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."
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
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.
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'm so confused.... rather that having everyone move up a room, why don't they just have the new guy move to the end of the line of rooms.... Infinite + Infinite = Infinite. Simple as.
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".
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.
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 EDIT AFTER 2 YEARS OF HAVING BANTER ABOUT THIS COMMENT IM NOT REPLYING TO ANYONE READ ALL OF MY COMMENTS AND REPLIES BELOW BEFORE YOU REPLY CHEERS AND THANKS FOR THE LIKES
@@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
i watched this like the year it came out without processing anything and watching it for the hell of it, and now i'm here and i am actually paying attention and trying to understand it
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
@@clayroberts2951 That's not how mathematicians think of infinites. They talk of sets of infinites so, counter-intuitively, some infinite sets are larger than other infinite sets (eg two sets of infinites added together is twice as large as a single set of infinite).
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.
@@Nobody-pp4vr this is making me have an exetental crisis that the customers never end and I just process an infinite line of people. Only having a lunch break and a longer break to go home and sleep. Help my brain is panicking.
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 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.
Hilbert Hotel is an analogy for a infinite list where each integer is identified by a unique identifier so an infinite number of Hilbert Hotels is basically an infinite number of infinite lists and for each of these lists, you'll still be able to write a number that doesn't appear in that infinite list and for these infinite number of infinite lists, you'll still be able to write a infinite list that doesn't appear in the set of those infinite number of infinite lists... I think.
If you can assign each Hilbert hotel with a natural number, then you can use the trick with the infinite buses to conclude that there still wouldn’t be enough space, as you can pair each room in each hotel with a room in only one hotel - I know it’s very weird but it’s how it works. Set theory is non-intuitive in a lot of ways.
An infinite number of Hilbert Hotels have an infinite number of floors, each floor has an infinite number of hallways and each hallway has an infinite number of rooms. Each room has an infinite number of bathrooms and each bathroom has an infinite number of showers.
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.
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!
I just checked in to the Hilbert Hotel and gotta say, they were very accommodating. They had everyone move down so I could stay in the first room. Great customer service. 10/10.
Ok never mind my last post. Ive only been here a few minutes and they’ve already told me to move several times. Ive been dragging my luggage down this long hall and I’m exhausted. You can’t always win with Priceline.
@@Grassmpl well technically, they would still have to theoretically pay for things like upkeep, so the pricing per room would have to be larger than the cost of upkeep per room + the cost of the lobby divided by infinity. it's basically a scenario where if it's making a profit, it makes infinity profit, and if it's not making a profit, its fucked.
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.
Me sleeping peacefully: Manager: Sir, you'll have to move to room 109230280248028301830210843141232 5 secs past: Manager: Sir, you'll have to move to room 9032859032751093012849235923853284923056839274903274903278537294
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 ?
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
No, the double method only makes a vacancy for a single infinite, it doesn't count for an infinite number of infinites. With only a single infinite bus you just multiply the rooms by 2, tell the person in room one to go to room 2, and the first person on the bus goes into room 1 and so on. With two infinity buses, multiply the rooms by 3. Tell the person in room one to go to room 3, the first person from bus one to go to room 1, the first person from bus 2 to go to room two and so on. But for an infinite number of buses, where are you supposed to tell where the person in room one is going to go? If you just multiply by 2 like you suggest, what are you going to tell the people on the first infinite bus? What are you going to tell the people on infinite bus 2 that is different from infinite bus 1? Then account for infinite infinite buses. With the spreadsheet method, you can actually who gets what room and direct them accordingly.
@@Абдулло-щ3е9э "No, the double method only makes a vacancy for a single infinite, it doesn't count for an infinite number of infinites." There is no difference in cardinaliy for an "(countably) infinite number of (countably) infinites" (infinte sets) and a single countably ifninite set. "With two infinity buses, multiply the rooms by 3" There is no need for that. Even "3 times" the number of natural numbers are not really "more" numbers. "But for an infinite number of buses, where are you supposed to tell where the person in room one is going to go? " To room 2. There is a bijection between the odd numbers and all natural numbers. So if you can assign the guests of all busses to the natural numbers then you can assign them to the odd numbers alone too.
"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."
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.
@@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?
But that "everybody" is infinite so they are going to keep coming in. It's just about how quickly can new customers walk in vs the time it takes to add a new room. Infinite buses with infinite seats and names as such would bring in customers faster than the infinite rooms that would need to be arranged for them. If instead each room could house infinite people, then it wouldn't have been an issue.
@@burhanhyder26 'But that "everybody" is infinite so they are going to keep coming in' Everybody moves instantaneously and simultaneously. All of the movement ends as soon as it starts. 'It's just about how quickly can new customers walk in vs the time it takes to add a new room All of that is done in an instant.
@@burhanhyder26 'then you're assuming a finite number' There is no such term as 'finite number', so I'm not making that assumption. 'Infinity has no end' Neither does any other point of any topological space, generally. For example, the point 1 doesn't have an 'end', neither does point 2, neither does Pi, etc. So what? 'There is no "all"' Lol. Kid, do you seriously not understand that this is about bijections and cardinalities? We are simply tasked with finding bijective functions between some sets.
