How An Infinite Hotel Ran Out Of Room

If there's a hotel with infinite rooms, could it ever be completely full? Could you run out of space to put everyone? The surprising answer is yes -- this is important to know if you're the manager of the Hilbert Hotel.
▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀
References: Ewald, W., & Sieg, W. (2013). David Hilbert's Lectures on the Foundations of Arithmetic and Logic 1917-1933. Springer Berlin Heidelberg. -- ve42.co/Ewald2013
Gamow, G. (1988). One, two, three--infinity: facts and speculations of science. Courier Corporation. -- ve42.co/Gamow1947
▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀
Special thanks to Patreon supporters: Paul Peijzel, Crated Comments, Anna, Mac Malkawi, Michael Schneider, Oleksii Leonov, Jim Osmun, Tyson McDowell, Ludovic Robillard, jim buckmaster, fanime96, Juan Benet, Ruslan Khroma, Robert Blum, Richard Sundvall, Lee Redden, Vincent, Marinus Kuivenhoven, Alfred Wallace, Arjun Chakroborty, Joar Wandborg, Clayton Greenwell, Pindex, Michael Krugman, Cy 'kkm' K'Nelson, Sam Lutfi, Ron Neal
▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀
Animation by JD Pounds and Jonny Hyman
Thumbnail by Ivy Tello
Music by Jonny Hyman and from Epidemic Sound and E's Jammy Jams (Hotel Lavish - Radio Nights, Steps in Time - Golden Age Radio, What Now - Golden Age Radio, Book Bag - E's Jammy Jams, Arabian Sand - E's Jammy Jams, Firefly in a Fairytale - Gareth Coker)
Written By Derek Muller and Alex Kontorovich
Sound Design by Jonny Hyman
▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀

[@ibizenco]

Hotel manager: "You want a room, sir? No problem. The last room at the end of the hall is still free. Just follow the hall and you'll get there. Eventually."

[@SuperBhavanishankar]

💀

[@Anzal.__]

Wrong

[@edu_was_taken9597]

Lmao I’ve seen this vid like 50 times and this comment it’s the best

[@TachyBunker]

Backrooms be like:

[@justanother_witheredrose894]

confused confusing confusion

[@parkermccarthy4265]

imagine checking into a hotel at 5 am and realizing you have to walk to room 900 quadrillion

[@Readybear77]

They wouldn't have to the 1st customer would be in room 1 the next customer would move into room 1 and the 1st into room 2 and so on so they don't have to walk that many doors

[@ankylo5550]

Bro a bot just replied to my comment on this post from ages ago with your exact comment

[@Readybear77]

@@ankylo5550 that's strange because someone else further down has said the exact same thing aswell 😱

[@justsomeguy6545]

The guy who has to walk to room 100 saptilion Lucky

[@Readybear77]

@@justsomeguy6545 😂 he won't though they just have to move down 1 door at the same time so the 1st person goes to room 2 the 2nd person moves into room 1 then the next person in line moves into room 1 and they all move down a room at the same time and so on so they won't have to walk infinity doors to get to their room

[@LuioTap]

"Hey,you need to move to the room 748374896246326423874,and the elevator is broken,sorry for it" "....."

[@Marcus-jl8jg]

💀💀💀💀

[@pandabrooke]

😂

[@cheetosnour.scratch-learn]

"hey, you need to move to room τ*10^79 and no elevators" response: "my feet will die.💀"

[@mohammadalhocheimi1706]

Nah what about the p2m pay to move hotel? Hey, sorry for this but you need to move to room 91 google, and to use an elevator, you need to pay $200qui.

[@Axol2138]

You need to move to room 1+ +1 ( 1+ +1 is uncountably infinite because we dont know what to add for 1+ so we add the awnser to +1 but there is none so we do 1+1 to do the equation 1+ +2 but it will become 1+ +1+ +1 for mathematical logic then the process repeats becomings 1+(1+(1+(1+(1+(1+(1+(1+(1+(1+… forever )

[@jellllllly]

I like how he explained it in such an understandable way to shield my brain from realizing I actually understood nothing.

[@dhruvgupta1063]

Underrated comment

[@raheembennett3981]

Basically imagine how you can fit an infinite number of numbers between 1 and 2 such as 1.1, 1.2, 1.9, 1.99999, etc. 1 - 2 is the hotel and countable infinity. 1.9999999 would be the uncountable infinity and people on bus

[@trygveplaustrum4634]

"All right, everyone, move to the room number that's twice your current room number." *Guy at Room One Billion:* "Ugh, fine..."

[@viethuongvothai686]

The guy assigned to room 1 quintillion: *Already turn into a skeleton getting to his room*

[@egg.007]

The guy who had a quintillion numerals in his room number:okay

[@freestylecreations9677]

How about just changing room number on door?

[@sachin-rathi]

@@freestylecreations9677 who will change the room number for empty rooms😂

[@Krishdylan]

Person at Octillion: turns into dust that can be vacuumed when trying to move.

[@Idek294]

Dude, the people staying in that hotel must be pissed having to move so much.

[@Ririn_Sama0517]

I'd imagine going for a vacation, and the only thing I'd be doing is changing rooms. If someone asks me what did I do during my vacation I could say I've been changing rooms the whole time.

[@beenguy5887]

Price you have to pay for having an infinite amount of vacation members

[@cheshire1]

A solution would be to only move the people who arrived in the last infinite group. That way everyone will move at most once. For the people who arrive in finite groups, you could just set aside the odd numbered rooms at the start and the do all the other stuff only on the even numbered ones.

