[@bennytan5017]

IT IS *ALEF NULL*

[@mochidoesart3481]

Pupper Playlist Night Manager: No it ain’t XDDD

[@jaysondavis9693]

Infinity=infinity but infinity is also an infinite times more powerful Now compare this to zero

[@laststand1618]

A wild universe deletion appears!

[@ilovecats6238]

everyone gangsta until the manager calls to fix the roof

[@purpleapple4052]

Impossible.

[@ajaymahajan3890]

There is no roof since there are infinite rooms

[@ripudamansingh4229]

lol!!!😂😂😂

[@Noname-67]

@@ajaymahajan3890 the roof is still there just infinitely high

[@somebody1870]

Oooooooooo fluck

[@hasanicahyadi9100]

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.

[@yellowstarproductions6743]

I agree

[@towatchvideos5592]

"Everyone is happy" Probably not, who would want to constantly be asked to switch rooms?

[@cristiangomes6101]

they switched rooms infinity amounts of times

[@MercurialMoon]

Even worse, they have to walk infinite amount of stairs

[@arafe.1012]

they tell different people to switch rooms

[@Noah-Runge]

Its an Infinite hotel. Not a five star infinte hotel. You get what you pay for

[@Cyberaser]

@@Noah-Runge Sounds like a hotel with negative infinite stars.

[@hahanamegobrrr6667]

"One night, The Infinite Hotel is completely full" *laughs in mathematics*

[@billyandrew]

To the nth °

[@figsenjoyer]

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

[@thomasbraun6097]

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.

[@mayoiga9178]

inifinite hotel cant be full right?

[@HuyenPhan-ir2wo]

And the night manager is now in depression. *CRIES IN MATHEMATICS*

[@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.

[@irsaa.3473]

wow same haha. this video is my childhood, it always feels nostalgic to be here again

[@stephenhofmann1012]

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.

[@vincentjiang6358]

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.

[@Swift-Prime]

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

[@tomlever]

Thank you! I couldn't believe nobody else was mentioning this. It would have terrible online reviews. Infinitely bad.

[@morallyconflictedtortoise6494]

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.

[@tomlever]

@@morallyconflictedtortoise6494 😀😆😂🤣

[@Petaurista13]

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.

[@5-minutetalkshow263]

you actually never get a room you move to room 3? well they actually need you in room 7. And so on

[@gracecalis5421]

Manager: Sir, we'd like to request that you move from Room 1 to Room 2 Guy: No Manager: Oh **entire hotel implodes**

[@MisterGn0me]

A Thanos move no doubt

[@yechankim7713]

You could just start from room 2 and ignore room 1

[@boubander9917]

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..

[@hooankee]

*entire hotel implodes* infinitely

[@Dennis19901]

@@yechankim7713 You could also start from room n+1 and leave everyone where they are

[@gilthenrill1024]

“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….

[@jensentota]

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.

[@SpaceGuyTDG810]

FAX 🤣🤣

[@overclockofficial6669]

I think if I asked to check in at a hotel and the receptionist asked what my bus seat was, I'd be more than a little concerned

[@blueee0088]

"And then, he named hotel "inn-finity""

[@twitterusersarefreakingstu2200]

That is clever.

[@exilley2134]

Underrated.

[@leonardodiserpierodavinci8016]

Ah, I see what you did there.

[@Neyobe]

Watch this comment be the first one with the most likes

[@Nathan-Croft]

I don't get it :(

[@segul2309]

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

[@Ambersworstenemy]

Something's wrong, I can feel it.

[@shintyty]

Infinite confusion

[@arslanakram043]

this theory is wrong the hotel is already FULL with infinite numbers of guest which are = to infinite numbers of rooms he said

[@moisesggomes]

@@arslanakram043 Yes, but just if you are considering only the countable infinity. But according to absolute infinity, not.

[@sigoy]

@@moisesggomes Ahhhhhh right, just clicked, of course, should have spotted it *frantically googles 'countable infinity'*

[@90schilllofi]

Relax and unwind with this soothing lofi track. Perfect for studying, reading, or just chilling out. 📚🎶

[@craz2580]

I rewatch this video from time to time only bc i like the animations, and hurting my brain

[@moonshadow1794]

This video should be called "how to lose an infinite amount of brain cells "

[@alieninwonderworld]

😂😂😂😂

[@Lyenati]

I only have 2 though so that’s impossible

[@YourKyckling]

@@Lyenati you saying that actually makes me believe you.