The hotel in the math problem So me from 2 years in the future here. 1st What was i thinking, this commet makes nearly no sense with how is structured 2nd what braindead people understood it enough to like it to 8k?
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?
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 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.
I remember reading the first part of this story years ago in an old book called 'Images of Infinity'. That book was full of trippy stories like this, I need to find it again.
Isn't it annoying, when a new Guest comes, Imagine doing something and everytime a new guest come then you have to pick up your things and move to the other room again and again, Infinitely
@@fairydreamz because when a new guest arrives, you cannot tell them to just go to room 69 or 420 or 12977526 because all those rooms are occupied. Whatever room number you give them, it’s already occupied. If you want to put the new guest in room 69, you have to move 69’s occupant to another room, and that room’s occupant to another room etc. If you tell everyone to move +1, you know everyone moves into a vacant room, and room 1 is also now vacant for the new guest. I have no idea if this is at all clear or helpful. Me try X
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.
@@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.
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!"
This reminds me of my undergrad computer science course on computability & Turing machines Essentially this is an example of Cantor's Diagonal Argument, a famous proof by Georg Cantor used to show that the set of real numbers is uncountably infinite and has a greater cardinality than the set of natural numbers. Cantor's argument assumes, for contradiction, that you can list all the real numbers between 0 and 1. Imagine each real number is expressed in its decimal expansion (e.g., 0.12345...). You construct a new number that cannot possibly be in the list by taking the diagonal digits (the nth digit from the nth number) and changing each digit (for example, changing 1 to 2 or any other number to ensure it differs from the original). This new number is guaranteed to differ from every number on the list at least in one decimal place, so it can't be on the original list, proving the set of real numbers is uncountable. This proof is used to decide computability, whether a Turing machine would halt or not
It's indeed the same proof/argument. Those with the ABBAs is a bit less complicated, because some real numbers have two decimal representations while the ABBAs don't and you have to handle this correctly in your proof for the real numbers.
Imagine living in one of the largest numbered room when the manager asked them to move double that. I hope they have their walking shoes because I didn't see a vehicle in the hotel.
it would take for literal ever because if it's infinite and each guest moves every time a new guest arrives they would never even get to step into their room.
@@user-jk8ev4vn6w course now the rest of all existence for them will consist of people leaving their rooms then going down to new rooms. Like how when you whip a rope in a certain way It causes that wave effect and starts travelling down only this time there is no end.
The issue is that there are more names than there are all of those seats, combined. There is one seat for every natural number. There is one name for every real number.
I stayed in room no 248529462297499924325673114579628592016. It was quite a pleasant stay at Hilbert Hotel. The staff were courteous and offered me complimentary desserts.
I stayed at room 125388715650668267533685225755555128877756397759884 It took me a year to get there 1/10 would not recommend and it took longer to leave
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
After a single experience, I would never return to this hotel, if I imagine that whenever somebody new accommodates, I have to change my room. Can't unpack my luggage, having disturbed sleeping all the time. If I come from dinner, there's already someone new in my room etc.
I initially stayed in room No.314159265358979323846. Everything was quite nice until the infinite bus came. I was forced to move to room No.628318530717958647692, that was a hell of a long walk down the hallway.
Stupid video. Trying to explain the unexplainable with logic and words, when words can't describe what is within infinity ... infinite is infinite. End of. Infinite rooms will never run out of rooms. It's infinite. Done.
@@michellenoirstudiosI went recently and was in room one then i had to move to room 57484321257990000086543211134578000986542212346789000086432133333335789000000000 and they added an escalator but it was out of order 😭
"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"
This is similar to what we learn in limits. E.g., lim x->♾️ (x+1)/x^2 = 0 Because x-squared in the denominator reaches infinity faster than the numerator x+1
'This is basically the limits theorem' Firstly, I am not aware of any theorems being called 'the limits theorems'. Secondly, limits are irrelevant here.
@@thetaomegatheta You might want to check your sources. Cardinality and bijection apply to 'finite sets'. So it doesn't apply to this problem with infinite sets. Over and out.
'You might want to check your sources. Cardinality and bijection apply to 'finite sets'' You might want to look up the relevant terms, because they apply to sets in general, and not just to finite sets. 'So it doesn't apply to this problem with infinite sets' You really need to follow your own advice and check your sources instead of making wild and incorrect guesses about topics covered in the first couple of weeks of calculus/real analysis.
They’re called “aleph” followed by the number of level of how uncountably infinite you want to go. So like aleph(1), aleph(2), all the way up into aleph(infinity).
This is God-level math. Not even exaggerating, this sort of math is literally something that only God can actually accomplish without simply resorting to 'more infinity' like us mere mortals.
And you need to change it another time so 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...
