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.
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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
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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
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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
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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."
💀
Wrong
Lmao I’ve seen this vid like 50 times and this comment it’s the best
Backrooms be like:
confused confusing confusion
imagine checking into a hotel at 5 am and realizing you have to walk to room 900 quadrillion
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
Bro a bot just replied to my comment on this post from ages ago with your exact comment
@@ankylo5550 that's strange because someone else further down has said the exact same thing aswell 😱
The guy who has to walk to room 100 saptilion Lucky
@@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
"Hey,you need to move to the room 748374896246326423874,and the elevator is broken,sorry for it" "....."
💀💀💀💀
😂
"hey, you need to move to room τ*10^79 and no elevators" response: "my feet will die.💀"
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.
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 )
I like how he explained it in such an understandable way to shield my brain from realizing I actually understood nothing.
Underrated comment
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
615 likes and only two replies?
Teacher: The test isn't that hard. The test:
Go study instead of watching videos and then the test won't be hard
@@satishchaudhary7978 r/whoosh
@@satishchaudhary7978 r/whoosh
@@satishchaudhary7978 r/whoosh
@@satishchaudhary7978 r/whoosh
Dude, the people staying in that hotel must be pissed having to move so much.
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.
Price you have to pay for having an infinite amount of vacation members
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.
I would just walk until I get hundreds of rooms away from the first avaliable one. Lots of walking, but worth it
I mean, they're infinitely moving.
"Hey honey how was work?" "Rough day. An infinite number of infinite buses showed up."
😂
"but now a big bus pulls up" I'm cooked
"Do you know my friend?" "Who?" "Abababababababababababababababababababababababa...."
The one with glasses or the one without?
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.
No but have you seen Ababaabaabababaabbbbbaaaa bbbbbbbbaba…?
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
They are customers
You'll have to build an infinite parking lot ahah
@@ihatethatrepairmen4255 Legit
Seriously i get annoyed while infinite people come in the hotel while iam peacefully eathing ramen
@@kookies_kooky7170 infinite supply of ramen in your infinitely large ramen room
"All right, everyone, move to the room number that's twice your current room number." *Guy at Room One Billion:* "Ugh, fine..."
The guy assigned to room 1 quintillion: *Already turn into a skeleton getting to his room*
The guy who had a quintillion numerals in his room number:okay
How about just changing room number on door?
@@freestylecreations9677 who will change the room number for empty rooms😂
Person at Octillion: turns into dust that can be vacuumed when trying to move.
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.
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
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.
There's 7 billion people and it can fit 7 billion rooms. There are leftovers here. 0.000000000000000000000000000001 stars
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
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.
Imagine spending the whole holiday just to reach to your room in an infinite hotel
😆😆😆😆
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.
Infinite holiday
Yes but you got an infinite life so it s not that long compared to the time you got
😂😂😂😂😂😂i think the same
Imagine disturbing an infinite amount of clients just to fit one more person in the hotel
I'm just saying that supporting an infinite number of people has got to put a toll on the economy
It's ok. When you are settling in an infinite hotel you have to deal with consequences.
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 ?
@@jeroen5736 I wish you luck in finding who's at the end of infinity. Spoiler Alert: It's Chuck Norris
It's ok your making an infinite amount of profit anyway, so even in an infinite amount demand a refund... hmmmm
I can't wrap my head around the concept of infinity.
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. 🤯
There's no such thing as infinity, it is by its own definition, not quantifiable.
Try visiting the DMV on the last day of the month.
Staying at this hotel is literally a workout 💀
A deathwish
I'll prefer to sleep on the road
“An infinite number of infinite busses.” - “Dear god.” “But now a big bus pulls up” - “No.”
Imagine the traffic by just standing behind the bus ;-;
Dear god... There's more. No...
Do you want the bucket?
@@gavinli1368 Yes!
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
"I love you " "I love you more" "I love you times infinity!" Me: pulls out spreadsheet.
💀
“Actually I think that you’ll find that will be quite literally impossible🤓”
I have mona
@@afigamming7958 yesss me too! (though I was pulling for venti 😔)
Crispy chicken sandwich and caramel brownie mcflurry
Finally, a job where I can use my PHD in math. A hotel manager.
This is the best explanation of countable vs uncountable I have heard so far.
Well you can't hold me countable!