[@Notcreative36]

I would just walk until I get hundreds of rooms away from the first avaliable one. Lots of walking, but worth it

[@migol1984]

I mean, they're infinitely moving.

[@SubmitToTheBiomass]

"Hey honey how was work?" "Rough day. An infinite number of infinite buses showed up."

[@helen7718]

😂

[@RAICHU_PRO_GAMING]

"but now a big bus pulls up" I'm cooked

[@user-oe1ox8eg3p]

"Do you know my friend?" "Who?" "Abababababababababababababababababababababababa...."

[@zamhaq8866]

The one with glasses or the one without?

[@nu1x]

Reminds me of a Monty Python sketch about interviewing a German person with a very long name, I almost died laughing it's so well delivered.

[@dalfgan817]

No but have you seen Ababaabaabababaabbbbbaaaa bbbbbbbbaba…?

[@neku-fn8dq]

Dont you hate it when you're working as hotel manager and then infinite amount of busses full of infinite people decided to use your hotel

[@ihatethatrepairmen4255]

They are customers

[@michelecaronti]

You'll have to build an infinite parking lot ahah

[@michelecaronti]

@@ihatethatrepairmen4255 Legit

[@kookies_kooky7170]

Seriously i get annoyed while infinite people come in the hotel while iam peacefully eathing ramen

[@randomhandle111]

@@kookies_kooky7170 infinite supply of ramen in your infinitely large ramen room

[@thatdude2492]

“An infinite number of infinite busses.” - “Dear god.” “But now a big bus pulls up” - “No.”

[@thetoiletpaperrollondalgom4592]

Imagine the traffic by just standing behind the bus ;-;

[@softtacos1]

Dear god... There's more. No...

[@gavinli1368]

Do you want the bucket?

[@softtacos1]

@@gavinli1368 Yes!

[@alexeyvlasenko6622]

Then a bigger bus pulls up, where all the passengers don't have unique names but have unique sets of social network connections to all the passengers with the infinite names... and every possible set of social network connections is represented

[@user-rr3ce3ls2o]

I booked 1 night in the Hilbert Hotel and it was horrible! It was 10pm at night when I arrived and the receptionist asked me to move to room 13739 and the elevator is still broken as many comments mentioned here, plus a 30003 seater bus pulled up and the receptionist asked me to shift to room 43742 and I had no time to collect my stuff I brought to the hotel with me. The other guy who took my original room who was on the bus also took my stuff, INCLUDING my laptop. Even when I was sleeping, I was asked to SHIFT to double of my room number and was like "F************ this" and completely checked out at 1 in the morning instead of 12 noon which I promised to the receptionist. Bad hotel, don't go here. Would give 0 stars if there was even an option.

[@zamhaq8866]

Remember that one time where someone pulled the fire alarm and the whole building had to evacuate the same emergency exit? Pranksters man. (Doordash also wont deliver here) 1 star

[@daleviker5884]

I stayed at the Hilbert Hotel back when it was known as the Premier Inn, Heathrow. There were so many people at breakfast that it just had to be a thought experiment.

[@zephpiala3634]

There's 7 billion people and it can fit 7 billion rooms. There are leftovers here. 0.000000000000000000000000000001 stars

[@KnowWithMalvika]

The bus with infinity number of guests came. They all needed to check out at same time. They checked out at 12 noon. Then, the host had infinite laundry to do. For that they needed infinite helpers, infinite kg of detergents, cleaners, etc. To produce that in a single day, the factories need to produce that in infinite quantity. Now the delivery trucks came to the nearby cross-circle. They will create a infinite traffic jam. Infinite parking will be needed. How could one deliver the product who is standing last second from intinity. It had to travel infinite km. Husshhhh!! So mess

[@theragingranga9484]

You think THAT'S bad? Let's assume 1% of the population is disagreeable. That means an infinite number of customers will refuse to leave their room and move to another one.

[@putmyfootupyoass]

Teacher: The test isn't that hard. The test:

[@satishchaudhary7978]

Go study instead of watching videos and then the test won't be hard

[@r6tker]

@@satishchaudhary7978 r/whoosh

[@TheCrimson_Phoenix]

@@satishchaudhary7978 r/whoosh

[@gamingstream4675]

@@satishchaudhary7978 r/whoosh

[@parkourcracker3984]

@@satishchaudhary7978 r/whoosh

[@Waterwolf221]

Imagine disturbing an infinite amount of clients just to fit one more person in the hotel

[@flygawnebardoflight]

I'm just saying that supporting an infinite number of people has got to put a toll on the economy

[@artyommoxid6233]

It's ok. When you are settling in an infinite hotel you have to deal with consequences.

[@jeroen5736]

maybe weird idea of me but why not put the one more guy on the end of infinity instead of the beginning. because if you can move everyone up one you should be able to put one at the end . maybe because infinity is not reality ?

[@flygawnebardoflight]

@@jeroen5736 I wish you luck in finding who's at the end of infinity. Spoiler Alert: It's Chuck Norris

[@owlman145]

It's ok your making an infinite amount of profit anyway, so even in an infinite amount demand a refund... hmmmm

[@tram_collections]

I can't wrap my head around the concept of infinity.