@@Independent_Man3 this is what instantly came to my mind. Even if you had that one guy share a room with someone there would still be another guy,considering how the names go on forever,so the number technically isn’t increasing,and that guy’s name gets added to the list,no matter how many times you add and add there will always be another person
As a hotel manager, I would install some sort of system where each room moves to a number I assign it. This is so no one has to move their bags or anything. Instead of the PA going to each person, the PA goes to each room, and the room knows where to move, and for the sake of imagination, it goes basically the speed of light to go to each room. This way, each room will not hit any other room. If there is a space left open, a room will appear in that missing space, which also goes basically the speed of light. The people inside the rooms do not notice a thing, and the rooms will stay intact due to some really strong material.. somehow. Now, for the people. For people like ABBA who need to explain a situation, there will be a microphone at the door if anyone needs to explain a problem to me. I also have a microphone to respond back if the people are an uncountable number of infinity. Otherwise, I install a gate that teleports people to their room which will open after I give my announcement on the PA. There are also teleporters in the room to go outside (when the guests will leave) or to go to one of many of our complementary rooms, like pools or restaurants. This way my hotel will not only be able to fit a countable number of people, it will also provide great service to my guests.
No one seems to be concerned about the infinite number of complaints from the guests who were asked to move rooms. The infinite number of bad ratings and comments given. The infinite number of compensation claims.
@@Релёкс84 Can you? Even with multiple new sets of people? Like, if one person shows up, gets booked, and the another person shows up, is there a way to book him without disturbing anyone who's already moved?
@@FatedHandJonathon Instead of making everyone change rooms, you can just make an infinite subset of them change rooms. And when someone else shows up, take another, disjoint infinite subset, and so on. Here's one way to do it: when a first person shows up, you make the powers of 2 move: 2 to 4, 4 to 8, 8 to 16 etc. When another person comes, do the powers of3: 3 to 9, 9 to 27 etc. and so on for every prime number. These subsets are all infinitely long, all disjoint, and infinitely many since there are infinitely many prime numbers. There are more efficient ways but this is just an example.
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
And do you know something even crazier, that there will be infinitely many guys for diagonals rooms too!! ( When the letter on new room is changed and so on with previously mentioned guys' name) Maths is dramatic for sure🤯
@@fatpanda9096 Solution for last problem: Just say to every excisting guest in every room: "Just go to room 10X your room if someone konk on the door. if you are room 1 go to room 10, if you are room 23 go to room 230. And then just go to room 10X your room if someone konk on the door again. Just say to every new guest from these buses: "Knok at number 1 room door and go inside, excisting guest will leave. And then just go to room 10X your room if someone konk on the door when you are in room number one or any other room (room 10, 100, 1000, 10000...)
@@customvegandiet9491 That cascade never resolves though, the hotel is still full and the guests never stop sending others down. The problem still exists that there are more unique guests than possible rooms.
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.
😂😂😂😂
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
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
@@Best_Indian_Guy OwO
Imagine being in room 91938479272466473829183 and have to go use the bathroom down the hallway
usually each room have a bathroom inside
No.
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.
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.
I'm so confused.... rather that having everyone move up a room, why don't they just have the new guy move to the end of the line of rooms....
Infinite + Infinite = Infinite. Simple as.
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.
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 EDIT AFTER 2 YEARS OF HAVING BANTER ABOUT THIS COMMENT IM NOT REPLYING TO ANYONE READ ALL OF MY COMMENTS AND REPLIES BELOW BEFORE YOU REPLY CHEERS AND THANKS FOR THE LIKES
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
911 what's your emergency?
Me: my brain isn't braining
"What's your Address, sir"
"I'm at the Hilbert Hotel, room #... Hello? Hello?"
i watched this like the year it came out without processing anything and watching it for the hell of it, and now i'm here and i am actually paying attention and trying to understand it
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
When the infinite number of infinite buses arrived, gotta admit I felt like giving up on my career as hotel manager.
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
@@clayroberts2951 That's not how mathematicians think of infinites. They talk of sets of infinites so, counter-intuitively, some infinite sets are larger than other infinite sets (eg two sets of infinites added together is twice as large as a single set of infinite).
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
This video actually gave me a headache I’m being completely serious
This is nothing. Try a video from Vsauce.
“Imagine if you were a hotel manager and a bus pulled up with an infinite number of people in it” No I will not imagine
Infinite work
So you've chosen to rebel? Understandable, have a nice day.
destroyed
@@Nobody-pp4vr this is making me have an exetental crisis that the customers never end and I just process an infinite line of people. Only having a lunch break and a longer break to go home and sleep. Help my brain is panicking.
This will need infinite time. So no one is getting a room. Sorry still working on it 🤷♀️
(Goes on vacation instead)
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 🤣
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.
5:27 What if there’s infinite Hilbert hotels?
Hilbert Hotel is an analogy for a infinite list where each integer is identified by a unique identifier so an infinite number of Hilbert Hotels is basically an infinite number of infinite lists and for each of these lists, you'll still be able to write a number that doesn't appear in that infinite list and for these infinite number of infinite lists, you'll still be able to write a infinite list that doesn't appear in the set of those infinite number of infinite lists... I think.