Imagine just unpacking and being told to move 100 rooms down
Literally laughed out loud at this one hahahaha 💀💀💀
Imagine just unpacking and being told to move 189,146,081,499,116 rooms down
Or a hundred infinities
@@vcreativeart16 r/yourjokebutworse
@@shahidkhan-uq9mm this is not reddit.
Customer: where’s my room sir? Hotel manager: at the end of the hall
*walks 4000 gigameters*
@@bigj9503 *walks infinite amounts of infinite distance for infinite time*
@@kordru and after infinity millenium ,probably you will reach there... Manager:Wishing that your age is infinite.. (o‿∩)
4 gigameters is already 2.485e+6 miles
by the time he reaches his room, he'll have infinite Grandchildrens and so on
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.
Bro F’d my brain up and thought I wouldn’t notice💀💀
Imagine being so unlucky that you don't even get a room in an infinite hotel.
Rng moment
It is your fault for being named ABABBABAAABBABAABABBABAABAB
@@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?
I know who it is, bad luck brian
Just don't have an infinitely long name, and you won't have a problem
This hotel's manager needs an infinite raise
Watch people make a problem with that
If for attending infinite people there are infinite managers and each manager gets an infinite raise how much money do u hv to raise
Btw u are manager
@@datboredguy4873 ∞^∞
What about inflation?
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.
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
But doesn't logic also say that for any decimal between 0 and 1, you'll find an integer by dropping the decimal point?
@@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
@@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.
@@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.
@@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
Just tell them to walk down the hall knocking every door until they find one empty. They will never return to ask questions.
This is why you don't need to learn math to be a good engineer
@@asedtf I did study engineering, and calculus was not my strength lol
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.
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.
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.
Please add an extra door in between the wall of rooms. So it's easy to move.
You need to talk to the management about that
@Dyslexic Mitochondria OMG hi I watch ur channeI. Absolutely love ur content
stibnite
it would take an infinite amount of effort to slip through that crack tho.
😂😂😂😂
It was SO SO cool to know! Thank you for this video 🎉
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.
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.
"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."
But then infinite people would leave, and all the other hotels are full. So only this infinite hotel has space.
...
Oof
@@Guztav1337 oh. I’ll go home then
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.
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
One thing for sure, the manager should be given a raise
I love how mathematicians literally need to invent a problem that doesn't exist
The hotel in the math problem
You don't tell me how many watermelons are in my swimming pool, I do
Fax
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?
It's to show how smart we are
I'm impressed that a bus has more capacity than a hotel.
There are multiple busses, not multiple hotels.
@@kelsey5818 but can the one hotel fit all the people from the last bus with infinite ababab s
@@oboy1918 just put them on an infinite bus with seats. Problem fixed.
That's one hell of a bus huh?
They had the same. There were just multiple buses
These videos make me feel stupid but they're so fascinating and entertaining
This is Cantor's diagonalization argument and it is vastly useful in disproving statements.
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.
“I quit” “But you’re the mana-“ “Nope, I quit”
True I did next week
😂😂😂😂😂😂😂
I quit
1 k like
When you have Inifnite mana as a mage in skinder 2
"Imagine a bus pulls up with an infinite number of people..." "Okay..." "Now imagine a BIG bus pulls up..."
like always, that part of the video showed up when i read your comment
@@CJBoxyeet ik right this always happens lol
No seats? Is that even legal?
And somehow he never mentions framerules.
@@CJBoxyeet omg IT'S RELATABLE IM DYING
Even though I know all of this, I still like to come back and watch this because it’s so well done
his answering questions nobody ever wondered to ask 🗣🔥🔥
"this is the hilbert hotel, and you're the manager" Me: "I quit."
LMAO
∞
ez
Same
accurate response
Manager: Can everyone please move from their room again Guest: B R U H....
Pol
I'm also pakistani
I'd check the heck outta there
Loool
LMAOOO
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 :)
You are hired
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)
Imagine being on the 374,395,106,285th bus and your the 206,305,936,253,194th passenger 💀
People in the hotel “I literally just finished unpacking stop moving us to another room.”
You never would finish unpacking your infinite items.
At that rate, I'd just keep all of my stuff in an suitcase...
Technically they would spend the entire day changing room
@@magnabueno5360*lifetime
Just about to put that
I was going to make a joke about infinity, but I'll never hear the end of it.