[@Lyenati]

Your Kyckling No, it makes sense. You can’t loose an infinite amount if there’s a finite amount.

[@YourKyckling]

@@Lyenati Then why did you specify that you had 2 IQ?

[@HiddenTalent_07]

"Everyone's happy. and the hotel's business is booming more than ever." *Angry maid walks by*

[@arnold8248]

This hotel has infinity maids

[@andrewt.7555]

@@arnold8248 who work an infinite number of shifts for an infinite amount of time. Also no retirement.

[@snockos6263]

I’m feeling like the maid being like 🤬🤯👺👹💩

[@ashupashu5559]

Infinite maids!

[@pragyanpranay3681]

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!

[@thienhuynh1361]

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

[@lkusa]

forget about the manager THE CLEANER HAS TO CLEAN AN INFINITE AMOUNT OF ROOMS

[@FuriouzJeth]

Omg

[@jimiplayscobo5877]

A maids Nightmare for sure :) Peace

[@tmounidharan]

There are infinite cleaners

[@lt.spookycarrot1925]

Naw it’s cool, they got an infinite wait staff

[@kylegregory2876]

@@jimiplayscobo5877 I can imagine smile ✌️

[@lukadjordjevic638]

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

[@TheSewDew]

What if there are infinite maids that look the same

[@nicolaidisnicolareis4839]

@@TheSewDew Oi! That's jokes aside a good theory!

[@steven401ytx]

No

[@shernandez6639]

DOROTA

[@noa1175]

There's actually an infinite amount of maids

[@OmegoDeLindo]

This channel makes exquisite content with the highest order. To that, I truly thank you for this remarkable channel. With fluid animations and easy explainations, this channel has made me into a being you cant fathem. I will gladly share this with my future children as it will help them grow into knowledgable human beings. Thank you for this wonderful content. Sincerely, A being from the UK

[@rahulkulk745]

Nice

[@StopTheUTTP]

Don't copy MrBeast (reply to me)

[@fandroid6491]

For a moment I thought you were one of those fake Mr. Beast bots

[@madelynb2189]

R U REAL? I LOVE MR BEAST PLS

[@gokulwarrier2648]

You misspelled “fathom”

[@AvniShukla29]

Very well explained and good illustration

[@lisabakker7288]

Builder: how many floors do you want? Manager: *yes*

[@faraz259]

Underrated

[@user-km5ok4gt6v]

~infinity~

[@someguywithahecktonofcomme9154]

Wait wouldint it get destroyed by the sun or it will stop at the max build high

[@lisabakker7288]

Back Huat Lee lol I never thought of that

[@sulojanasukumaran2373]

Imagine waiting for the elevator of this hotel...

[@asheekarizqiirhamna4105]

Infinity time

[@ishansharma7909]

No tension! The hotel has infinite numbers of elevators 😉

[@batoulabbad1755]

There should be infinite number of elevators

[@Mn12074]

Its fast as light

[@nicbentulan]

@Chim Chim Genie maybe it's not a button for each floor but rather one keypad where you input floor numbers?

[@user-mz6zn1od9h]

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.

[@minarimyoui2223]

I’ve been in love with this the first time I saw it

[@liam.28]

same

[@ramy8338]

Everyone's chillin' until karen refuses to move to the next room

[@Healthandwealth9422]

Profits: *crashes* in a second

[@ChrisHinners008]

The hotel still has room, having infinite space, there will always be more room. So it can’t be full

[@zackschaefer]

@@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.

[@tricklander87]

@@zackschaefer my brain is kinda crashing now

[@oshiriz6486]

imagine infinite amount of karens

[@SANumber169]

"The hardworking night manager" looks like the cleaning lady has to work harder

[@themanguy2110]

nah, they hired an infinite number of cleaning works for their infinite cleaning crew

[@eeshanmarathe3369]

@@themanguy2110 Should've hired Infinite Managers

[@jeanllup6150]

@@themanguy2110 An infinite number of cleaning ladies is clearly too much, while a finite number is ridiculously low. I guess the Head Manager is having a hard time too

[@clairdeloona]

@@jeanllup6150 I think we should hire half of infinity (before you say anything I know what that means)

[@ravelnavarro9625]

@@clairdeloona how do you get half of something that isn't countable

[@diktrishabiswas]

Anyone else who is watching this video for years instead of going to therapy. Cause this is so therapeutic 😭🙌🏻

[@avivastudios2311]

Are you talking about the guys voice? I think his voice is the best Ted ed has.

