How An Infinite Hotel Ran Out Of Room

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Veritasium

Veritasium

3 роки тому

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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КОМЕНТАРІ: 72 000
@ibizenco
@ibizenco 2 роки тому
Hotel manager: "You want a room, sir? No problem. The last room at the end of the hall is still free. Just follow the hall and you'll get there. Eventually."
@SuperBhavanishankar
@SuperBhavanishankar 2 роки тому
💀
@Anzal.__
@Anzal.__ 2 роки тому
Wrong
@edu_was_taken9597
@edu_was_taken9597 2 роки тому
Lmao I’ve seen this vid like 50 times and this comment it’s the best
@TachyBunker
@TachyBunker 2 роки тому
Backrooms be like:
@justanother_witheredrose894
@justanother_witheredrose894 2 роки тому
confused confusing confusion
@Waterwolf221
@Waterwolf221 2 роки тому
Imagine disturbing an infinite amount of clients just to fit one more person in the hotel
@flygawnebardoflight
@flygawnebardoflight 2 роки тому
I'm just saying that supporting an infinite number of people has got to put a toll on the economy
@artyommoxid6233
@artyommoxid6233 2 роки тому
It's ok. When you are settling in an infinite hotel you have to deal with consequences.
@jeroen5736
@jeroen5736 2 роки тому
maybe weird idea of me but why not put the one more guy on the end of infinity instead of the beginning. because if you can move everyone up one you should be able to put one at the end . maybe because infinity is not reality ?
@flygawnebardoflight
@flygawnebardoflight 2 роки тому
@@jeroen5736 I wish you luck in finding who's at the end of infinity. Spoiler Alert: It's Chuck Norris
@owlman145
@owlman145 2 роки тому
It's ok your making an infinite amount of profit anyway, so even in an infinite amount demand a refund... hmmmm
@LuioTap
@LuioTap 2 місяці тому
"Hey,you need to move to the room 748374896246326423874,and the elevator is broken,sorry for it" "....."
@Marcus-jl8jg
@Marcus-jl8jg 2 місяці тому
💀💀💀💀
@pandabrooke
@pandabrooke Місяць тому
😂
@cheetosnour.scratch-learn
@cheetosnour.scratch-learn Місяць тому
"hey, you need to move to room τ*10^79 and no elevators" response: "my feet will die.💀"
@mohammadalhocheimi1706
@mohammadalhocheimi1706 Місяць тому
Nah what about the p2m pay to move hotel? Hey, sorry for this but you need to move to room 91 google, and to use an elevator, you need to pay $200qui.
@Axol2138
@Axol2138 Місяць тому
You need to move to room 1+ +1 ( 1+ +1 is uncountably infinite because we dont know what to add for 1+ so we add the awnser to +1 but there is none so we do 1+1 to do the equation 1+ +2 but it will become 1+ +1+ +1 for mathematical logic then the process repeats becomings 1+(1+(1+(1+(1+(1+(1+(1+(1+(1+… forever )
@jellllllly
@jellllllly 2 місяці тому
I like how he explained it in such an understandable way to shield my brain from realizing I actually understood nothing.
@dhruvgupta1063
@dhruvgupta1063 5 днів тому
Underrated comment
@raheembennett3981
@raheembennett3981 4 дні тому
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
@Idek294
@Idek294 2 роки тому
Dude, the people staying in that hotel must be pissed having to move so much.
@Ririn_Sama0517
@Ririn_Sama0517 2 роки тому
I'd imagine going for a vacation, and the only thing I'd be doing is changing rooms. If someone asks me what did I do during my vacation I could say I've been changing rooms the whole time.
@beenguy5887
@beenguy5887 2 роки тому
Price you have to pay for having an infinite amount of vacation members
@cheshire1
@cheshire1 2 роки тому
A solution would be to only move the people who arrived in the last infinite group. That way everyone will move at most once. For the people who arrive in finite groups, you could just set aside the odd numbered rooms at the start and the do all the other stuff only on the even numbered ones.
@Notcreative36
@Notcreative36 2 роки тому
I would just walk until I get hundreds of rooms away from the first avaliable one. Lots of walking, but worth it
@migol1984
@migol1984 2 роки тому
I mean, they're infinitely moving.
@somebody9651
@somebody9651 2 роки тому
Imagine spending the whole holiday just to reach to your room in an infinite hotel
@chanchalsharma8196
@chanchalsharma8196 2 роки тому
😆😆😆😆
@RandyButternubs917
@RandyButternubs917 2 роки тому
Then imagine the manager telling you to move to the number twice your room number you're already in. Might as well just start your hike back to the front desk.
@dv9239
@dv9239 2 роки тому
Infinite holiday
@user-Number346
@user-Number346 2 роки тому
Yes but you got an infinite life so it s not that long compared to the time you got
@nuralyh_ahmd
@nuralyh_ahmd 2 роки тому
😂😂😂😂😂😂i think the same
@user-oe1ox8eg3p
@user-oe1ox8eg3p 2 місяці тому
"Do you know my friend?" "Who?" "Abababababababababababababababababababababababa...."
@zamhaq8866
@zamhaq8866 Місяць тому
The one with glasses or the one without?
@nu1x
@nu1x Місяць тому
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.
@SubmitToTheBiomass
@SubmitToTheBiomass 2 місяці тому
"Hey honey how was work?" "Rough day. An infinite number of infinite buses showed up."
@helen7718
@helen7718 2 місяці тому
😂
@trygveplaustrum4634
@trygveplaustrum4634 2 роки тому
"All right, everyone, move to the room number that's twice your current room number." *Guy at Room One Billion:* "Ugh, fine..."
@viethuongvothai686
@viethuongvothai686 2 роки тому
The guy assigned to room 1 quintillion: *Already turn into a skeleton getting to his room*
@egg.007
@egg.007 2 роки тому
The guy who had a quintillion numerals in his room number:okay
@freestylecreations9677
@freestylecreations9677 2 роки тому
How about just changing room number on door?