@@speedforce8970
More wordy than a Kamala Harris word salad
If you can assign each Hilbert hotel with a natural number, then you can use the trick with the infinite buses to conclude that there still wouldn’t be enough space, as you can pair each room in each hotel with a room in only one hotel - I know it’s very weird but it’s how it works. Set theory is non-intuitive in a lot of ways.
An infinite number of Hilbert Hotels have an infinite number of floors, each floor has an infinite number of hallways and each hallway has an infinite number of rooms.
Each room has an infinite number of bathrooms and each bathroom has an infinite number of showers.
An infinite number of infinite Hilbert hotels is still aleph zero. The last bus is aleph one so it would still not fit in the hotels.
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
@@AvenDonn 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.
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.
I just checked in to the Hilbert Hotel and gotta say, they were very accommodating. They had everyone move down so I could stay in the first room. Great customer service. 10/10.
Ok never mind my last post. Ive only been here a few minutes and they’ve already told me to move several times. Ive been dragging my luggage down this long hall and I’m exhausted. You can’t always win with Priceline.
this is amazing
You will have a lifetime of moving rooms every few seconds....and you call that 'great customer service'??????
They can charge 1 cent each and still make beyond 6 figures.
@@Grassmpl well technically, they would still have to theoretically pay for things like upkeep, so the pricing per room would have to be larger than the cost of upkeep per room + the cost of the lobby divided by infinity.
it's basically a scenario where if it's making a profit, it makes infinity profit, and if it's not making a profit, its fucked.
"You have infinite rooms and someone is in every room what do you do?"
"Retire"
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
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...
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.
Me sleeping peacefully:
Manager: Sir, you'll have to move to room 109230280248028301830210843141232
5 secs past:
Manager: Sir, you'll have to move to room 9032859032751093012849235923853284923056839274903274903278537294
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
“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've been to this hotel. Parking is a nightmare and yes, it was full but there's a nice little guesthouse next door that usually has free rooms.
Underrated comment
Oh Hi ABBAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA!!
@@somemonkeythingfrombjsofal4654 i pretty sure thatS ABABABABABABABABABABBABABABABABABBABABABABBBBBBBABBABABAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBAAABABABABABBAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBABABABABABABABABABBABABABABABABABABABABABABBABABABBABABABABABBABABABABBABABBABBBBBBBBBBAAAAAAAAAAAAAAABBBBBBBBBBBBBBBABABAAAAAAAAAAAAABBBBBBBBBBBBBAAAAAABABABBBAABBAABBAA
@@beeabee7307 ABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABBABAABBABABABABABABABBABABABABABABABABBABABABABAABABABABBABABABABA
𓆩😇𓆪 ༻𝐆⍟𝐓⁷༺ 🐹🐰ᘻᗩᘻᗩᘻᓍᓍ🐶🦁 𝙋𝙎𝙔ヾ(⌐■_■)ノ♪ ᴏᴘᴘᴀ ɢᴀɴɢɴᴀᴍ sᴛʏʟᴇ😎🕺🐴
"You have to walk to room 100 decillion"
"You serious?"
This is still one of the very first rooms in the hotel. So he was lucky.
Bottomline, this hotel is a big problem. It's not ideal for a place of rest since you're always on the move.
Not to mention the noise from all those coaches.
you would get a new room before you reach your room aswell
@@lucasliebetrau8995 yeah bruh
.
Heheh
"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
@Freestyle Creations who will change the room number for empty rooms😂
Person at Octillion: turns into dust that can be vacuumed when trying to move.
@Freestyle Creations ou sh*t another problem. Where does the staff sleep.
Let's give credit to the manager, he deserves infinite salary for working infinite hours trying to sort out this infine problem of infinities.
he gets infinite money with a consequence that he can never leave because he’s always busy managing the hotel
There are shifts....
he also deserves infinite breaks
@@noobnaut but then those breaks would also have to be infinite since he works infinite hours 😮
@@IAmVortex-edits my god
2:04 infinite, infinity buses is the same as a bus with infinite people, so just double everyones room number.
Yes and no. If you number any bus and any seat, what room will guest 42 in bus 1703 get?
You still need to assign the rooms, and you haven't made anything easier for yourself.
No, the double method only makes a vacancy for a single infinite, it doesn't count for an infinite number of infinites.
With only a single infinite bus you just multiply the rooms by 2, tell the person in room one to go to room 2, and the first person on the bus goes into room 1 and so on.
With two infinity buses, multiply the rooms by 3. Tell the person in room one to go to room 3, the first person from bus one to go to room 1, the first person from bus 2 to go to room two and so on.
But for an infinite number of buses, where are you supposed to tell where the person in room one is going to go? If you just multiply by 2 like you suggest, what are you going to tell the people on the first infinite bus? What are you going to tell the people on infinite bus 2 that is different from infinite bus 1? Then account for infinite infinite buses.
With the spreadsheet method, you can actually who gets what room and direct them accordingly.
@@Абдулло-щ3е9э "No, the double method only makes a vacancy for a single infinite, it doesn't count for an infinite number of infinites."