[@florianwalter704]

Note to myself: Always book room number 0. So I won't get kicked out.

[@Tiqerboy]

Except it doesn't exist in that hotel because all the rooms are natural numbers, therefore integers 1 and up.

[@mr.lejend1825]

Wouldn’t Room 0 just be the lobby

[@blackretsu7452]

u would get kicked out at the n+1 and the cycle continues

[@anthonybenci9035]

That’s the lobby!

[@nothingmuch1039e9]

Its the lobby!

[@sonni6181]

_"The Infinite Hotel Room is full"_ *Task failed successfully*

[@danyagrigoriev292]

:)

[@yoona462]

:)

[@kittycake1294]

:)

[@jonyprepperisrael60]

:)

[@jonandres2975]

:)

[@lmSheep]

You start off understanding and following the video, and then eventually trail off and end up in the comments

[@nswij62]

Damn! You a mind reader?

[@POOFAYMANN]

It doesn't make any sense. If it was an infinite hotel it couldn't be full

[@ares_bluesteel]

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.

[@therevolutionaryrevolution]

literally

[@EmilianoCarlito]

Sheepy. Exactly what I done! 😂

[@wehitextracellularidiombit4907]

Where mathematics meet poetry. I still come back to this video once in a while for the sole purpose of taking a small hike in some high altitude vale of wonderment.

[@RobloxKid123]

“Banking an infinite amount of dollars” Inflation: “Do I look like a joke to you”

[@serowan]

"HE MIGHT LOSE HIS JOB" Isn't he already gonna lose his job because hes constantly kicking guests out of their room?

[@user-ws5ei9zf8p]

But he makes infinity dollars a night who cares if he loses his job

[@serowan]

@@user-ws5ei9zf8p no job means no profit means no money means no infinitu dollars

[@krishafyme]

@M. Woller have you read the fault in our stars, "Some infinites as bigger than other infinites" #)

[@Swift-Prime]

He's just on an infinite amount of weed

[@kek848]

After one paycheck he can retire

[@Dylan-Frost]

2:55 imagine being in room 50 and suddenly having to move to the quadrillionth room

[@TheDankBoi69]

That would be horrible

[@minhucam5026]

Same imagine being in room 100

[@felixjaphygaming9115]

how would the elevator work if it had infinie buttons

[@princeofallnegros4035]

@@felixjaphygaming9115 You would just go to your room. 🙄

[@felixjaphygaming9115]

with an elevator, of course

[@helloooooo140]

After this extraordinary performance, the night manager was given a raise and now makes 7.50/hr from 7.25

[@blahajgang]

imagine taking an elevator to the final floor 💀

[@kimhyejin3939]

Um that would take infinite time? 💀

[@littleantukins4415]

AAAAAA

[@thatsreeeal]

this hotel has no final floor because there are infinitely many :D

[@dieselboy.7637]

Do you know what infinity is?

[@NelsonLAN]

"The Infinite Hotel Room is full" Brain.exe has stopped working.

[@hidde3508]

Every room has a guest, so it' s full.

[@sobervision1049]

Its funny how the "infinite" hotel only has one employee

[@epicgaming7813]

Hidde Lekanne Deprez but then they move to the next room, which apparently didn’t exist

[@hidde3508]

@@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.

[@epicgaming7813]

Hidde Lekanne Deprez I’m sorry I’m too lazy to read all that oof

[@SomewhatDapperExtraterrestrial]

Teacher: "The homework isn't that complicated" The homework:

[@afaresfors]

underrated

[@DaDerpyCarrot]

i'd rather drop out

[@JPL454]

This is not complicated 😅

[@mish4272]

No caps, this is actually my homework.