[@MzeeMoja1]

It’s a concept that is really difficult to grapple with, especially when thinking of it in terms of an infinite universe which means that there would be an infinite number of possibilities. I asked ChatGPT whether in an infinite universe there is a planet full of dogs and this was the response: In an infinite universe, the possibility of a planet full of dogs does indeed exist, according to the concept of infinite possibilities. Here's why: 1. **Infinite Space:** In an infinite universe, there are an infinite number of planets and celestial bodies. With such vastness, virtually any conceivable configuration of planets and environments is possible, including planets that are inhabited entirely by dogs. 2. **Probability and Randomness:** In a universe with infinite possibilities, random fluctuations and chaotic processes can give rise to a wide range of outcomes. While the likelihood of a planet being inhabited entirely by dogs may be extremely low, it is not impossible within the framework of infinite possibilities. 3. **Variety of Environments:** Planets can have a wide range of environments, from rocky and barren to lush and habitable. In an infinite universe, there are bound to be planets with environments that are conducive to the existence and proliferation of certain species, including dogs. It's important to note that the concept of a planet full of dogs is purely hypothetical and speculative. While it may seem fantastical, the idea illustrates the vastness and diversity of potential configurations within an infinite universe. In reality, our understanding of the universe is still limited, and we have yet to explore even a fraction of its vastness. -Ends- Basically anything that can happen in an infinite universe will happen. 🤯

[@josephlightfoot414]

There's no such thing as infinity, it is by its own definition, not quantifiable.

[@pburant]

Try visiting the DMV on the last day of the month.

[@chiraggowda4928]

Finally, a job where I can use my PHD in math. A hotel manager.

[@ericoschmitt]

Just tell them to walk down the hall knocking every door until they find one empty. They will never return to ask questions.

[@asedtf]

This is why you don't need to learn math to be a good engineer

[@ericoschmitt]

@@asedtf I did study engineering, and calculus was not my strength lol

[@denispol79]

An engineer enters a burning building and sees a fire extinguisher on a wall. He grabs it and puts the fire down. A mathematician enters a burning building and sees a fire extinguisher on a wall. He just walks out, because there's a clear obvious solution.

[@Kingdo99a]

This to me seems more like a thought experiment on efficiency, extra rules and assumptions had to be made to come up with a answer. Im no mathematician, but I would have thought it didnt mater In what way an infinite amount of people arrived, or in how many groups. They all wanted the same thing and could be considered a single entity. Meaning a universal less efficient method could have been used.

[@SeeAndDreamify]

Hmm, this won't work because eventually they will get tired of looking. But that is illustrating a flaw in the solutions in the video too. All of them assume that all guests are capable and willing to follow your instructions, and given an infinite number of guests, I think that is guaranteed to not be the case for some of them.

[@somebody9651]

Imagine spending the whole holiday just to reach to your room in an infinite hotel

[@chanchalsharma8196]

😆😆😆😆

[@RandyButternubs917]

Then imagine the manager telling you to move to the number twice your room number you're already in. Might as well just start your hike back to the front desk.

[@dv9239]

Infinite holiday

[@user-Number346]

Yes but you got an infinite life so it s not that long compared to the time you got

[@nuralyh_ahmd]

😂😂😂😂😂😂i think the same

[@user-wx8zp5ye1x]

Staying at this hotel is literally a workout 💀

[@NEKOSAIKOU.]

A deathwish

[@mukulkashyap4506]

I'll prefer to sleep on the road

[@SwapravaNath]

This is the best explanation of countable vs uncountable I have heard so far.

[@rikardnorlen752]

Well you can't hold me countable!

[@Kumpulas]

Customer: where’s my room sir? Hotel manager: at the end of the hall

[@bigj9503]

*walks 4000 gigameters*

[@kordru]

@@bigj9503 *walks infinite amounts of infinite distance for infinite time*

[@Utkarsh2607]

@@kordru and after infinity millenium ,probably you will reach there... Manager:Wishing that your age is infinite.. (o‿∩)

[@Snoowy_FN]

4 gigameters is already 2.485e+6 miles

[@bschristopher916]

by the time he reaches his room, he'll have infinite Grandchildrens and so on

[@battlesheep2552]

Imagine you go to this hotel, your room number is some absurdly high number. It takes hours to get to it, and you're dead tired once you do. You're about ready to throw yourself on the bed when you hear over the PA: "please move to the room number that is 2 times your current number".

[@ememmeme8722]

That's why we support emperor palpatine. He will get rid of these infinite hotels with his infinite power.

[@iBetThisNameWillWork]

Imagine being the 8183748595937262628385837251416363626273849595th person off the buss.

[@gladiatoranc]

There are an infinite number of rooms, therefore it would take some people infinite walking and would never get to their room even if they had infinite life...therefore some rooms would always be empty...

[@tomsvoboda2309]

@@gladiatoranc There are infinitely many, but all of them can be reached in a finite time. Just as you can count from 0 to any natural number by repeatedly adding 1 in a finite time (possibly absurdly high, but still finite).

[@gladiatoranc]

@@tomsvoboda2309 Even if you had infinite time and infinite walking speed you could never get to the infinite last room, there are no last rooms...You would be constantly filling up the hotel for eternity without ever getting it filled up.

[@antimatterj6005]

My CS professor wasn’t able to explain the difference between countable and uncountable Infinity as well as you just had. Thank you for helping me understand that lesson 4 years later lol.

[@RyanShabbir]

Bro F’d my brain up and thought I wouldn’t notice💀💀

[@Namiizan]

"An infinite number of infinite buses show up. What can you do?" Well, for a start I could quit my job

[@spike480p]

Wt-

[@azure_vxiii]

And get hired as a waiter for an infinite restaurant? 😜

[@mimi-ix3fb]

@@azure_vxiii big oof

[@bijan2210]

Just tell them to move forward until they give up or find an empty room.

[@TheSUGA1202]

How much is the paycheck cause even if its infinite i wouldnt be paid enough.

[@RxktPlayz]

People in the hotel “I literally just finished unpacking stop moving us to another room.”

[@SkillTimO]

You never would finish unpacking your infinite items.