There is no difference in cardinaliy for an "(countably) infinite number of (countably) infinites" (infinte sets) and a single countably ifninite set.
"With two infinity buses, multiply the rooms by 3"
There is no need for that. Even "3 times" the number of natural numbers are not really "more" numbers.
"But for an infinite number of buses, where are you supposed to tell where the person in room one is going to go? "
To room 2. There is a bijection between the odd numbers and all natural numbers. So if you can assign the guests of all busses to the natural numbers then you can assign them to the odd numbers alone too.
"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.
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
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
Manger: *writing*
2938 years later....
Manger: *still writing*
Guest:"Why the fu-"
"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
After the first minute, I just stared blankly at the screen and stopped processing the math...
JESUS
Oh wait
*JESUS*
Same
**hmm**
UH *WHAT*
@@Xiunoi bruh
I like how we just ignore that the infinite people will be entering the hotel forever
Everybody moves instantaneously.
But that "everybody" is infinite so they are going to keep coming in. It's just about how quickly can new customers walk in vs the time it takes to add a new room. Infinite buses with infinite seats and names as such would bring in customers faster than the infinite rooms that would need to be arranged for them. If instead each room could house infinite people, then it wouldn't have been an issue.
@@burhanhyder26
'But that "everybody" is infinite so they are going to keep coming in'
Everybody moves instantaneously and simultaneously. All of the movement ends as soon as it starts.
'It's just about how quickly can new customers walk in vs the time it takes to add a new room
All of that is done in an instant.
@@thetaomegatheta then you're assuming a finite number. Infinity has no end. There is no "all".
@@burhanhyder26
'then you're assuming a finite number'
There is no such term as 'finite number', so I'm not making that assumption.
'Infinity has no end'
Neither does any other point of any topological space, generally. For example, the point 1 doesn't have an 'end', neither does point 2, neither does Pi, etc.
So what?
'There is no "all"'
Lol.
Kid, do you seriously not understand that this is about bijections and cardinalities? We are simply tasked with finding bijective functions between some sets.
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*
I love how mathematicians literally need to invent a problem that doesn't exist
The hotel in the math problem
So me from 2 years in the future here.
1st What was i thinking, this commet makes nearly no sense with how is structured
2nd what braindead people understood it enough to like it to 8k?
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
The people whose room numbers are huge: "You can check out any time you like, but you can never leave."
LMAO BEST COMMENT IF YOU KNOW THE SONG
@@tastygiggidy633 Yeah Xdd
The song is Hotel California by the Eagles.
Then how can you checkout or check-in in the first place
@@saswatsarangi6669 phone
Me as the manager to the infinite people:
"Just pay the room rent at the reception and and enter any room you find empty"
No empty rooms initially. You fail to house anybody.
@@thetaomegatheta guests dont know that
They do.
@@thetaomegatheta i dont care untill they pay the rent
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
"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
I remember reading the first part of this story years ago in an old book called 'Images of Infinity'. That book was full of trippy stories like this, I need to find it again.
Let us know when you find it. Sounds interesting
If you find the title you’ve got 114 people who are curious to know it too so please share
yes
@@aurelien5747 the title is in the comment though
@@JordanII. damn, I just read the comment again, I need to pay more attention, thanks
Finally! Some one talks about it! I've talked to my manager but he hadn't helped! Thanks!
"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.
Isn't it annoying, when a new Guest comes, Imagine doing something and everytime a new guest come then you have to pick up your things and move to the other room again and again, Infinitely
I don’t understand why this was necessary when there are infinite rooms to begin with does the hotel manager not know what rooms are unoccupied?
@@fairydreamz All rooms are occupied. And even though all rooms are occupied, the hotel manager still found a way to accommodate for more guests...
@@fairydreamz u either didn't see the video or u didn't understand it
@@fairydreamz because when a new guest arrives, you cannot tell them to just go to room 69 or 420 or 12977526 because all those rooms are occupied. Whatever room number you give them, it’s already occupied.
If you want to put the new guest in room 69, you have to move 69’s occupant to another room, and that room’s occupant to another room etc.
If you tell everyone to move +1, you know everyone moves into a vacant room, and room 1 is also now vacant for the new guest.
I have no idea if this is at all clear or helpful. Me try X
LyTheFairy thank you!
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
I would hate that hotel 💀 Imagine being asked to move to another room everytime someone arrives 💀💀
If you leave it frees up a room for another customer
@@ayamelee9020 im on the side of math not the consumer on this one. I’m sorry
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.
Ikr✋💀
@@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.
"you pull out an infinite spread sheet ofc"
the manager: you are joking right ?
But you are the manager-
@@your_jerr then i hope i'm been paid an infinite salary
Ur paid a finite salary.
@°гค๓єภ° You: Then how much money do I get?
The CEO: 0.1 cent every day I'm really generous right? ;)
That printer is dead
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 😔
This reminds me of my undergrad computer science course on computability & Turing machines
Essentially this is an example of Cantor's Diagonal Argument, a famous proof by Georg Cantor used to show that the set of real numbers is uncountably infinite and has a greater cardinality than the set of natural numbers.