[@marcnassif2822]

@@mish4272 Same, BA1 MT at EPFL and this is part of my Computer Science homework

[@Ehbebsbhxhebnens]

For people who are confused, you can't just make the newcomers go to the "new room" because they are fully booked and infinite guests bcs then they wouldn't go to their room

[@sola2943]

This thought project is invalid if "every" room is full. If every room is full then no room is empty and therefore the newcome will by no means rightly receive accommodation without evicting someone else.

[@AnasSaahirHuq-or9bv]

@@sola2943No one needs to be evicted, you do not get it. The idea is that because this is a hotel with infinite rooms you can just *make* infinite empty rooms by moving your guests to the next room(according to whatever strategy). The reason why the next room would be empty is because the guest in that room would move to the next room; leaving the room they were just in unoccupied. This process is the same for the guest in the next room and guest in the room after that and so on. This goes on infinitely, countably infinite. If you do not understand, research countable infinity and what exactly its existence means. I recommend watching “Infinity is bigger than you think-Numberphile” on KZbin.

[@vibingtomatoe]

In case anyone’s confused: ‘n’ is the position number. So n+1 = position number + 1. So if the first room is Room 1 + 1= Room 2. Room 1 is the ‘nth’ term. So if someone asks for Room 18, you can just say 18+1= 19

[@DavidMuri-rm4ym]

Yeah and that's making the assumption that only one person can stay in each of the countable Infinity amount of rooms but instead if the limit was 5 people in a room out of the accountable Infinity amount of rooms then the hotel would store about countable Infinity 5 amount of people

[@rodmoazzami]

legends says the guests are still moving to the next room

[@ananyaavarma15]

HAHAHAAHA

[@Petaurista13]

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.

[@MouseGoat]

Math says so to

[@setekreling4956]

Yes R, they r

[@dfdxdfdydfdz]

they need to be

[@nguyentranduchungpotter3241]

I rated this Hilbert's hotel 1 star They kept making me change my room

[@rhamzellibay4098]

No matter how you rate the hotel, it will always be a 3-star hotel because average

[@ctleans6326]

@@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.

[@rhamzellibay4098]

@@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.

[@ctleans6326]

​@@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.

[@rhamzellibay4098]

@@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.

[@kaitlynsarah2]

"Square root rooms, like room radical 2, and room pi, where the guests expect free desert" Best line.

[@ThangLe-cj8qy]

Love to watch it every morning 😅

[@lemlemwoldemichael7693]

Builder: how many floors would you like manager: yes

[@drippinbroomy4830]

Yes

[@oscarmichel8893]

Builder : how many floors would you like ? Manager : how many bread did you eat in your life

[@kerwwyngonzales9547]

666 likes

[@tevoi8057]

Legend says they are still building to this day

[@Staeve64]

minus 111 likes please

[@donbaneado]

Infinite hotel? *_Trivag∞_*

[@timothybryce1948]

@DaFragileTomato yes it is

[@crimeson4292]

@DaFragileTomato its infinitely underrated

[@alainapostsstuffonoccasion4758]

Best comment ever

[@lapsedisasterarea7672]

You got me there 😂

[@ir0ngamer393]

bendydick cumonmyback best username ever

[@andrewfranklin7767]

You can checkout anytime you like ... But you can never leave!

[@shreyaskulkarni526]

Imagine coming to this hotel with infinite rooms and still not getting a room

[@gwainexe9065]

When you come in with an infinite amount of others, each with a infinitely long name consisting of a and b.

[@nguyennhatnguyen8255]

Binary: Allow me to introduce myself

[@nguyennhatnguyen8255]

AAAAAAAAAAAAAAAAAAA.................= 11111111111111111111111............. BBBBBBBBBBBBBBBBBBBBB..............=0000000000000000000...........

[@_uditsingh]

Legend has it, He works for TRIVAGO now.

[@elias-ml6eo]

Hotel?

[@dinomarsic4688]

Trivago

[@Natalia-hf3et]

😁

[@FishlandicFishy]

Hotel? Trivago.