@sachin-rathi
@sachin-rathi 2 роки тому
@@freestylecreations9677 who will change the room number for empty rooms😂
@Krishdylan
@Krishdylan 2 роки тому
Person at Octillion: turns into dust that can be vacuumed when trying to move.
@parkermccarthy4265
@parkermccarthy4265 2 роки тому
imagine checking into a hotel at 5 am and realizing you have to walk to room 900 quadrillion
@Readybear77
@Readybear77 2 роки тому
They wouldn't have to the 1st customer would be in room 1 the next customer would move into room 1 and the 1st into room 2 and so on so they don't have to walk that many doors
@ankylo5550
@ankylo5550 2 роки тому
Bro a bot just replied to my comment on this post from ages ago with your exact comment
@Readybear77
@Readybear77 2 роки тому
@@ankylo5550 that's strange because someone else further down has said the exact same thing aswell 😱
@justsomeguy6545
@justsomeguy6545 2 роки тому
The guy who has to walk to room 100 saptilion Lucky
@Readybear77
@Readybear77 2 роки тому
@@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
@user-rr3ce3ls2o
@user-rr3ce3ls2o Місяць тому
I booked 1 night in the Hilbert Hotel and it was horrible! It was 10pm at night when I arrived and the receptionist asked me to move to room 13739 and the elevator is still broken as many comments mentioned here, plus a 30003 seater bus pulled up and the receptionist asked me to shift to room 43742 and I had no time to collect my stuff I brought to the hotel with me. The other guy who took my original room who was on the bus also took my stuff, INCLUDING my laptop. Even when I was sleeping, I was asked to SHIFT to double of my room number and was like "F************ this" and completely checked out at 1 in the morning instead of 12 noon which I promised to the receptionist. Bad hotel, don't go here. Would give 0 stars if there was even an option.
@zamhaq8866
@zamhaq8866 Місяць тому
Remember that one time where someone pulled the fire alarm and the whole building had to evacuate the same emergency exit? Pranksters man. (Doordash also wont deliver here) 1 star
@daleviker5884
@daleviker5884 Місяць тому
I stayed at the Hilbert Hotel back when it was known as the Premier Inn, Heathrow. There were so many people at breakfast that it just had to be a thought experiment.
@zephpiala3634
@zephpiala3634 29 днів тому
There's 7 billion people and it can fit 7 billion rooms. There are leftovers here. 0.000000000000000000000000000001 stars
@KnowWithMalvika
@KnowWithMalvika 3 дні тому
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
@tram_collections
@tram_collections 3 місяці тому
I can't wrap my head around the concept of infinity.
@MzeeMoja1
@MzeeMoja1 14 днів тому
It’s a concept that is really difficult to grapple with, especially when thinking of it in terms of an infinite universe which means that there would be an infinite number of possibilities. I asked ChatGPT whether in an infinite universe there is a planet full of dogs and this was the response: In an infinite universe, the possibility of a planet full of dogs does indeed exist, according to the concept of infinite possibilities. Here's why: 1. **Infinite Space:** In an infinite universe, there are an infinite number of planets and celestial bodies. With such vastness, virtually any conceivable configuration of planets and environments is possible, including planets that are inhabited entirely by dogs. 2. **Probability and Randomness:** In a universe with infinite possibilities, random fluctuations and chaotic processes can give rise to a wide range of outcomes. While the likelihood of a planet being inhabited entirely by dogs may be extremely low, it is not impossible within the framework of infinite possibilities. 3. **Variety of Environments:** Planets can have a wide range of environments, from rocky and barren to lush and habitable. In an infinite universe, there are bound to be planets with environments that are conducive to the existence and proliferation of certain species, including dogs. It's important to note that the concept of a planet full of dogs is purely hypothetical and speculative. While it may seem fantastical, the idea illustrates the vastness and diversity of potential configurations within an infinite universe. In reality, our understanding of the universe is still limited, and we have yet to explore even a fraction of its vastness. -Ends- Basically anything that can happen in an infinite universe will happen. 🤯
@josephlightfoot414
@josephlightfoot414 11 днів тому
There's no such thing as infinity, it is by its own definition, not quantifiable.
@pburant
@pburant 8 днів тому
Try visiting the DMV on the last day of the month.
@thatdude2492
@thatdude2492 2 роки тому
“An infinite number of infinite busses.” - “Dear god.” “But now a big bus pulls up” - “No.”
@thetoiletpaperrollondalgom4592
@thetoiletpaperrollondalgom4592 2 роки тому
Imagine the traffic by just standing behind the bus ;-;
@softtacos1
@softtacos1 2 роки тому
Dear god... There's more. No...
@gavinli1368
@gavinli1368 2 роки тому
Do you want the bucket?
@softtacos1
@softtacos1 2 роки тому
@@gavinli1368 Yes!
@alexeyvlasenko6622
@alexeyvlasenko6622 2 роки тому
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
@neku-fn8dq
@neku-fn8dq 2 роки тому
Dont you hate it when you're working as hotel manager and then infinite amount of busses full of infinite people decided to use your hotel
@ihatethatrepairmen4255
@ihatethatrepairmen4255 2 роки тому
They are customers
@michelecaronti
@michelecaronti 2 роки тому
You'll have to build an infinite parking lot ahah
@michelecaronti
@michelecaronti 2 роки тому
@@ihatethatrepairmen4255 Legit
@kookies_kooky7170
@kookies_kooky7170 2 роки тому
Seriously i get annoyed while infinite people come in the hotel while iam peacefully eathing ramen
@randomhandle111
@randomhandle111 2 роки тому
@@kookies_kooky7170 infinite supply of ramen in your infinitely large ramen room
@theragingranga9484
@theragingranga9484 Місяць тому
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.
@ismailsahin3232
@ismailsahin3232 Місяць тому
The logic of the last example is how they proved there are more decimal numbers between 0 and 1 than there are integers from 0 to infinity
@okgaming7886
@okgaming7886 24 дні тому
But doesn't logic also say that for any decimal between 0 and 1, you'll find an integer by dropping the decimal point?