Cantor's argument assumes, for contradiction, that you can list all the real numbers between 0 and 1. Imagine each real number is expressed in its decimal expansion (e.g., 0.12345...).
You construct a new number that cannot possibly be in the list by taking the diagonal digits (the nth digit from the nth number) and changing each digit (for example, changing 1 to 2 or any other number to ensure it differs from the original).
This new number is guaranteed to differ from every number on the list at least in one decimal place, so it can't be on the original list, proving the set of real numbers is uncountable.
This proof is used to decide computability, whether a Turing machine would halt or not
It's indeed the same proof/argument. Those with the ABBAs is a bit less complicated, because some real numbers have two decimal representations while the ABBAs don't and you have to handle this correctly in your proof for the real numbers.
Guest: Just finished arranging their items in the room.
Manager: Please move down a room.
Guest: AGAIN?!
Imagine living in one of the largest numbered room when the manager asked them to move double that. I hope they have their walking shoes because I didn't see a vehicle in the hotel.
Lol
My guess is they can teleport, at leas then the people at the end won’t be stuck in purgatory.
it would take for literal ever because if it's infinite and each guest moves every time a new guest arrives they would never even get to step into their room.
Imagine moving 100 rooms 😳
Thank you so much!! As a hotel manager this is a problem i run into everyday, this video is so helpful!
How many rooms you got? Any vacancy?
@Boba Tea loll
@Boba Tea but his name is phppphhhh-> soooo….
@@Zephyrfish1 loll
This had 420 likes and I just ruined it😌
Problem: * literally starts out with every room being full*
Also problem: we have plenty of space for infinitely more infinities
Aah yes the common deer man.
@@radiohosted indeed
That's the beauty of infinity
@@user-jk8ev4vn6w course now the rest of all existence for them will consist of people leaving their rooms then going down to new rooms. Like how when you whip a rope in a certain way It causes that wave effect and starts travelling down only this time there is no end.
@@TheScarletSlayer Surely they would have mention this on trip advisor? I guess its natural selection then!
If the manager can write infinite seats on a spreadsheet in 2:40 than he can write all the people’s name that still aren’t on the list.
The issue is that there are more names than there are all of those seats, combined.
There is one seat for every natural number.
There is one name for every real number.
"than he can write all the people’s name that still aren’t on the list."
No, he cannot, as proven in the video.
"this is the hilbert hotel, and you're the manager"
Me: "I quit."
LMAO
∞
ez
Same
accurate response
I stayed in room no 248529462297499924325673114579628592016. It was quite a pleasant stay at Hilbert Hotel. The staff were courteous and offered me complimentary desserts.
I stayed one room before you.
Actually I ask the staff for desserts.
Actually i stayed in room no. 2¹⁰⁰⁰ i lost good amount of weight and became cristiano ronaldo
im in room 483247390343728432843243243432432432432432432432 and its nice! great view, pretty awesome buffet, theres even a pool there!
i was in room no.65685674523686743562486219867156, honestly it was pretty clean and the food was pleasant
I stayed at room 125388715650668267533685225755555128877756397759884
It took me a year to get there 1/10 would not recommend and it took longer to leave
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?
You are just like my favourite math teacher, using simple and concrete ways to explain something about math that is as abstract as this one
"All infinities are equal, but some are more equal than others"
- Not George Orwell
Is that his name or just the word 'not'
@@thatnike2604 just the word not
Lol animal farm reference
@@desktoleaf6042 lol
+that nike what if it wasnt a he
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
“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
After a single experience, I would never return to this hotel, if I imagine that whenever somebody new accommodates, I have to change my room. Can't unpack my luggage, having disturbed sleeping all the time. If I come from dinner, there's already someone new in my room etc.
*"Well you pull out an infinite spreadsheet"*
Ah yes, just another normal day at work
Perfect timing i saw the comment just as he said it
honestly just excel right?
Lol
in infinite universe lol.
@MatZ hello fellow cs major (i assume)
“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
I initially stayed in room No.314159265358979323846. Everything was quite nice until the infinite bus came. I was forced to move to room No.628318530717958647692, that was a hell of a long walk down the hallway.
Stupid video. Trying to explain the unexplainable with logic and words, when words can't describe what is within infinity ... infinite is infinite. End of. Infinite rooms will never run out of rooms. It's infinite. Done.
Ah, I was in room No.2. I was actually forced to No.314159265358979323846, it was horrible.
There was no infinite escalator?
@@michellenoirstudiosI went recently and was in room one then i had to move to room 57484321257990000086543211134578000986542212346789000086432133333335789000000000 and they added an escalator but it was out of order 😭
Bro actually did all that math 💀
This video has been in my feed since the last 2 years today I finally gave in.
This animation is like the same graphics as a dream a very vivid dream. Not an insult, very comforting actually.
Reminded me of Boobah honestly lol
Exactly, i feel like i was in dream when i watched the video, i even asked myself am i awake or not
What dreams are you having?