[@cordatus7209]

😂😂😂😂😂

[@sonicstar505]

Ok but if the hotel is infinite, would it even get full it the first place

[@clocksan9553]

+Jess Express why wouldn't it? there's an infinite amount of guests the hotel room is infinite, and each room is occupied. therefore, the number of hotel guests is infinite hilbert hotel is basically another way of saying that infinity +1 = infinity

[@cwjakesteel]

+Jess Express IMO, the first problem is assuming that a hotel with infinite rooms wouldn't take up all the space in the universe to accommodate space to build roads so that buses can bring in more guests. A hotel with infinite amount of people would automatically contain all people as the video introduces the paradox that the hotel is "full" while at the same time not. In the video's final solution, the hotel also has an infinite number of empty rooms as only multiples of primes are filled, so why couldn't the hotel be in that state from the beginning? The video's argument defeats its own premise for its argument and all the math involved is nullified.

[@flappyfeet1147]

+Jess Express No it wouldn't, and that's the point behind the hypothetical scenario of the infinite hotel, there are so many technical loopholes; essentially making the point of how hard it is to really grasp the concept of infinity.

[@sayuas4293]

+clock san It seems to me that since infinity+infinity+infinity...etc=infinity, he doesnt need any new solutions for more infinite numbers of guests. Infinite rooms are enough for an infinite amount of buses with each infinite amounts of guests.

[@clocksan9553]

Sayuas nope, it doesn't work that way. infinities interacting with each other in the basic mathematical operation is a big no no. that means, infinity plus/minus/times/divided by infinity can't work. you have to use another solution. well, at least in calculus. i've no idea how it is in a more advanced mathematics. did you know that some infinities are bigger than the other? yup, it's confusing. and that is the entire point of hilbert hotel. infinity is such a hard concept to grasp because of how counter intuitive it is

[@watarusakurai7030]

直感に反するが分かりやすい例え

[@preciosagaleng4032]

I love how you have to walk to walk to walk 10000 floors or more up because an infinite number of busses with an infinite number of people came into the hotel and the hotel doesn't have elevators Edit:also the room service needs a vacation they have been walking since the big bang

[@Cris69420]

TED-Ed : The infinity hotel is full Me: Excuse me, wtf

[@tristanhuiperez536]

Ahahahaha true

[@987654321ABC1000]

because it's countably Infinite

[@frey8893]

淼淼 8 Billion is countable

[@game-clips9657]

Yes, i really don't understand the first problem

[@987654321ABC1000]

it's one-to-one and onto, so that's why an infinity hotel can be full, one person for one room each

[@oasis1282]

Mind tickling.

[@PrajwalNayak-so5uv]

Sometimes I also have these kind of illogical doubts which seems to be logical, just like Paradoxes of Zeno, but I used to not think much about it as no one gives it importance saying that it is illogical and has an obvious answer. But now Zeno gave me MOTIVATION to think more and have these kind of confusing doubts, or to be precise, Paradoxes

[@modus3493]

The real paradox is how there’s still some sort of economy after this single man gained infinite money

[@petegrusky2715]

Because everyone works for the manager .

[@CC-hx8gj]

Donovan Reynolds whatever country this is both has a GDP of infinity, a GDP per capita of infinity, and a GINI of 100.

[@abrahampowell6792]

Because he has cheats on

[@frederickang7058]

Manager

[@fldsfmfr8277]

@@abrahampowell6792 HESOYAM

[@Uwu-bj7bq]

Elevator: *stops working* People in the 999.999.999.999.999 floor: ö

[@ander.ramosv]

ö

[@sneezyguy793]

Ö

[@darwinlucero8423]

The 999.999.999.999.999 people: "I'll just take the stairs."

[@FelixTsang]

Jump™

[@budokan450]

*ö*

[@user-yb5uz6hh2g]

Can we stop to appreciate how much calculation the receptionist Has to do?

[@chadwicklin2091]

Just from my understanding it seems like the difficulty lies in how to catagorize infinite number systemetically

[@_icscata_]

Technically, an infinity is unlimited but the only limitation is our thinking about the limitation…. That doesn’t make the infinity less of an infinity if we cannot comprehend it….. 😅

[@otherlego]

“He could lose his job” bruh he makes infinity dollars are you on weed

[@anymaths]

you can watch my maths videos.