@ismailsahin3232
@ismailsahin3232 24 дні тому
@@okgaming7886 no because 0,1 and 0,01 and 0,001 all will give 1 when you drop the decimal even though they are different numbers
@okgaming7886
@okgaming7886 24 дні тому
@@ismailsahin3232 fair, but for every case of a leading zero that can be dropped from an integer, there's a decimal with a trailing zero that can be dropped, e.g. .10, .100, .1000 are all .1. So that still should work out even, should it not? Perhaps a better axiom is that you can always reverse it and drop the decimal.
@ismailsahin3232
@ismailsahin3232 24 дні тому
@@okgaming7886 yes but that doesnt mean it will even out, also i think the point was that integers are countable infinity where as decimals are not. When given a 2 integers you know how many integers are there between them where as there is always infinite number of decimals between 2 different decimals.
@okgaming7886
@okgaming7886 24 дні тому
@@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
@NeerajSingh-jf8mz
@NeerajSingh-jf8mz 2 роки тому
Imagine being so unlucky that you don't even get a room in an infinite hotel.
@criticallyconk4944
@criticallyconk4944 2 роки тому
Rng moment
@user-vb8zo6kh4j
@user-vb8zo6kh4j 2 роки тому
It is your fault for being named ABABBABAAABBABAABABBABAABAB
@futotesan
@futotesan 2 роки тому
@@user-vb8zo6kh4j Or for being named ABABBABAAABCABAABABBABAABAB....or E...and don't even get me started with a name like Futote...not an A or a B in the name. How's the Hotel manager supposed to work with that?
@Woocet
@Woocet 2 роки тому
I know who it is, bad luck brian
@alexeyvlasenko6622
@alexeyvlasenko6622 2 роки тому
Just don't have an infinitely long name, and you won't have a problem
@alanhulseii9093
@alanhulseii9093 2 роки тому
Imagine just unpacking and being told to move 100 rooms down
@francisbacon3949
@francisbacon3949 2 роки тому
Literally laughed out loud at this one hahahaha 💀💀💀
@vcreativeart16
@vcreativeart16 2 роки тому
Imagine just unpacking and being told to move 189,146,081,499,116 rooms down
@jhsevs
@jhsevs 2 роки тому
Or a hundred infinities
@shahidkhan-uq9mm
@shahidkhan-uq9mm 2 роки тому
@@vcreativeart16 r/yourjokebutworse
@jhsevs
@jhsevs 2 роки тому
@@shahidkhan-uq9mm this is not reddit.
@SwapravaNath
@SwapravaNath Місяць тому
This is the best explanation of countable vs uncountable I have heard so far.
@rikardnorlen752
@rikardnorlen752 10 днів тому
Well you can't hold me countable!
@user-wx8zp5ye1x
@user-wx8zp5ye1x 13 днів тому
Staying at this hotel is literally a workout 💀
@NEKOSAIKOU.
@NEKOSAIKOU. 13 днів тому
A deathwish
@mukulkashyap4506
@mukulkashyap4506 6 днів тому
I'll prefer to sleep on the road
@IriaChannel
@IriaChannel 2 роки тому
This hotel's manager needs an infinite raise
@skullscope
@skullscope 2 роки тому
Watch people make a problem with that
@datboredguy4873
@datboredguy4873 2 роки тому
If for attending infinite people there are infinite managers and each manager gets an infinite raise how much money do u hv to raise
@datboredguy4873
@datboredguy4873 2 роки тому
Btw u are manager
@seederorg2489
@seederorg2489 2 роки тому
@@datboredguy4873 ∞^∞
@unholycrusader69
@unholycrusader69 2 роки тому
What about inflation?
@Namiizan
@Namiizan 2 роки тому
"An infinite number of infinite buses show up. What can you do?" Well, for a start I could quit my job
@spike480p
@spike480p 2 роки тому
Wt-
@azure_vxiii
@azure_vxiii 2 роки тому
And get hired as a waiter for an infinite restaurant? 😜
@mimi-ix3fb
@mimi-ix3fb 2 роки тому
@@azure_vxiii big oof
@bijan2210
@bijan2210 2 роки тому
Just tell them to move forward until they give up or find an empty room.
@TheSUGA1202
@TheSUGA1202 2 роки тому
How much is the paycheck cause even if its infinite i wouldnt be paid enough.
@RyanShabbir
@RyanShabbir Місяць тому
Bro F’d my brain up and thought I wouldn’t notice💀💀
@antimatterj6005
@antimatterj6005 2 місяці тому
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.
@RxktPlayz
@RxktPlayz 2 роки тому
People in the hotel “I literally just finished unpacking stop moving us to another room.”
@SkillTimO
@SkillTimO 2 роки тому
You never would finish unpacking your infinite items.
@lizlee8715
@lizlee8715 2 роки тому
At that rate, I'd just keep all of my stuff in an suitcase...
@magnabueno5360
@magnabueno5360 2 роки тому
Technically they would spend the entire day changing room
@cytusdux7439
@cytusdux7439 2 роки тому
@@magnabueno5360*lifetime
@doomkenka
@doomkenka 2 роки тому
Just about to put that
@alexguy7395
@alexguy7395 2 роки тому
It’s funny how this assumes that the guests don’t care about moving from their hotel rooms a crap ton of times
@jaspertyler4557
@jaspertyler4557 2 роки тому
by technicality, it's just to show there would be enough rooms to fit everyone, and the new people could just enter the empty rooms that are confirmed to exist.
@tanshiro8593
@tanshiro8593 2 роки тому
Maybe they infinitely fast
@nataliaborys1554
@nataliaborys1554 2 роки тому
Imagine being in room 1028 and suddenly the manager tells you to move to room 2056. That's one hell of a walk.
@ELREASON44
@ELREASON44 2 роки тому
@@nataliaborys1554 It would really be a disaster going from room 2^60 to double that number.
@rattle7215
@rattle7215 2 роки тому
an infinite number of times...
@rafalkaminski5120
@rafalkaminski5120 Місяць тому
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.
@chiraggowda4928
@chiraggowda4928 Місяць тому
Finally, a job where I can use my PHD in math. A hotel manager.