This guy... :)
well done.
n1
Get out
nice dad joke
Some infinities are bigger than others. That's some love story movie stuff right there. 😢
I like watching this video at least once every year. Idky but I find myself rewatching it.
It’s funny how this assumes that the guests don’t care about moving from their hotel rooms a crap ton of times
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.
Maybe they infinitely fast
Imagine being in room 1028 and suddenly the manager tells you to move to room 2056. That's one hell of a walk.
@@nataliaborys1554 It would really be a disaster going from room 2^60 to double that number.
an infinite number of times...
“Infinity + 1” is a kid argument i never guessed would be supported by actual math
Most kids probably got it from vsauce so hey
@@Wirgah didn't he say infinity plus 1 is also infinity?
@@afo985both are infinity but infinity+1 is a higher kind of infinity
@@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.
@@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.
What a smart explanation!
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
This is kinda of stuff mathematicians imagine when they're high
100th like
101st like
But it indeed lead to the creation of the computer nso that's a plus for the crazy.
601st like
Muahahaha 667th like, I broke the funny number.
"Imagine there's a hotel with infinite rooms..." Already lost me, buddy.
Just think of a hotel with many rooms
Lol
@@Guztav1337 I cant Like there should be an end of the rooms 😭🤚 It might be the 100000 rooms but WITH AN ENDD
Same
Hallway
People staying at this hotel : “Ahhh I can finally rest.” Hotel Receptionist: “Move to room 314159265 quadrillion.”
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.
"An infinite number of infinite buses show up. What can you do?" Well, for a start I could quit my job
Wt-
And get hired as a waiter for an infinite restaurant? 😜
@@azure_vxiii big oof
Just tell them to move forward until they give up or find an empty room.
How much is the paycheck cause even if its infinite i wouldnt be paid enough.
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".
That's why we support emperor palpatine. He will get rid of these infinite hotels with his infinite power.
Imagine being the 8183748595937262628385837251416363626273849595th person off the buss.
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...
@@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).
@@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.
Infinite is so weird because there can't be more so you can almost morph the number infinite to be more or less anything because it's just... Infinite.
i want more videos about David Hilbert!
All I care about is the infinite buffet...
@Darth Sidious ice cream 🍨 line will also be infinite
If you eat an infinite amount of food, you will have an infinite mass, which means you will be a black hole with an event horizon that's infinitely large. You won't be in the hotel, the hotel will be in you!
all i care about infinite money
Bag eggs poggers
there's even greater things than that in heaven.
“This hotel can’t run out of room!” “Yeah but what if it did?”
....."but it can't tho" "Yeah but what if it DID??" repeat x infinity
No what if just tell them to learn about infinity first 😂
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
That's a question for another 'what if'
Lol, good one
Imagine being the only person there. I reckon it’d feel like being the only one at a hotel, if that makes sense! lol
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 😂
Incorrect. We can manage everybody at once.
Imagine walking up to the manager and he says “Ok, you’ll be staying in room 3874920”
Guess I'll die
Guess im flash
@@kingblake902 guess I'm superman
@@HarryKaneIsGoated flash is faster plus there isn’t a way for Superman to fly so he will have to walk/run
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
Could you imagine if you just got to room 500 quadrillion and you had to go to room 1 quintillion
Imagine the 809,293,384,203,392nd person just needs milk from their local store but remember they need to walk to the exit
*"Well you pull out an infinite spreadsheet"* Ah yes, just another normal day at work
Rip off
Stolen comment
@@fernandobanda5734 half the comments on youtube are stolen, buddy.
Its actually normal day at work. Its called Excel
How many rows does a spreadsheet typically has? 256? No. Probably the square of that. That would make it 65,..., eh, thousand something. Okay, it's an infinite spreadsheet!
When the infinite number of infinite buses arrived, gotta admit I felt like giving up on my career as hotel manager.
Lol
Just think of the infinite profit.
Yeah and youre just a manager so youre getting the same wage even though hotel profits are infinite for the owners
Same like …
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
Honestly I would be pissed if I have to move rooms so many times
I’ve been recommended this video many times before THIS IS THE TIME I WATCH IT
let me just ask why theres so many people coming to *that* specific hotel
Insert Thonk Face
Maybe all the hotels werent infinite and this the only infinite hotel and all of the other ones where full
free pizza pockets every thursday and sunday
An all you can eat buffet :p
*hmmmmmmm*
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.
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.