[@yongironi1367]

I always hear "on crack" but never "on weed" 😂

[@boski.creations]

Hahahaha

[@lorenzoperrone760]

Rincoglionito, if he loses his job, he'd lose an infinite amount of money

[@SStupendous]

exactly, he has an infinite amount of money so that doesn't matter it's not like his Boss is going to take his money back if he quits

[@Mo-nj2hp]

Job: night manager in a hotel Requirements: PhD in applied mathematics

[@wandering2320]

@@TJYuh32 expenses: infinite $ per hour

[@jasonchiu272]

@@TJYuh32 Additional requirements: Must be capable of sorting out an infinite number of people within 24 hrs.

[@frost_co]

@@jasonchiu272 8-12* seriously suggested:: ability to complete supertasks

[@jestfullgremblim8002]

Lmao

[@mrcricket275]

@@TJYuh32 per nano sec

[@emilythorne3100]

The first video from Ted-Ed that fails to teach me something that I was supposed to grasp from middle school.

[@zhizhongpu8937]

Great video!

[@wyatt7454]

Imagine staying at a hotel and the guys asks you to move to room 2 to 36 power

[@mrcastravete8220]

Wyatt you would move to room 68.719.476.736

[@caiooctavio]

maybe the elevator is infinitely fast

[@orangeapplekiwi6795]

@@caiooctavio yes, but with infinite floor you could never reach anywhere

[@thebookless3381]

*You could never reach the truth**

[@Fred_the_1996]

@@thebookless3381 ohshitthat'sdeep

[@Veronica-hl9eh]

why is no one talking about how pissed the cleaning lady looks edit: wtf nearly 5k likes?!?!

[@baileym43ish]

oh she's not pissed because of the infinite number of room she has to clean by 3pm. she enjoys her job and is thankful to have it. no, she pissed her young and irresponsible but infinitely gorgeous niece called in sick yet again this week. and she knows for damn sure her niece is not sick; she's going out again with her going-no-where boyfriend of her's who says he is a "day trader".... whatever that is! good for nothing so-and-so.

[@adthya9209]

* angry cleaning lady noises *

[@Gamer-uf1kl]

Cause we left you for that

[@Sinnbad21]

You must be talking about consuela

[@abibagri1]

We need infinite number of ladies for cleaning job

[@trusevich]

-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?

[@sola2943]

Congratulations. That is why this thought experiment is for people who can't tie the shoelaces on both of their shoes.

[@kennethferland5579]

The Real number infinite Hotel can still accomadate any number of countable infinities, just instruct only residents with whole number rooms to move and leave all others in place, effectivly carving a natural number subset out of the real number hotel and utilizing only it. The problem is when an uncountable infinity of guests arrive at either hotel when any guests are present as their is no way to avoid a collision via a reliable formula.

[@thetaomegatheta]

'The problem is when an uncountable infinity of guests arrive at either hotel when any guests are present as their is no way to avoid a collision via a reliable formula' You can just smush everybody into an interval in the case of real-valued Hilbert's Hotel, for example, onto (0,1) (like with the function f(x)=1/x+1/(x-1)), leaving 'rooms' R\(0,1) 'free'. In fact, all infinite sets have bijectional mappings onto some of their own proper subsets.

[@colamalfoy]

Nobody gonna give props to the cleaning lady at this hotel ? /:

[@jerajera01]

Who said the cleaner's a lady?

[@Cuzjudd]

Who says there's not infinite of her?

[@derfzgrld]

@@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 ;)

[@max010113]

@@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.

[@jdogmpd7369]

JeraJera01 they show her

[@dasannaki7851]

Fun facts: If a man jumps off the top of this building,it will take him infinite amount of time to land

[@martonferenczi7894]

Fun Fact: it is impossible to jump off the top of this building since it is infinitely high so there is no top.

[@ryanramjattan8714]

A: Suicide is impossible B: Flying is now possible

[@finn596]

"What happened to him?" "He died of thirst"

[@thegod2291]

I mean u can never go that high , eventhough u did and jump u will fall and not fall at the same time.

[@semicolon2599]

@@martonferenczi7894 There is a top. it just takes an infinite amount of time to reach it.

[@The21stGamer]

Coming back to this after actually learning basic algebraic notation felt like seeing the light.

[@thahorinhasankhan2630]

"the infinite hotel is full" math: moye moye

[@_icscata_]

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…..