@alifputrawan9565
@alifputrawan9565 2 роки тому
I'm impressed that a bus has more capacity than a hotel.
@kelsey5818
@kelsey5818 2 роки тому
There are multiple busses, not multiple hotels.
@oboy1918
@oboy1918 2 роки тому
@@kelsey5818 but can the one hotel fit all the people from the last bus with infinite ababab s
@kelsey5818
@kelsey5818 2 роки тому
@@oboy1918 just put them on an infinite bus with seats. Problem fixed.
@Jellyduckface1
@Jellyduckface1 2 роки тому
That's one hell of a bus huh?
@gigaomnom3849
@gigaomnom3849 2 роки тому
They had the same. There were just multiple buses
@Kumpulas
@Kumpulas 2 роки тому
Customer: where’s my room sir? Hotel manager: at the end of the hall
@bigj9503
@bigj9503 2 роки тому
*walks 4000 gigameters*
@kordru
@kordru 2 роки тому
@@bigj9503 *walks infinite amounts of infinite distance for infinite time*
@Utkarsh2607
@Utkarsh2607 2 роки тому
@@kordru and after infinity millenium ,probably you will reach there... Manager:Wishing that your age is infinite.. (o‿∩)
@Snoowy_FN
@Snoowy_FN 2 роки тому
4 gigameters is already 2.485e+6 miles
@bschristopher916
@bschristopher916 2 роки тому
by the time he reaches his room, he'll have infinite Grandchildrens and so on
@diegovasquez840
@diegovasquez840 2 місяці тому
If you couldn’t figure this one out, don’t worry, you’re not alone. When Cantor published his now famous results on cardinality, it was so paradoxical that almost nobody accepted it. But Hilbert did, and created this analogy to help justify it to befuddled minds.
@RonaldRaygun-tg4zl
@RonaldRaygun-tg4zl 2 місяці тому
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.
@yesIdostudy
@yesIdostudy 9 днів тому
It was SO SO cool to know! Thank you for this video 🎉
@mcmona4171
@mcmona4171 2 роки тому
"I love you " "I love you more" "I love you times infinity!" Me: pulls out spreadsheet.
@sen4845
@sen4845 2 роки тому
💀
@gregoryb4322
@gregoryb4322 2 роки тому
“Actually I think that you’ll find that will be quite literally impossible🤓”
@afigamming7958
@afigamming7958 2 роки тому
I have mona
@mcmona4171
@mcmona4171 2 роки тому
@@afigamming7958 yesss me too! (though I was pulling for venti 😔)
@aadenkeehn8112
@aadenkeehn8112 2 роки тому
Crispy chicken sandwich and caramel brownie mcflurry
@putmyfootupyoass
@putmyfootupyoass 2 роки тому
Teacher: The test isn't that hard. The test:
@satishchaudhary7978
@satishchaudhary7978 2 роки тому
Go study instead of watching videos and then the test won't be hard
@r6tker
@r6tker 2 роки тому
@@satishchaudhary7978 r/whoosh
@TheCrimson_Phoenix
@TheCrimson_Phoenix 2 роки тому
@@satishchaudhary7978 r/whoosh
@gamingstream4675
@gamingstream4675 2 роки тому
@@satishchaudhary7978 r/whoosh
@parkourcracker3984
@parkourcracker3984 2 роки тому
@@satishchaudhary7978 r/whoosh
@diamondtrike4963
@diamondtrike4963 2 місяці тому
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
@shepardog8180
@shepardog8180 18 днів тому
These videos make me feel stupid but they're so fascinating and entertaining
@MonikasPhantom
@MonikasPhantom 2 роки тому
“I quit” “But you’re the mana-“ “Nope, I quit”
@OliverEye
@OliverEye 2 роки тому
True I did next week
@jaiadit2406
@jaiadit2406 2 роки тому
😂😂😂😂😂😂😂
@bodhiboy1
@bodhiboy1 2 роки тому
I quit
@kristynahladikova8077
@kristynahladikova8077 2 роки тому
1 k like
@orenge-hw9nx
@orenge-hw9nx 2 роки тому
When you have Inifnite mana as a mage in skinder 2
@NonsenseFabricator
@NonsenseFabricator 2 роки тому
"Imagine there's a hotel with infinite rooms..." Already lost me, buddy.
@Guztav1337
@Guztav1337 2 роки тому
Just think of a hotel with many rooms
@manuelr.7461
@manuelr.7461 2 роки тому
Lol
@bozhanatoneva1973
@bozhanatoneva1973 2 роки тому
@@Guztav1337 I cant Like there should be an end of the rooms 😭🤚 It might be the 100000 rooms but WITH AN ENDD
@reaperlucario3155
@reaperlucario3155 2 роки тому
Same
@Okaz_
@Okaz_ 2 роки тому
Hallway
@idoscripts
@idoscripts 2 місяці тому
his answering questions nobody ever wondered to ask 🗣🔥🔥
@tanveer_badar_
@tanveer_badar_ Місяць тому
This is Cantor's diagonalization argument and it is vastly useful in disproving statements.
@-kaori
@-kaori 15 годин тому
It doesn't make sense to me, can you explain it? I don't see why the person with these diagonal letters wouldn't be on the list, if every combination of the 2 letters is supposedly on the list.
@royalminstrel
@royalminstrel 2 роки тому
"Imagine a bus pulls up with an infinite number of people..." "Okay..." "Now imagine a BIG bus pulls up..."
@CJBoxyeet
@CJBoxyeet 2 роки тому
like always, that part of the video showed up when i read your comment
@3aloosh623
@3aloosh623 2 роки тому
@@CJBoxyeet ik right this always happens lol
@Roboman1807
@Roboman1807 2 роки тому
No seats? Is that even legal?
@yakked
@yakked 2 роки тому
And somehow he never mentions framerules.
@kbgiver
@kbgiver 2 роки тому
@@CJBoxyeet omg IT'S RELATABLE IM DYING
@ericoschmitt
@ericoschmitt 2 роки тому
Just tell them to walk down the hall knocking every door until they find one empty. They will never return to ask questions.