[@lizlee8715]

At that rate, I'd just keep all of my stuff in an suitcase...

[@magnabueno5360]

Technically they would spend the entire day changing room

[@cytusdux7439]

@@magnabueno5360*lifetime

[@doomkenka]

Just about to put that

[@ismailsahin3232]

The logic of the last example is how they proved there are more decimal numbers between 0 and 1 than there are integers from 0 to infinity

[@okgaming7886]

But doesn't logic also say that for any decimal between 0 and 1, you'll find an integer by dropping the decimal point?

[@ismailsahin3232]

@@okgaming7886 no because 0,1 and 0,01 and 0,001 all will give 1 when you drop the decimal even though they are different numbers

[@okgaming7886]

@@ismailsahin3232 fair, but for every case of a leading zero that can be dropped from an integer, there's a decimal with a trailing zero that can be dropped, e.g. .10, .100, .1000 are all .1. So that still should work out even, should it not? Perhaps a better axiom is that you can always reverse it and drop the decimal.

[@ismailsahin3232]

@@okgaming7886 yes but that doesnt mean it will even out, also i think the point was that integers are countable infinity where as decimals are not. When given a 2 integers you know how many integers are there between them where as there is always infinite number of decimals between 2 different decimals.

[@okgaming7886]

@@ismailsahin3232 I don't see how it wouldn't. If we can prove there's a rule to convert any unique decimal into an equally unique integer, logic should hold there can't be more of them. But I also don't buy the contradiction that a hotel with infinite rooms could become full. If it's full, it isn't infinite; if it's infinite, it isn't full. This entire problem seems to depend on temporarily forgetting the premise that it's infinite, then remembering it, so what do I know? lol

[@game-cholic2969]

One thing for sure, the manager should be given a raise

[@laoaidan2400]

“Infinity + 1” is a kid argument i never guessed would be supported by actual math

[@Wirgah]

Most kids probably got it from vsauce so hey

[@afo985]

@@Wirgah didn't he say infinity plus 1 is also infinity?

[@Alt.E32]

@@afo985both are infinity but infinity+1 is a higher kind of infinity

[@rhynoorhyon5291]

@@Alt.E32 wrong. infinity+1 is still a countable infinity, and therefore infinity. The infinity described in this video with the ABABABBABAB bus was Aleph Null, the first order of uncountable infinities.

[@Alt.E32]

@@rhynoorhyon5291 honestly i just looked at it this way: If we were both in an infinite race and i started 10 seconds earlier, i would be further ahead of you even if we ran an infinite distance the entire time (granted we ran the same speed consistently throughout). That logic might be flawed though.

[@alanhulseii9093]

Imagine just unpacking and being told to move 100 rooms down

[@francisbacon3949]

Literally laughed out loud at this one hahahaha 💀💀💀

[@vcreativeart16]

Imagine just unpacking and being told to move 189,146,081,499,116 rooms down

[@jhsevs]

Or a hundred infinities

[@shahidkhan-uq9mm]

@@vcreativeart16 r/yourjokebutworse

[@jhsevs]

@@shahidkhan-uq9mm this is not reddit.

[@rafalkaminski5120]

I would love to watch" the story for another" time". Ist there already movie to this trailer?😂. Your movies are great. I love the simplicity you're bringing in complex questions. Thank you for that.

[@diegovasquez840]

If you couldn’t figure this one out, don’t worry, you’re not alone. When Cantor published his now famous results on cardinality, it was so paradoxical that almost nobody accepted it. But Hilbert did, and created this analogy to help justify it to befuddled minds.

[@RonaldRaygun-tg4zl]

Indeed. Some guys here think they are smarter than Hilbert, Goedel and Cantor together. Maybe they should look up those names and then think again.

[@blueninjasm6707]

Imagine walking up to the manager and he says “Ok, you’ll be staying in room 3874920”

[@meXicansUppaflY2]

Guess I'll die

[@kingblake902]

Guess im flash

[@HarryKaneIsGoated]

@@kingblake902 guess I'm superman

[@ZoomTheSpeedster]

@@HarryKaneIsGoated flash is faster plus there isn’t a way for Superman to fly so he will have to walk/run

[@screw9627]

The thing is that's not the biggest number that u have to face lmao but imagine going to the exit after going to your room

[@luigi.gaming]

The people whose room numbers are huge: "You can check out any time you like, but you can never leave."

[@tastygiggidy633]

LMAO BEST COMMENT IF YOU KNOW THE SONG

[@theblackreaper4395]

@@tastygiggidy633 Yeah Xdd

[@paulmurray2729]

The song is Hotel California by the Eagles.

[@saswatsarangi6669]

Then how can you checkout or check-in in the first place

[@gabrielferes]

@@saswatsarangi6669 phone

[@shepardog8180]

These videos make me feel stupid but they're so fascinating and entertaining

[@morrischristopher5366]

Great video, but I noticed a potential inaccuracy in the explanation regarding infinite rooms. Here's the issue: The guest labeled "no room" wouldnt occur in an infinite spreadsheet. Even if a new infinite guest bus comes over the next minute, it would still have a room because we can infinitely shift existing guests one room over, creating a chain reaction with infinite vacancies. The true challenge lies in managing (assigning/tracking) an infinite number of guests, not a lack of space. Our finite human methods struggle with handling infinity. Therefore, the answer to "Could you run out of space?" is definitively no. Infinite rooms can accommodate everyone. Hire me as the Manager of the Hilbert Hotel :)

[@Pokekidb_ac]

You are hired

[@shavojohn4241]

You cannot shift guests infinitely many rooms, the only valid move is to shift simultaneously each one of the different guests a finite number of rooms (this number depends on each guest)

[@alexguy7395]

It’s funny how this assumes that the guests don’t care about moving from their hotel rooms a crap ton of times

[@jaspertyler4557]

by technicality, it's just to show there would be enough rooms to fit everyone, and the new people could just enter the empty rooms that are confirmed to exist.