[@lakshya4876]

😭😭😭I can't

[@corue]

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*

[@renewincelestian5007]

SIKE THATS THE WRONG NUMBER

[@jackybaby0]

Renewin Celestian 😂

[@yellowing5152]

Or 1.6055465e+61

[@triplekill3874]

How do I read this?😂

[@leebochance1]

Technically it could still be way worse

[@elaxerblaxer]

Infinity isn’t really a number it’s more of a concept So let’s say you have an infinite amount of rooms and guests When you add one guest, nothing really changes As Infinity+One = Infinity Even if you add 10 people, A billion, A trillion, Even Adding infinity amount of people will not change the number of guests as infinity almost always keeps its form as never ending

[@thetaomegatheta]

'Even if you add 10 people, A billion, A trillion, Even Adding infinity amount of people will not change the number of guests as infinity almost always keeps its form as never ending 1' Your line of thought breaks the moment there is an infinite bus of guests with real-valued (as opposed to natural-valued) seat numbers. You will not be able to fit them all in this hotel, no matter how you try.

[@sqjmkyswpgfzv]

6分間しっかり考えながらたまに巻き戻しつつちゃんと観たけど、何もわからんかったや

[@rahulkulk745]

Wait for some more years I watched this video 4-5 years ago but when I watched it again after so many years I understood what the concept is about Goodluck😁

[@sqjmkyswpgfzv]

@@rahulkulk745 thank you!!!

[@TheRealGuywithoutaMustache]

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/∞

[@raynerfr]

Ali Raza why not Negative Infinity?

[@kato3415]

@@raynerfr How to losing your braincell

[@raynerfr]

Ice Pumpkin I’m sorry, what?

[@kato3415]

@@raynerfr can u count negative in finity to infinity?

[@raynerfr]

Ice Pumpkin uhhhh, no? It’s literally impossible to count to negative/infinity

[@DJStoneProductions]

It’s funny how I thought i might be able to understand this

[@jessicasuchy6411]

DJ Stone Productions Hahahaha sameeeee

[@geraldjames999]

Jessica Suchy freal 😂😂😂💀😭

[@rockmove3547]

Im So Smart so i dont know what is there hard to understand So probably you still understood more than me

[@Samuel-bw6hg]

😂

[@PercabethLovernot]

Same

[@y2kmedia118]

What's really sad about this thought experiment is that if this hotel was actually real, the owners won't be satisfied with the infinite guests and would greed for more.

[@official-obama]

but how? would they use hyperbolic space?

[@alexandermcclure6185]

@@official-obama just get infinitely many infinite buses of infinite passengers!

[@nurtodaud3220]

Good job

[@danielecatona8292]

I got stuck at "imagine a hotel"

[@somebodyyoudontknow2663]

M.woller im confused

[@Kostis7Music]

hahhahhahah

[@p3t3r826]

@@somebodyyoudontknow2663 We all are

[@waIdemar44]

Trivago.

[@shajimathew8461]

Lol

[@Furieni]

I was OK til’ 2n, but then everything changed when the fire nation attacked.

[@NoneNone-qp3kj]

this is a genius joke that u should be getting more credit for honestly

[@crystallava5002]

Laughing infinitely hard at the comments xD but this was one of my favorite ones 😂 well done hehe

[@CharlesAnthonyLerasan]

Only a few understands this. Made my day

[@anymaths]

watch my maths tricks videos.

[@ravendalath4323]

When the winged hussars arrived

[@BhavithaLankipalli]

So here from infinite no. Of places in infinite no. Of roads in infinite no. Of vehicles with infinite no. Of people wishing to stay infinite hotel and ends up moving from one room to another and getting annoyed, that infinite no. Of people start fighting and soon the fight enlarges and infinite no. Of people get violent while fighting and there is infinite amount of blood all over the hotel ( poor lady working there *) and they keep fighting and start killing each other and eventually they end up smashing things around and the hotel crashes down and also leads to the damage of infinite building surrounding it leading to infinite no. Of deaths Lesson learnt: don’t go crazy…..