@@billcraig5614 Dude calm down, I only said what came to mind. It doesn't hurt anyone and I didn't insult anyone.
@@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.
@@billcraig5614 Incredible how much of a smart ass you sound!
He is a dumb troll, ignore him.
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
The key insight learned from this is the distinction between infinity and all: they are not synonymous.
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.
I feel bad for the guy that has to walk forever just to go to his room that he will never reach
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
The guy waiting an infinity inside the bus to get out, will dream of being able to walk to his room.
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.
*the backrooms*
@fred McMurray the other end
props to the guy at the front desk. he’s a genius. grasped the concept of infinity no problem, then created an infinite spreadsheet within what. minutes? seconds, even? what a champ
Dude has infinite iq😂
He's got infinite fingers so types really quickly.
for real what an intelligent man, amazing skill
It's us
@@2004_Indian_Guy OwO
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|
imagine walking to room 5944853485448534853485348534853845 and reaching it, and then right when you enter the door “every one move to the room double your number 💀”
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!"
I would be glad if I don't have to move to double my room number though.
Imagine when checking out of the infinite room all the way to the front.
"sorry sir, could you move from room number 40000000000 to room 80000000000 please"
infinitiest underrated comment here
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 😔
I am sorry for the cleaning person... she left one morning to clean the rooms and never came back...
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.
@@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...
@@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.
@@AdityaRaj_24 you are right! I suppose the secret of the success here is to get investors for this enterprise...
@@AdityaRaj_24 but would be stupid management wise, whose gonna pay them all xD
whoever manages to get into room 1 must be the luckiest man out there..
Similar argument is used to prove that set of real numbers have cardinality more than set of natural numbers, using set of infinite binary string. Famously known as The Cantor's diagonal argument. We all have studied it in our university maths syllabus.
*slaps the roof of the party bus* "This bad boy can fit so much ABBA in it"
😭😂
LOL
Bruh 😂
True
😭?
Host: You can bring as many friends to the party as you’d like. Derek: Hold my bus...
Well you're here early
o
@@Spl33ney I was on the first bus.
lol how did u get so many likes just coz you got a lot of subs XD
Ha ha lmao 🤣
imagine having to move to the room double your number but your in room 500M🧫
I hope the manager is getting paid pretty well
"Imagine theres a hotel with infinite rooms." "All the rooms are occupied." *[visible confusion]*
Exactly my thoughts and I still can't get over it because everything that comes afterwards feels like bs.
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
@@slavetzkyrickyjames4305 get out with your math
@@slavetzkyrickyjames4305 tf you mean countable is it really "infinity" then
@@opioidhamster3205 you gonna understand after you finish the school, probably
"Everyone move to the room with double your current room number" The guy in room 387494985726478569420: 🙃
69420 Nice
Hahaahahahaha 😭
Every room should have a calculator then 🤣
@@calebtan8682 Just not funny Edit: I didn't find it funny ok so chill Caleb Tan is my G
@@WilIiyum okay lol
"Walk to the room double your number, simple, right?" The person in Rayo's number: F*** this, hell naw
Never thought my life would come to the point where I'd be looking at the basic explanation of infinity.
Shoutout to the architects who built an infinite number of rooms Edit: how did this get so many likes
Nah, architects just sit around and usually make unlogical plans. Thank the construction workers and site leaders
@@AT-tx7gb ye
@@AT-tx7gb ehh they're still prolly building
And the engineers who designed a building with the load capacity for an infinite amount of weight
perhaps an infinite number of architects each built one room
"But that's a story for another time." I hope you plan to leave us in finite suspense.
Niiice 👌
Please leave 😑
You should get a medal for that comment
😂
I'm guessing the hotel has infinite storeys
Imagine being in room 790 septilion and going to room 1.58 octilion
I prefer small infinity. The kind that fits in the area of a penny, by cutting the area in half, repeatedly, for an infinite number of times. That's Infinity you can hold in your hand rather than walking until you run out of life.
“Oh just move to the room double your room number.” “But I’m… at room 9,000,000,000,000,000,000,005.”
"So what? There are infinitely many people in higher-numbered rooms"
He means that the person in that room will walk for a very long time until getting to the right room
Sure, keep walking, either you reach your room or die trying!
“Start walking, bitch.”
@@gabrieldavis4434 UNDERATED REPLY OML I DIED
The most interesting thing I will watch ever in my life