@asedtf
@asedtf 2 роки тому
This is why you don't need to learn math to be a good engineer
@ericoschmitt
@ericoschmitt 2 роки тому
@@asedtf I did study engineering, and calculus was not my strength lol
@denispol79
@denispol79 2 роки тому
An engineer enters a burning building and sees a fire extinguisher on a wall. He grabs it and puts the fire down. A mathematician enters a burning building and sees a fire extinguisher on a wall. He just walks out, because there's a clear obvious solution.
@Kingdo99a
@Kingdo99a 2 роки тому
This to me seems more like a thought experiment on efficiency, extra rules and assumptions had to be made to come up with a answer. Im no mathematician, but I would have thought it didnt mater In what way an infinite amount of people arrived, or in how many groups. They all wanted the same thing and could be considered a single entity. Meaning a universal less efficient method could have been used.
@SeeAndDreamify
@SeeAndDreamify 2 роки тому
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.
@joshtonpi2271
@joshtonpi2271 Місяць тому
Even though I know all of this, I still like to come back and watch this because it’s so well done
@morrischristopher5366
@morrischristopher5366 Місяць тому
Great video, but I noticed a potential inaccuracy in the explanation regarding infinite rooms. Here's the issue: The guest labeled "no room" wouldnt occur in an infinite spreadsheet. Even if a new infinite guest bus comes over the next minute, it would still have a room because we can infinitely shift existing guests one room over, creating a chain reaction with infinite vacancies. The true challenge lies in managing (assigning/tracking) an infinite number of guests, not a lack of space. Our finite human methods struggle with handling infinity. Therefore, the answer to "Could you run out of space?" is definitively no. Infinite rooms can accommodate everyone. Hire me as the Manager of the Hilbert Hotel :)
@Pokekidb_ac
@Pokekidb_ac Місяць тому
You are hired
@shavojohn4241
@shavojohn4241 6 днів тому
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)
@BobLegoman
@BobLegoman 2 роки тому
*slaps the roof of the party bus* "This bad boy can fit so much ABBA in it"
@plasienorzokie2187
@plasienorzokie2187 2 роки тому
😭😂
@matiasandreupinanaradrigan7862
@matiasandreupinanaradrigan7862 2 роки тому
LOL
@manuelr.7461
@manuelr.7461 2 роки тому
Bruh 😂
@jamesontv4805
@jamesontv4805 2 роки тому
True
@h4nishi
@h4nishi 2 роки тому
😭?
@liber2350
@liber2350 2 роки тому
“This hotel can’t run out of room!” “Yeah but what if it did?”
@thewatchidiot
@thewatchidiot 2 роки тому
....."but it can't tho" "Yeah but what if it DID??" repeat x infinity
@Himoooo
@Himoooo 2 роки тому
No what if just tell them to learn about infinity first 😂
@ethrick.k.1292
@ethrick.k.1292 2 роки тому
Then your question would go on for infinite as so would your doubt of this fact because infinity is as unlimited as the very definition as soon as you recognize how infinity is as it stretches farther than your perception
@laxmanrawat748
@laxmanrawat748 2 роки тому
That's a question for another 'what if'
@mustafabahaj9832
@mustafabahaj9832 2 роки тому
Lol, good one
@argentinman682
@argentinman682 Місяць тому
Imagine being on the 374,395,106,285th bus and your the 206,305,936,253,194th passenger 💀
@game-cholic2969
@game-cholic2969 2 місяці тому
One thing for sure, the manager should be given a raise
@colinginn7025
@colinginn7025 2 роки тому
I was going to make a joke about infinity, but I'll never hear the end of it.
@colonelhacker3661
@colonelhacker3661 2 роки тому
This guy... :)
@sicklymoonlight
@sicklymoonlight 2 роки тому
well done.
@user-ke2dl9se5l
@user-ke2dl9se5l 2 роки тому
n1
@wa6488
@wa6488 2 роки тому
Get out
@toast1757
@toast1757 2 роки тому
nice dad joke
@juliansantos5579
@juliansantos5579 2 роки тому
“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
@Nobody-pp4vr
@Nobody-pp4vr 2 роки тому
Infinite work
@jahnvivi5939
@jahnvivi5939 2 роки тому
So you've chosen to rebel? Understandable, have a nice day.
@dperfett
@dperfett 2 роки тому
destroyed
@Dovenchiko
@Dovenchiko 2 роки тому
@@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.
@wiameena39
@wiameena39 2 роки тому
This will need infinite time. So no one is getting a room. Sorry still working on it 🤷‍♀️ (Goes on vacation instead)
@ApolloAgain
@ApolloAgain Місяць тому
People staying at this hotel : “Ahhh I can finally rest.” Hotel Receptionist: “Move to room 314159265 quadrillion.”
@yayyyyyyyyyyyyyyyyyyq
@yayyyyyyyyyyyyyyyyyyq 2 місяці тому
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
@cluckinbell1992
@cluckinbell1992 2 роки тому
"I can't get into my room. I've been in Room 27." "You've been moved to Room 945,172,370,837,362. Also, the elevator is broken. Use the stairs." "I'm just gonna leave."
@Guztav1337
@Guztav1337 2 роки тому
But then infinite people would leave, and all the other hotels are full. So only this infinite hotel has space.
@manuelr.7461
@manuelr.7461 2 роки тому
...
@funny_ol_kat
@funny_ol_kat 2 роки тому
Oof
@lamhw
@lamhw 2 роки тому
@@Guztav1337 oh. I’ll go home then
@JohnSmith-ox3gy
@JohnSmith-ox3gy 2 роки тому
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.
@ethankylem.francisco5722
@ethankylem.francisco5722 2 місяці тому
What a smart explanation!
@someone-lollmao
@someone-lollmao 3 місяці тому
Never thought my life would come to the point where I'd be looking at the basic explanation of infinity.
@thetntsheep4075
@thetntsheep4075 3 роки тому
This must be the world's most inconvenient hotel to stay in. "Sorry sir, could we get you to move down another room please" "What? That's like the infinitieth time!"
@tachzusamm
@tachzusamm 3 роки тому
I would be glad if I don't have to move to double my room number though.