[@tanshiro8593]

Maybe they infinitely fast

[@nataliaborys1554]

Imagine being in room 1028 and suddenly the manager tells you to move to room 2056. That's one hell of a walk.

[@ELREASON44]

@@nataliaborys1554 It would really be a disaster going from room 2^60 to double that number.

[@rattle7215]

an infinite number of times...

[@mcmona4171]

"I love you " "I love you more" "I love you times infinity!" Me: pulls out spreadsheet.

[@sen4845]

💀

[@gregoryb4322]

“Actually I think that you’ll find that will be quite literally impossible🤓”

[@afigamming7958]

I have mona

[@mcmona4171]

@@afigamming7958 yesss me too! (though I was pulling for venti 😔)

[@aadenkeehn8112]

Crispy chicken sandwich and caramel brownie mcflurry

[@joshtonpi2271]

Even though I know all of this, I still like to come back and watch this because it’s so well done

[@yesIdostudy]

It was SO SO cool to know! Thank you for this video 🎉

[@pandaescarlate7268]

I love how mathematicians literally need to invent a problem that doesn't exist

[@bobherobrine3415]

The hotel in the math problem

[@dickhammerbush172]

You don't tell me how many watermelons are in my swimming pool, I do

[@recoupxtra7270]

Fax

[@unapersonaelegante4399]

Some weeks ago I did a test that said: Victor written all number from 1 to 2021 but he missed the space between each other, which number will be in the position 2021? And I though, why would I ever need to know that?

[@BumHoleTickler]

It's to show how smart we are

[@idoscripts]

his answering questions nobody ever wondered to ask 🗣🔥🔥

[@argentinman682]

Imagine being on the 374,395,106,285th bus and your the 206,305,936,253,194th passenger 💀

[@NeerajSingh-jf8mz]

Imagine being so unlucky that you don't even get a room in an infinite hotel.

[@criticallyconk4944]

Rng moment

[@user-vb8zo6kh4j]

It is your fault for being named ABABBABAAABBABAABABBABAABAB

[@futotesan]

@@user-vb8zo6kh4j Or for being named ABABBABAAABCABAABABBABAABAB....or E...and don't even get me started with a name like Futote...not an A or a B in the name. How's the Hotel manager supposed to work with that?

[@Woocet]

I know who it is, bad luck brian

[@alexeyvlasenko6622]

Just don't have an infinitely long name, and you won't have a problem

[@colinginn7025]

I was going to make a joke about infinity, but I'll never hear the end of it.

[@colonelhacker3661]

This guy... :)

[@sicklymoonlight]

well done.

[@user-ke2dl9se5l]

n1

[@wa6488]

Get out

[@toast1757]

nice dad joke

[@diamondtrike4963]

4:57 If you're confused remember that both the list and amount of letters are infinite. Using this diagonal is a sure fire way to eliminate a single person with out a room, it can't match with anything

[@tanveer_badar_]

This is Cantor's diagonalization argument and it is vastly useful in disproving statements.

[@-kaori]

It doesn't make sense to me, can you explain it? I don't see why the person with these diagonal letters wouldn't be on the list, if every combination of the 2 letters is supposedly on the list.

[@royalminstrel]

"Imagine a bus pulls up with an infinite number of people..." "Okay..." "Now imagine a BIG bus pulls up..."

[@CJBoxyeet]

like always, that part of the video showed up when i read your comment

[@3aloosh623]

@@CJBoxyeet ik right this always happens lol

[@Roboman1807]

No seats? Is that even legal?

[@yakked]

And somehow he never mentions framerules.

[@kbgiver]

@@CJBoxyeet omg IT'S RELATABLE IM DYING

[@randys2669]

"Everyone move to the room with double your current room number" The guy in room 387494985726478569420: 🙃

[@Catnipyy]

69420 Nice

[@saffamarwahomar]

Hahaahahahaha 😭

[@calebtan8682]

Every room should have a calculator then 🤣

[@WilIiyum]

@@calebtan8682 Just not funny Edit: I didn't find it funny ok so chill Caleb Tan is my G

[@calebtan8682]

@@WilIiyum okay lol

[@ApolloAgain]

People staying at this hotel : “Ahhh I can finally rest.” Hotel Receptionist: “Move to room 314159265 quadrillion.”

[@ethankylem.francisco5722]

What a smart explanation!

[@liber2350]

“This hotel can’t run out of room!” “Yeah but what if it did?”

[@thewatchidiot]

....."but it can't tho" "Yeah but what if it DID??" repeat x infinity

[@Himoooo]

No what if just tell them to learn about infinity first 😂

[@ethrick.k.1292]

Then your question would go on for infinite as so would your doubt of this fact because infinity is as unlimited as the very definition as soon as you recognize how infinity is as it stretches farther than your perception

[@laxmanrawat748]

That's a question for another 'what if'

[@mustafabahaj9832]

Lol, good one

[@JrsFTW]

This hotel sounds like literal hell. Imagine being disturbed Infinitely to Infinitely walk down a hallway to your next room. I would literally prefer to sleep in the dirt than be subjected to near endless walking at this hotel.

[@billcraig5614]

Incredible how little thought you were able to give to this thought experiment! I won't be surprised if your next argument is that there is no way that there would be enough bath towels to go around so this could never really happen.