@@xxwre07 idk man haha
Same idk why I like it
"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"
XD
Lmao
SpongeBob reference
Just ask the other guest to move in any room that Isnt occupied
@@sandeepvivek6134 no one understands your comment lmao
This is similar to what we learn in limits.
E.g., lim x->♾️ (x+1)/x^2 = 0
Because x-squared in the denominator reaches infinity faster than the numerator x+1
'This is basically the limits theorem'
Firstly, I am not aware of any theorems being called 'the limits theorems'.
Secondly, limits are irrelevant here.
@@thetaomegatheta I didn't want to get too technical. I meant the L'Hôpital's rule. It's totally the same. Trust me.
L'Hopital has no relevance to this topic.
What does have relevance is terms like 'bijection' and 'cardinality'.
@@thetaomegatheta You might want to check your sources. Cardinality and bijection apply to 'finite sets'. So it doesn't apply to this problem with infinite sets. Over and out.
'You might want to check your sources. Cardinality and bijection apply to 'finite sets''
You might want to look up the relevant terms, because they apply to sets in general, and not just to finite sets.
'So it doesn't apply to this problem with infinite sets'
You really need to follow your own advice and check your sources instead of making wild and incorrect guesses about topics covered in the first couple of weeks of calculus/real analysis.
“Imagine infinity. Now imagine More infinity. Thought that was all? Now I want you to imagine even more infinity...”
Gee thanks
I'm dying!🤣🤣🤣
If you can imagine more infinity, than you failed the first time.
They’re called “aleph” followed by the number of level of how uncountably infinite you want to go.
So like aleph(1), aleph(2), all the way up into aleph(infinity).
This is God-level math. Not even exaggerating, this sort of math is literally something that only God can actually accomplish without simply resorting to 'more infinity' like us mere mortals.
This comment has 666 likes if u ruined it reply to me
*slaps the roof of the party bus* "This bad boy can fit so much ABBA in it"
😭😂
LOL
Bruh 😂
True
😭?
* new person arrives *
Manager: Time to hear infinite doors closing and opening
Either you hear each door sound sequentially, or all door sounds at the same time.
@@BS23Designs yeah, sequentially for eternity
all doors sounds at the same time?
...
Like when a villager were to repeatedly open and close a door continously
i saw this and my mind was thinking of the minecraft door sound😂
Video starts at 0:01
Very helpful
Thank you 🙏
Nice
😂
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
Imagine having to wake up in the middle of the night to change rooms so ABABABAAAABBBAAABBB can have a room
But then you have to move again so ABABABABABABAAAAAAAAAAAAAAAAAAAAAAAABABABBBBBBA can have a room
And then again for BBABABBBAABAABABABABABABBAABABABBABABAABABABABABABABABBABABABABABABABABABABAABABABABABBAB to have a room.
And then you have to change room once again so BABAAABBBABABABABBABABABABAVABABABABAABBAABAABABBABA can have a room
@@mola3371 And then you have to change again so that ARABABABABABAAAAAAAAAAAAAAABABABABABABABABAB could have a room.
And you need to change it another time so 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...
Imagine being that guy who doesn’t get a room: “Yea... this hotel sucks”
Infinite 1 star reviews from everyone on the uncountable bus
There will be uncountably infinite such guys.
man, that's gotta suck to be like the one person that experiences the one-to-infinity chance of that happening to you
@@Independent_Man3 this is what instantly came to my mind. Even if you had that one guy share a room with someone there would still be another guy,considering how the names go on forever,so the number technically isn’t increasing,and that guy’s name gets added to the list,no matter how many times you add and add there will always be another person
Fortunately you would have an infinite number of friends with whom to commiserate
1:36 that one guy who spent a year getting to room 900,000,000 and now has to go to room 1,800,000,000
Ngl the people in that hotel were really pissed when they found out they had to walk 34 million doors down
XD
“Yeah so uh your room number is 34 million… Good luck.”
lol
@@vangyng s
@@mr.sk1ll3d96 s
The wifi company would have a field day in this hotel.
I wonder how to water pipes and electric systems are arranged too.
Imagine cleaning, or if somebody gets sick with measles
I know right lol
@@eness379 because it would be Infineite internet so it would be you know
@@eness379 Infineite internet is impossible
I've seen multiple videos on this subject, and if it's not the most complete, it's by far the simplest and most clear I've seen. Great job
;
He really nailed it with the abba guy
bro he just copied the other video made by Ted ED exactly
@@nathansun9009 It's a thought experiment presented by mathematician David Hilbert in 1924, not something that "Ted Ed" came up with.
ههه٧٧
Whatever room guest AAAAAAAAAA... got would be certainly scary
"Imagine you were an hotel manager and a bus with infinite number of people in it"
No, I don't think I will
No thanks; I like sleep.
I would have a panic attack
Such a hotel has an infinite number of managers
It basically working. Doesn't matter how many people you will serve. Till you are alive it can be an infinite number
Wait, that doesn’t make sense
"Sweetie, wake up. We have to move rooms again."
"I told you we should have gone for the infinite AirBNB."