@00_Cupid
@00_Cupid 3 роки тому
Imagine when checking out of the infinite room all the way to the front.
@souheilallegue2342
@souheilallegue2342 3 роки тому
"sorry sir, could you move from room number 40000000000 to room 80000000000 please"
@xeon2k8
@xeon2k8 3 роки тому
infinitiest underrated comment here
@lyrelyreharponfire
@lyrelyreharponfire 3 роки тому
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 😔
@battlesheep2552
@battlesheep2552 3 роки тому
Imagine you go to this hotel, your room number is some absurdly high number. It takes hours to get to it, and you're dead tired once you do. You're about ready to throw yourself on the bed when you hear over the PA: "please move to the room number that is 2 times your current number".
@ememmeme8722
@ememmeme8722 3 роки тому
That's why we support emperor palpatine. He will get rid of these infinite hotels with his infinite power.
@iBetThisNameWillWork
@iBetThisNameWillWork 3 роки тому
Imagine being the 8183748595937262628385837251416363626273849595th person off the buss.
@gladiatoranc
@gladiatoranc 3 роки тому
There are an infinite number of rooms, therefore it would take some people infinite walking and would never get to their room even if they had infinite life...therefore some rooms would always be empty...
@tomsvoboda2309
@tomsvoboda2309 3 роки тому
@@gladiatoranc There are infinitely many, but all of them can be reached in a finite time. Just as you can count from 0 to any natural number by repeatedly adding 1 in a finite time (possibly absurdly high, but still finite).
@gladiatoranc
@gladiatoranc 3 роки тому
@@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.
@chasemika3836
@chasemika3836 2 місяці тому
I like watching this video at least once every year. Idky but I find myself rewatching it.
@hearTelus
@hearTelus Місяць тому
i want more videos about David Hilbert!
@pakistaniyoutuber581
@pakistaniyoutuber581 2 роки тому
Manager: Can everyone please move from their room again Guest: B R U H....
@lans241283
@lans241283 2 роки тому
Pol
@MuhammadWaseem-kj5ye
@MuhammadWaseem-kj5ye 2 роки тому
I'm also pakistani
@williamjames7293
@williamjames7293 2 роки тому
I'd check the heck outta there
@benjo3355
@benjo3355 2 роки тому
Loool
@YYZed12
@YYZed12 2 роки тому
LMAOOO
@laoaidan2400
@laoaidan2400 2 роки тому
“Infinity + 1” is a kid argument i never guessed would be supported by actual math
@Wirgah
@Wirgah 2 роки тому
Most kids probably got it from vsauce so hey
@afo985
@afo985 2 роки тому
@@Wirgah didn't he say infinity plus 1 is also infinity?
@Alt.E32
@Alt.E32 2 роки тому
@@afo985both are infinity but infinity+1 is a higher kind of infinity
@rhynoorhyon5291
@rhynoorhyon5291 2 роки тому
@@Alt.E32 wrong. infinity+1 is still a countable infinity, and therefore infinity. The infinity described in this video with the ABABABBABAB bus was Aleph Null, the first order of uncountable infinities.
@Alt.E32
@Alt.E32 2 роки тому
@@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.
@GoIdappI555
@GoIdappI555 Місяць тому
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
@RigidRush
@RigidRush 8 днів тому
I’ve been recommended this video many times before THIS IS THE TIME I WATCH IT
@autowarranty2852
@autowarranty2852 2 роки тому
"this is the hilbert hotel, and you're the manager" Me: "I quit."
@zhounen790
@zhounen790 2 роки тому
LMAO
@user-dv9ze9tt4l
@user-dv9ze9tt4l 2 роки тому
@nickdanvers547
@nickdanvers547 2 роки тому
ez
@axolotl6564
@axolotl6564 2 роки тому
Same
@reinhard7731
@reinhard7731 2 роки тому
accurate response
@mmicoski
@mmicoski 2 роки тому
I am sorry for the cleaning person... she left one morning to clean the rooms and never came back...
@AdityaRaj_24
@AdityaRaj_24 2 роки тому
Well if there are infinite number of rooms and infinite number of person living in each of them, then maybe there would be arrangments for an infinite number of cleaning person each assigned one room to clean.
@mmicoski
@mmicoski 2 роки тому
@@AdityaRaj_24 that's a good idea. And if the manager tries to save money (in salaries) and allocate one cleaning person teach 10 rooms, he still will pay infinite salaries...
@AdityaRaj_24
@AdityaRaj_24 2 роки тому
@@mmicoski well he gotta pay infinite salleries because he is receiving infinite room charges from his customers. And suppose that the manager is charging 100 bucks for each room and paying 10 bucks for getting each room cleaned. Now here the room charge paid by each customer is finite and the sallery given to each cleaning person is finite. But the income of the hotel (which is finite from each room, say 30 bucks per room) is infinite! So we gotta say it's a smart move to construct such a hotel.
@mmicoski
@mmicoski 2 роки тому
@@AdityaRaj_24 you are right! I suppose the secret of the success here is to get investors for this enterprise...
@tharindurajakaruna1590
@tharindurajakaruna1590 2 роки тому
@@AdityaRaj_24 but would be stupid management wise, whose gonna pay them all xD
@NitishKr_Stats
@NitishKr_Stats Місяць тому
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.
@greedy49
@greedy49 2 місяці тому
that manager deserves a raise for dealing with infinite infinitive
@Eye-Of-The-Beholder
@Eye-Of-The-Beholder 2 роки тому
*"Well you pull out an infinite spreadsheet"* Ah yes, just another normal day at work
@ronaldhamac3787
@ronaldhamac3787 2 роки тому
Perfect timing i saw the comment just as he said it
@theghostcookie2772
@theghostcookie2772 2 роки тому
honestly just excel right?
@Relatess
@Relatess 2 роки тому
Lol
@AS-qi2lq
@AS-qi2lq 2 роки тому
in infinite universe lol.