[@JrsFTW]

@@billcraig5614 Dude calm down, I only said what came to mind. It doesn't hurt anyone and I didn't insult anyone.

[@DeputyDiddle]

@@billcraig5614 dude what are you even talking about? They didn't say anything about this theoretical experiment being possible or impossible. You literally just read his comment, thought of your own thing, and then got mad at them for the thing you yourself thought of.

[@heavyguy4660]

@@billcraig5614 Incredible how much of a smart ass you sound!

[@mickeyagrawal2001]

He is a dumb troll, ignore him.

[@chasemika3836]

I like watching this video at least once every year. Idky but I find myself rewatching it.

[@someone-lollmao]

Never thought my life would come to the point where I'd be looking at the basic explanation of infinity.

[@MonikasPhantom]

“I quit” “But you’re the mana-“ “Nope, I quit”

[@OliverEye]

True I did next week

[@jaiadit2406]

😂😂😂😂😂😂😂

[@bodhiboy1]

I quit

[@kristynahladikova8077]

1 k like

[@orenge-hw9nx]

When you have Inifnite mana as a mage in skinder 2

[@pakistaniyoutuber581]

Manager: Can everyone please move from their room again Guest: B R U H....

[@lans241283]

Pol

[@MuhammadWaseem-kj5ye]

I'm also pakistani

[@williamjames7293]

I'd check the heck outta there

[@benjo3355]

Loool

[@YYZed12]

LMAOOO

[@TheReal_JakeTheDog]

"hey what's up?" "Oh, nothing, hbu?" "Not a lot. So what room are you in?" "Oh, im just in room 4,842,035,836,822,992,575,635,286,621. And you?" "....34...." "Hey, we're pretty close to each other!"

[@yayyyyyyyyyyyyyyyyyyq]

Well now we know who to call if we ever get an infinite hotel with infinite amounts of problems that will be solved for eternity infinitely

[@jairus2008]

I feel bad for the guy that has to walk forever just to go to his room that he will never reach

[@benjaminraymundo6711]

Actually he will one day reach it but its would be soooooo long that it might feel like eternity but it will come eventually. That's how infinity works

[@nadineullrich3809]

The guy waiting an infinity inside the bus to get out, will dream of being able to walk to his room.

[@user-wb7ez9ud4p]

The funny part is: no single person would walk for infinity to get to his room! Every single person would have an exact room number, and thus an exact time it would take to get there. The time may be arbitrarily long but always FINITE! That's the beauty of countable infinity, it's so manageable.

[@cresbalundo8845]

*the backrooms*

[@sharonsia1351]

@fred McMurray the other end

[@cluckinbell1992]

"I can't get into my room. I've been in Room 27." "You've been moved to Room 945,172,370,837,362. Also, the elevator is broken. Use the stairs." "I'm just gonna leave."

[@Guztav1337]

But then infinite people would leave, and all the other hotels are full. So only this infinite hotel has space.

[@manuelr.7461]

...

[@funny_ol_kat]

Oof

[@lamhw]

@@Guztav1337 oh. I’ll go home then

[@JohnSmith-ox3gy]

But you can not as there ia a never endingvstream of new areivals as infinite number of busses full of infinite number of new people.

[@guillaumelagueyte1019]

Regarding the infinite number of buses with infinitely many people, I like the solution of using prime numbers. First, send guest in room 1 to the 1st prime number, then guest in room 2 to the 2nd prime number, etc. Now all the rooms with prime numbers are occupied, and the others are free. Put the people of bus 1 into the rooms 2^2, 2^3, 2^4, etc., as these aren't prime numbers they're all free. Put the people out bus 2 into the rooms 3^2, 3^3, 3^4, etc. After you do it for all prime numbers, all the powers of prime numbers will be occupied. Bonus, all the rooms with multiple prime factors (e.g. room 15 = 3*5) are now vacant, so you even squeezed some free space out of that trick.

[@greedy49]

that manager deserves a raise for dealing with infinite infinitive

[@autowarranty2852]

"this is the hilbert hotel, and you're the manager" Me: "I quit."

[@zhounen790]

LMAO

[@user-dv9ze9tt4l]

∞

[@nickdanvers547]

ez

[@axolotl6564]

Same

[@reinhard7731]

accurate response

[@harrisont2004]

“Oh just move to the room double your room number.” “But I’m… at room 9,000,000,000,000,000,000,005.”

[@esquilax5563]

"So what? There are infinitely many people in higher-numbered rooms"

[@Keke_offi]

He means that the person in that room will walk for a very long time until getting to the right room

[@arghyadeeppal9638]

Sure, keep walking, either you reach your room or die trying!

[@gabrieldavis4434]

“Start walking, bitch.”

[@kristinaalshami2178]

@@gabrieldavis4434 UNDERATED REPLY OML I DIED

[@FISHYY_MTB]

Imagine being the only person there. I reckon it’d feel like being the only one at a hotel, if that makes sense! lol

[@GoIdappI555]

i love how that it is a infinity hotel and the rooms are at the right but then there is also the fact where there is building there too

[@NonsenseFabricator]

"Imagine there's a hotel with infinite rooms..." Already lost me, buddy.

[@Guztav1337]

Just think of a hotel with many rooms

[@manuelr.7461]

Lol

[@bozhanatoneva1973]

@@Guztav1337 I cant Like there should be an end of the rooms 😭🤚 It might be the 100000 rooms but WITH AN ENDD

[@reaperlucario3155]

Same

[@Okaz_]

Hallway

[@user-or4ow3gt4w]

Well, that's one of the explanations why |R| > |Q| (R - real numbers, Q - rational, |R| - roughly, number of numbers in the set of real numbers). We cannot associate each real number with a natural number (just like with the rooms in the video), but we can with rational numbers. Therefore, |N| = |Z| = |Q| < |R|

[@imphilippinesculture]

Imagine the 809,293,384,203,392nd person just needs milk from their local store but remember they need to walk to the exit

[@alifputrawan9565]

I'm impressed that a bus has more capacity than a hotel.