[@game_ender4317]

I loved staying in this hotel when I was there a few septillion years back. Good thing in recent times such as then, they only allow checking in between 7:00 AM and 7:01 AM, on February 29 when it occurs on the turn of the century, when its a blue moon and full solar eclipse, so that we we arent having to move around too much. I got there and I was assigned room 27, as there were at least 26 other people who checked in that day too. However I had to move next when just 1 bus of only like 10^10^12,794.383835 people arrived. The elevators used infinitely efficient wormholes and warp drives for faster travel, so the other guy who had to take the stairs must have been there longer ago before they installed new elevators. However next I had to move to a ridiculous room because get this: At 7:00 AM, February 29 58288482848483145838359602100 B.C., an infinitely wide line of infinitely long buses came, but that wasn't it apparently that was just a single parade, and there were INFINITE parades. They ended up assigning people by their parade number, bus number, and seat number for prime numbers (like really stay sonewhere else

[@Majestic469]

This is a lie. You can only build 256 blocks high.

[@andrewhernandez4563]

Who said you had to build vertically

[@Majestic469]

Andrew Hernandez NANI?!??

[@daireenignacio1175]

Oh yeah

[@sharoberry9874]

Well, it’s obviously not real. Don’t think too much into it

[@sharoberry9874]

Cyan Plush Captain Wh- Oh. Oh. _Oh._ *_OHHHHHHH_*

[@nomadx3313]

day 10 of quarentine : I don't know what i am watching anymore ....

[@halamk657]

🤣🤣🤣🤣🤣

[@semihk3345]

Same maaan same

[@AdenVids]

helpmre

[@ECliPSE-lx4by]

I have stayed at home for 2 months YaY.

[@ajishavayoli]

This one is suggested by one of my friend 😂

[@mavromarana]

So what if some of the guests can't do math? They won't find their room cuz they don't know what 9^9 is(neither do I💀)

[@sophie________]

calculator

[@pjplaysdoom]

A neater solution I thought of for the infinitely many coaches of infinitely many guests: Regard the current occupants of the hotel as coach 0, then those who arrive are in coaches 1, 2, 3, ..... We can partition the positive integers into an infinite list of infinite lists by considering what is the highest power of 2 that exactly divides the room number. So we have the odd numbers 1, 3, 5, 7... then those divisible by 2 but not by 4, i.e. 2, 6, 10, 14... then those divisible by 4 but not by 8, i.e. 4, 12, 20, 28.... and so on. We put the person on seat n in coach k in the nth number that is divisible by 2 to the power k but not by 2 to the power (k + 1). So seat n on coach k goes to room number (n*2^(k + 1) - 2^k). No rooms are wasted, and every coachload of people is evenly spread through the hotel. If you are sat next to someone on bus 100, your room numbers in the hotel will differ by exactly 2^(101). And the first person on coach k ends up in room 2^k.

[@pursuitoficarus200]

"The infinite hotel is full" I'm sorry w h a t

[@hyperplayer22]

T h e WHAT?

[@doapin6240]

W h a t

[@pursuitoficarus200]

professor snape Which is exactly what's imploding my brain

[@mahernurhussen2398]

Well the reason is that also the number of guests is infinite

[@wfwf9917]

@@mahernurhussen2398 but infinite minus infinite is 0 like 1 minus 1 is 0

[@Cheeseanonioncrisps]

Then one day the unthinkable happens: All the guests leave this awful clearly understaffed, hotel because they're tired of changing rooms every five minutes. The night manager loses his job and is replaced by a new manager who shuts off every floor after the fourth one- turning the hotel from a rickety, vertigo inducing, nightmare to a fairly normal hotel. The money that was previously spent on feeding and caring for an infinite number of guests is spent on refurbishing the place and it soon reopens as one of the poshest hotels in the country.

[@willevans3133]

+Cheeseanonioncrisps With the hotel previously having an infinite amount of money, it would be the poshest, finest hotel in the country

[@THEPELADOMASTER]

+Will Evans Well you'd have to spend the infinite money just to bring down the infinite amount of rooms you don't want to keep.

[@ayoutubechannel1023]

+Cheeseanonioncrisps Applause.

[@marianacaplan711]

+THEPELADOMASTER or, you can just board up the door to anything above the 4th floor and not worry about stuff rotting or the infinity rooms getting unstable because you are in corporate america and why spend money on doing something where there is a cheap fix?

[@THEPELADOMASTER]

Mariana Caplan Just imagine the infinite floors falling down because the whole structure gave in