@natecallon9755
@natecallon9755 2 роки тому
@MatZ hello fellow cs major (i assume)
@jairus2008
@jairus2008 2 роки тому
I feel bad for the guy that has to walk forever just to go to his room that he will never reach
@benjaminraymundo6711
@benjaminraymundo6711 2 роки тому
Actually he will one day reach it but its would be soooooo long that it might feel like eternity but it will come eventually. That's how infinity works
@nadineullrich3809
@nadineullrich3809 2 роки тому
The guy waiting an infinity inside the bus to get out, will dream of being able to walk to his room.
@user-wb7ez9ud4p
@user-wb7ez9ud4p 2 роки тому
The funny part is: no single person would walk for infinity to get to his room! Every single person would have an exact room number, and thus an exact time it would take to get there. The time may be arbitrarily long but always FINITE! That's the beauty of countable infinity, it's so manageable.
@cresbalundo8845
@cresbalundo8845 2 роки тому
*the backrooms*
@sharonsia1351
@sharonsia1351 2 роки тому
@fred McMurray the other end
@-Gunnarsson
@-Gunnarsson 12 днів тому
The guy working in the lobby can only handle one customer at the time. And only one queue. That means the first bus showing up will be maximum 😂
@thetaomegatheta
@thetaomegatheta 12 днів тому
Incorrect. We can manage everybody at once.
@guillaumelagueyte1019
@guillaumelagueyte1019 Місяць тому
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.
@luigi.gaming
@luigi.gaming 2 роки тому
The people whose room numbers are huge: "You can check out any time you like, but you can never leave."
@tastygiggidy633
@tastygiggidy633 2 роки тому
LMAO BEST COMMENT IF YOU KNOW THE SONG
@theblackreaper4395
@theblackreaper4395 2 роки тому
@@tastygiggidy633 Yeah Xdd
@paulmurray2729
@paulmurray2729 2 роки тому
The song is Hotel California by the Eagles.
@saswatsarangi6669
@saswatsarangi6669 2 роки тому
Then how can you checkout or check-in in the first place
@gabrielferes
@gabrielferes 2 роки тому
@@saswatsarangi6669 phone
@JrsFTW
@JrsFTW 2 роки тому
This hotel sounds like literal hell. Imagine being disturbed Infinitely to Infinitely walk down a hallway to your next room. I would literally prefer to sleep in the dirt than be subjected to near endless walking at this hotel.
@billcraig5614
@billcraig5614 2 роки тому
Incredible how little thought you were able to give to this thought experiment! I won't be surprised if your next argument is that there is no way that there would be enough bath towels to go around so this could never really happen.
@JrsFTW
@JrsFTW 2 роки тому
@@billcraig5614 Dude calm down, I only said what came to mind. It doesn't hurt anyone and I didn't insult anyone.
@DeputyDiddle
@DeputyDiddle 2 роки тому
@@billcraig5614 dude what are you even talking about? They didn't say anything about this theoretical experiment being possible or impossible. You literally just read his comment, thought of your own thing, and then got mad at them for the thing you yourself thought of.
@heavyguy4660
@heavyguy4660 2 роки тому
@@billcraig5614 Incredible how much of a smart ass you sound!
@mickeyagrawal2001
@mickeyagrawal2001 2 роки тому
He is a dumb troll, ignore him.
@Average_Roblox_God
@Average_Roblox_God Місяць тому
The most interesting thing I will watch ever in my life
@NevrrPresntt
@NevrrPresntt 4 дні тому
Some infinities are bigger than others. That's some love story movie stuff right there. 😢
@SIRMMA
@SIRMMA 2 роки тому
When the infinite number of infinite buses arrived, gotta admit I felt like giving up on my career as hotel manager.
@V4_3C
@V4_3C 2 роки тому
Lol
@ruan13o
@ruan13o 2 роки тому
Just think of the infinite profit.
@ianh1504
@ianh1504 2 роки тому
Yeah and youre just a manager so youre getting the same wage even though hotel profits are infinite for the owners
@Pink_blox1
@Pink_blox1 2 роки тому
Same like …
@clayroberts2951
@clayroberts2951 2 роки тому
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
@pandaescarlate7268
@pandaescarlate7268 2 роки тому
I love how mathematicians literally need to invent a problem that doesn't exist
@bobherobrine3415
@bobherobrine3415 2 роки тому
The hotel in the math problem
@dickhammerbush172
@dickhammerbush172 2 роки тому
You don't tell me how many watermelons are in my swimming pool, I do
@recoupxtra7270
@recoupxtra7270 2 роки тому
Fax
@unapersonaelegante4399
@unapersonaelegante4399 2 роки тому
Some weeks ago I did a test that said: Victor written all number from 1 to 2021 but he missed the space between each other, which number will be in the position 2021? And I though, why would I ever need to know that?
@BumHoleTickler
@BumHoleTickler 2 роки тому
It's to show how smart we are
@Bblozy
@Bblozy 20 годин тому
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 💀”
@pavanrajesh-ts6pg
@pavanrajesh-ts6pg 2 місяці тому
youtube has be recomending this from long time finally i have seen it
@aletheiai
@aletheiai 3 роки тому
"But that's a story for another time." I hope you plan to leave us in finite suspense.
@earthling_parth
@earthling_parth 3 роки тому
Niiice 👌
@dierandomdie
@dierandomdie 3 роки тому
Please leave 😑
@RumoredAtmos
@RumoredAtmos 3 роки тому
You should get a medal for that comment
@28peruvian
@28peruvian 3 роки тому
😂
@lockstockandcarol
@lockstockandcarol 3 роки тому
I'm guessing the hotel has infinite storeys
@eyados-fo6sg
@eyados-fo6sg 23 дні тому
whoever manages to get into room 1 must be the luckiest man out there..
@zekeanimatedvideos11132
@zekeanimatedvideos11132 26 днів тому
"Walk to the room double your number, simple, right?" The person in Rayo's number: F*** this, hell naw
@cu7695
@cu7695 2 роки тому
This is kinda of stuff mathematicians imagine when they're high
@camsandhu340
@camsandhu340 2 роки тому
100th like
@goodlightpringles6335
@goodlightpringles6335 2 роки тому
101st like
@WisdomLearner
@WisdomLearner 2 роки тому
But it indeed lead to the creation of the computer nso that's a plus for the crazy.