[@kelsey5818]

There are multiple busses, not multiple hotels.

[@oboy1918]

@@kelsey5818 but can the one hotel fit all the people from the last bus with infinite ababab s

[@kelsey5818]

@@oboy1918 just put them on an infinite bus with seats. Problem fixed.

[@Jellyduckface1]

That's one hell of a bus huh?

[@gigaomnom3849]

They had the same. There were just multiple buses

[@mmicoski]

I am sorry for the cleaning person... she left one morning to clean the rooms and never came back...

[@AdityaRaj_24]

Well if there are infinite number of rooms and infinite number of person living in each of them, then maybe there would be arrangments for an infinite number of cleaning person each assigned one room to clean.

[@mmicoski]

@@AdityaRaj_24 that's a good idea. And if the manager tries to save money (in salaries) and allocate one cleaning person teach 10 rooms, he still will pay infinite salaries...

[@AdityaRaj_24]

@@mmicoski well he gotta pay infinite salleries because he is receiving infinite room charges from his customers. And suppose that the manager is charging 100 bucks for each room and paying 10 bucks for getting each room cleaned. Now here the room charge paid by each customer is finite and the sallery given to each cleaning person is finite. But the income of the hotel (which is finite from each room, say 30 bucks per room) is infinite! So we gotta say it's a smart move to construct such a hotel.

[@mmicoski]

@@AdityaRaj_24 you are right! I suppose the secret of the success here is to get investors for this enterprise...

[@tharindurajakaruna1590]

@@AdityaRaj_24 but would be stupid management wise, whose gonna pay them all xD

[@RigidRush]

I’ve been recommended this video many times before THIS IS THE TIME I WATCH IT

[@-Gunnarsson]

The guy working in the lobby can only handle one customer at the time. And only one queue. That means the first bus showing up will be maximum 😂

[@thetaomegatheta]

Incorrect. We can manage everybody at once.

[@thetntsheep4075]

This must be the world's most inconvenient hotel to stay in. "Sorry sir, could we get you to move down another room please" "What? That's like the infinitieth time!"

[@tachzusamm]

I would be glad if I don't have to move to double my room number though.

[@00_Cupid]

Imagine when checking out of the infinite room all the way to the front.

[@souheilallegue2342]

"sorry sir, could you move from room number 40000000000 to room 80000000000 please"

[@xeon2k8]

infinitiest underrated comment here

[@lyrelyreharponfire]

What about the hotel staff? I hope they have infinite amount. They always ask where is the room service but not how is the room service 😔

[@morbiusfan3176]

"Imagine theres a hotel with infinite rooms." "All the rooms are occupied." *[visible confusion]*

[@goncalocalqus1766]

Exactly my thoughts and I still can't get over it because everything that comes afterwards feels like bs.

[@slavetzkyrickyjames4305]

Because it's countable infinity so there's a bijection then an uncountable infinity appeared and it doesn't have bijection which means it won't fit to countable infinity because it's not fixated

[@ok4350]

@@slavetzkyrickyjames4305 get out with your math

[@opioidhamster3205]

@@slavetzkyrickyjames4305 tf you mean countable is it really "infinity" then

[@last-dinosaur]

@@opioidhamster3205 you gonna understand after you finish the school, probably

[@eyados-fo6sg]

whoever manages to get into room 1 must be the luckiest man out there..

[@NevrrPresntt]

Some infinities are bigger than others. That's some love story movie stuff right there. 😢

[@BobLegoman]

*slaps the roof of the party bus* "This bad boy can fit so much ABBA in it"

[@plasienorzokie2187]

😭😂

[@matiasandreupinanaradrigan7862]

LOL

[@manuelr.7461]

Bruh 😂

[@jamesontv4805]

True

[@h4nishi]

😭?

[@Eye-Of-The-Beholder]

*"Well you pull out an infinite spreadsheet"* Ah yes, just another normal day at work

[@ronaldhamac3787]

Perfect timing i saw the comment just as he said it

[@theghostcookie2772]

honestly just excel right?

[@Relatess]

Lol

[@AS-qi2lq]

in infinite universe lol.

[@natecallon9755]

@MatZ hello fellow cs major (i assume)

[@NasAndChico]

Honestly I would be pissed if I have to move rooms so many times

[@Average_Roblox_God]

The most interesting thing I will watch ever in my life

[@SIRMMA]

When the infinite number of infinite buses arrived, gotta admit I felt like giving up on my career as hotel manager.

[@V4_3C]

Lol

[@ruan13o]

Just think of the infinite profit.

[@ianh1504]

Yeah and youre just a manager so youre getting the same wage even though hotel profits are infinite for the owners

[@Pink_blox1]

Same like …

[@clayroberts2951]

I really didn’t get his argument there, an infinite number of buses doesn’t change the number of people, 1 infinite number bus has just as many people as an infinite number of buses

[@StarSupernova59]

"What would happen if infinite of infinite buses with infinite of infinite passangers show up?" Show them the 2nd floor.

[@the_jingo]

Good one

[@trevorbeatz5741]

lol

[@StarSupernova59]

*THATS ALOT OF ROOMS*

[@1tzL1t]

Lol

[@HaLKer5]

Big brain time

[@cantthinkofnameyeah7249]

The key insight learned from this is the distinction between infinity and all: they are not synonymous.