When u have 280likes but only a single reply
@@Ace-rm5cu the yt comment section can't house infinite, that's why
@@LollyPopTuttu i didnt understand
@@dragonslayer8789 replies to comments are limited up to 500.
Lmfao
"What would happen if infinite of infinite buses with infinite of infinite passangers show up?"
Show them the 2nd floor.
Good one
lol
*THATS ALOT OF ROOMS*
Lol
Big brain time
Man the janitor is a powerful guy that can clean all of infinite hotel
This is infinitely confusing but infinitely interesting at the same time.
See me getting likes without no reason
Yes
"Are you all hungry?"
"Sorry we're full"
*The best answer*
Not really. Don’t move anyone. Just place the new guests into new rooms. That’s how a hotel works.
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
Imagine an infinite number of people walking down an infinitely long corridor in the middle of the night cause the manager wants them to change rooms
k timmy were movin leave your bags
The video hurt my brain enough
As a hotel manager, I would install some sort of system where each room moves to a number I assign it. This is so no one has to move their bags or anything. Instead of the PA going to each person, the PA goes to each room, and the room knows where to move, and for the sake of imagination, it goes basically the speed of light to go to each room. This way, each room will not hit any other room. If there is a space left open, a room will appear in that missing space, which also goes basically the speed of light. The people inside the rooms do not notice a thing, and the rooms will stay intact due to some really strong material.. somehow. Now, for the people. For people like ABBA who need to explain a situation, there will be a microphone at the door if anyone needs to explain a problem to me. I also have a microphone to respond back if the people are an uncountable number of infinity. Otherwise, I install a gate that teleports people to their room which will open after I give my announcement on the PA. There are also teleporters in the room to go outside (when the guests will leave) or to go to one of many of our complementary rooms, like pools or restaurants. This way my hotel will not only be able to fit a countable number of people, it will also provide great service to my guests.
No one seems to be concerned about the infinite number of complaints from the guests who were asked to move rooms. The infinite number of bad ratings and comments given. The infinite number of compensation claims.
That’s fine the room is only 0.00000000000000000001€
They also get infinite revenue though
have you ever thought that infinite people don't check in at the exact same time?
@@Amazre my finite mind cannot grasp this
All it takes is one idiot to break the air conditioner and the entire system is boned.
I think the reason why this hotel doesn't run out of room is because everyone is just pissed and leaves after moving around so much
You can always ensure that any given person moves at most once during their stay, and that most people don't move at all.
@@Релёкс84 Can you? Even with multiple new sets of people? Like, if one person shows up, gets booked, and the another person shows up, is there a way to book him without disturbing anyone who's already moved?
@@FatedHandJonathon Instead of making everyone change rooms, you can just make an infinite subset of them change rooms. And when someone else shows up, take another, disjoint infinite subset, and so on.
Here's one way to do it: when a first person shows up, you make the powers of 2 move: 2 to 4, 4 to 8, 8 to 16 etc. When another person comes, do the powers of3: 3 to 9, 9 to 27 etc. and so on for every prime number. These subsets are all infinitely long, all disjoint, and infinitely many since there are infinitely many prime numbers. There are more efficient ways but this is just an example.
They have infinite patience
@@Релёкс84 Man, that would absolutely suck for the guy in room g64 minus 2.
I rate Hilbert's Hotel 1 star. We always need to move in another room, INFINITELY.
I rate it -1000000000 stars
I rate infinte number of stars
I rate it -infinity number of stars. I can't even get a decent nights sleep because I am asked to keep moving rooms!
SOMEbody has an irrelevancy issue :* :* :*
TripAdvisor gets sick of the infinite number of reviews as well....
Holy crap this was incredibly insightful
I loved how the infinite bus had the two wheels at the front and then no wheels for the rest of it
The bus has infinite strength because it can hold infinite people xD
@@neerajrajpal lol
@@neerajrajpal no inf wheels):
@@Tyeler80 xO
Infinite scrapping sound
"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
@@arja27 get out with your math
@@arja27 tf you mean countable is it really "infinity" then
@@opioidhamster3205 you gonna understand after you finish the school, probably
The guy with the name on the diagonal can have my room. I’m moving to a hotel that doesn’t need you to change rooms so often.
lol
And do you know something even crazier, that there will be infinitely many guys for diagonals rooms too!! ( When the letter on new room is changed and so on with previously mentioned guys' name)
Maths is dramatic for sure🤯
There's an infinite amount of hotels.
@@fatpanda9096 Solution for last problem:
Just say to every excisting guest in every room: "Just go to room 10X your room if someone konk on the door. if you are room 1 go to room 10, if you are room 23 go to room 230. And then just go to room 10X your room if someone konk on the door again.
Just say to every new guest from these buses: "Knok at number 1 room door and go inside, excisting guest will leave. And then just go to room 10X your room if someone konk on the door when you are in room number one or any other room (room 10, 100, 1000, 10000...)
@@customvegandiet9491 That cascade never resolves though, the hotel is still full and the guests never stop sending others down. The problem still exists that there are more unique guests than possible rooms.