[@thetaomegatheta]

Haha. You seem to have decided to remake your comment after being humiliated yet again. But sure, let's go over this once more: That 'insight' is extremely obvious to all math-literate people, especially considering that the word 'infinity' refers to some points in spaces like Alexandrov compactification. This 'insight' is not what the video is about.

[@pavanrajesh-ts6pg]

youtube has be recomending this from long time finally i have seen it

[@Qkotman]

After the first minute, I just stared blankly at the screen and stopped processing the math...

[@AAA_A12]

JESUS Oh wait *JESUS*

[@_Hajar_]

Same

[@Xiunoi]

**hmm**

[@Xiunoi]

UH *WHAT*

[@paqlallaqldifi122_7]

@@Xiunoi bruh

[@physicsgirl]

Host: You can bring as many friends to the party as you’d like. Derek: Hold my bus...

[@Spl33ney]

Well you're here early

[@tunahankaratay1523]

o

[@physicsgirl]

@@Spl33ney I was on the first bus.

[@Siddiquii]

lol how did u get so many likes just coz you got a lot of subs XD

[@ayushjaiswal.]

Ha ha lmao 🤣

[@user-rm8qu5yp1o]

Could you imagine if you just got to room 500 quadrillion and you had to go to room 1 quintillion

[@Michael-pp8lz]

I hope the manager is getting paid pretty well

[@IriaChannel]

This hotel's manager needs an infinite raise

[@skullscope]

Watch people make a problem with that

[@datboredguy4873]

If for attending infinite people there are infinite managers and each manager gets an infinite raise how much money do u hv to raise

[@datboredguy4873]

Btw u are manager

[@seederorg2489]

@@datboredguy4873 ∞^∞

[@unholycrusader69]

What about inflation?

[@humooon79]

"Imagine if there is a hotel with infinite rooms and you are the manager, what would you do?" "I'd quit"

[@Guztav1337]

sad

[@jillonderdonk7836]

Lol

[@justaloser4178]

Y would U quit? There is infinite money!!!!!!!! Who cares about the customers of the bus? You can be a billionaire with the customers you already have!

[@e5858]

Demolish it for infinite resources

[@antocost]

You could get infinite tips xD

[@hearTelus]

i want more videos about David Hilbert!

[@Voiid_edits]

I feel bad for the people that had to walk to room 900000 quintillion

[@cu7695]

This is kinda of stuff mathematicians imagine when they're high

[@camsandhu340]

100th like

[@goodlightpringles6335]

101st like

[@WisdomLearner]

But it indeed lead to the creation of the computer nso that's a plus for the crazy.

[@shivaanrambally9611]

601st like

[@kevinboros7427]

Muahahaha 667th like, I broke the funny number.

[@pixieb9166]

I would hate that hotel 💀 Imagine being asked to move to another room everytime someone arrives 💀💀

[@ClassicBentobox]

If you leave it frees up a room for another customer

[@ClassicBentobox]

@@ayamelee9020 im on the side of math not the consumer on this one. I’m sorry

[@user-zt8yq8fj3h]

That's only if someone arrives AND there's already infinite people there, not just it someone arrives. If there were like 100 then they'd just go to room 101.

[@huutao3012]

Ikr✋💀

[@korayacar1444]

@@ayamelee9020 If you were to manage this hotel, you'd probably want to leave most (100% in the limit) guests alone, and there's a very simple trick to do this. Just consider the rooms that have powers of 10 as their number. These rooms themselves form an infinite sequence, yet they make up a 0% proportion of the hotel in total. I'll now refer to these as the 'switch rooms'. I will also refer to guests by their previous room number. If guest n wants to leave, just shift guest 1 to room n, and fill in from the shift rooms. (If room n is a shift room, simply fill in from the higher shift rooms instead.) If a guest wants a room, make space in room 1 using the shift rooms. If countably infinitely many guests want a room, draw a bijection to the natural numbers, vacate all odd shift rooms (guest in shift room n goes to shift room 2n for all natural n), and fill the odd shift rooms with the new guests. If countably infinitely many guests want to leave, draw a bijection to the natural numbers, fill the gaps using the guests in the odd shift rooms, and fill the shift rooms back in (guest in shift room 2n goes to shift room n for all natural n). If an uncountable number of guests want a room, turn them all away. Using this method, any long-time resident of the hotel will eventually be assigned a room which isn't a shift room, and 100% of guests would be satisfied.

[@sidleyparkhermit6391]

Einstein's happiest thought: a painter falling off a roof with all his painting paraphernalia falling alongside him Hilbert's happiest thought: how you could annoy an infinite number of people an infinite number of times

[@Blueguy4O44]

The 1st guy to get in is the most lucky person ever

[@Vooteria]

"You have infinite rooms right?" "Yeah" "So that means you will never run out of rooms" "Makes sense" "Then would i like to get one?" "No all of them are full"

[@Anu_boi]

XD

[@kyletheawkwardpineapple7076]

Lmao

[@mahmudbinumar4754]

SpongeBob reference

[@zarifamsyar6274]

Just ask the other guest to move in any room that Isnt occupied

[@overseer-0191]

@@sandeepvivek6134 no one understands your comment lmao

[@aletheiai]

"But that's a story for another time." I hope you plan to leave us in finite suspense.

[@earthling_parth]

Niiice 👌

[@dierandomdie]

Please leave 😑

[@RumoredAtmos]

You should get a medal for that comment

[@28peruvian]

😂

[@lockstockandcarol]

I'm guessing the hotel has infinite storeys