@shivaanrambally9611
@shivaanrambally9611 2 роки тому
601st like
@kevinboros7427
@kevinboros7427 2 роки тому
Muahahaha 667th like, I broke the funny number.
@lemon9833
@lemon9833 2 місяці тому
Shoutout To Rezo where i First Heard about the Hilbert Hotel, But he had a different Start To work with infinity guests who needs infibity rooms
@thegoofer1999
@thegoofer1999 Місяць тому
this'd be a good horror game idea you play as a guy trying to find their room and every now and then you can see hallucinations and others you have to break into rooms to get food and other stuff
@randys2669
@randys2669 2 роки тому
"Everyone move to the room with double your current room number" The guy in room 387494985726478569420: 🙃
@Catnipyy
@Catnipyy 2 роки тому
69420 Nice
@saffamarwahomar
@saffamarwahomar 2 роки тому
Hahaahahahaha 😭
@calebtan8682
@calebtan8682 2 роки тому
Every room should have a calculator then 🤣
@WilIiyum
@WilIiyum 2 роки тому
@@calebtan8682 Just not funny Edit: I didn't find it funny ok so chill Caleb Tan is my G
@calebtan8682
@calebtan8682 2 роки тому
@@WilIiyum okay lol
@pixieb9166
@pixieb9166 2 роки тому
I would hate that hotel 💀 Imagine being asked to move to another room everytime someone arrives 💀💀
@ClassicBentobox
@ClassicBentobox 2 роки тому
If you leave it frees up a room for another customer
@ClassicBentobox
@ClassicBentobox 2 роки тому
@@ayamelee9020 im on the side of math not the consumer on this one. I’m sorry
@user-zt8yq8fj3h
@user-zt8yq8fj3h 2 роки тому
That's only if someone arrives AND there's already infinite people there, not just it someone arrives. If there were like 100 then they'd just go to room 101.
@huutao3012
@huutao3012 2 роки тому
Ikr✋💀
@korayacar1444
@korayacar1444 2 роки тому
@@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.
@cantthinkofnameyeah7249
@cantthinkofnameyeah7249 12 днів тому
The key insight learned from this is the distinction between infinity and all: they are not synonymous.
@thetaomegatheta
@thetaomegatheta 12 днів тому
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.
@whatdidyousay245
@whatdidyousay245 6 днів тому
imagine having to move to the room double your number but your in room 500M🧫
@morbiusfan3176
@morbiusfan3176 2 роки тому
"Imagine theres a hotel with infinite rooms." "All the rooms are occupied." *[visible confusion]*
@goncalocalqus1766
@goncalocalqus1766 2 роки тому
Exactly my thoughts and I still can't get over it because everything that comes afterwards feels like bs.
@slavetzkyrickyjames4305
@slavetzkyrickyjames4305 2 роки тому
Because it's countable infinity so there's a bijection then an uncountable infinity appeared and it doesn't have bijection which means it won't fit to countable infinity because it's not fixated
@ok4350
@ok4350 2 роки тому
@@slavetzkyrickyjames4305 get out with your math
@opioidhamster3205
@opioidhamster3205 2 роки тому
@@slavetzkyrickyjames4305 tf you mean countable is it really "infinity" then
@last-dinosaur
@last-dinosaur 2 роки тому
@@opioidhamster3205 you gonna understand after you finish the school, probably
@BonnieBugsy
@BonnieBugsy 2 роки тому
"Sweetie, wake up. We have to move rooms again." "I told you we should have gone for the infinite AirBNB."
@Ace-rm5cu
@Ace-rm5cu 2 роки тому
When u have 280likes but only a single reply
@LollyPopTuttu
@LollyPopTuttu 2 роки тому
@@Ace-rm5cu the yt comment section can't house infinite, that's why
@dragonslayer8789
@dragonslayer8789 2 роки тому
@@LollyPopTuttu i didnt understand
@sunshowere
@sunshowere 2 роки тому
@@dragonslayer8789 replies to comments are limited up to 500.
@SaFi-fh1in
@SaFi-fh1in 2 роки тому
Lmfao
@xStars_.Quads2
@xStars_.Quads2 6 днів тому
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.
@namesIan
@namesIan 3 місяці тому
This was a fun watch
@harrisont2004
@harrisont2004 2 роки тому
“Oh just move to the room double your room number.” “But I’m… at room 9,000,000,000,000,000,000,005.”
@esquilax5563
@esquilax5563 2 роки тому
"So what? There are infinitely many people in higher-numbered rooms"
@Keke_offi
@Keke_offi 2 роки тому
He means that the person in that room will walk for a very long time until getting to the right room
@arghyadeeppal9638
@arghyadeeppal9638 2 роки тому
Sure, keep walking, either you reach your room or die trying!
@gabrieldavis4434
@gabrieldavis4434 2 роки тому
“Start walking, bitch.”
@kristinaalshami2178
@kristinaalshami2178 2 роки тому
@@gabrieldavis4434 UNDERATED REPLY OML I DIED
@Qkotman
@Qkotman 2 роки тому
After the first minute, I just stared blankly at the screen and stopped processing the math...
@AAA_A12
@AAA_A12 2 роки тому
JESUS Oh wait *JESUS*
@_Hajar_
@_Hajar_ 2 роки тому
Same
@Xiunoi
@Xiunoi 2 роки тому
**hmm**
@Xiunoi
@Xiunoi 2 роки тому
UH *WHAT*
@paqlallaqldifi122_7
@paqlallaqldifi122_7 2 роки тому
@@Xiunoi bruh
@TheReal_JakeTheDog
@TheReal_JakeTheDog 25 днів тому
"hey what's up?" "Oh, nothing, hbu?" "Not a lot. So what room are you in?" "Oh, im just in room 4,842,035,836,822,992,575,635,286,621. And you?" "....34...." "Hey, we're pretty close to each other!"
@LapisMan
@LapisMan 2 години тому
just tell the extra people to walk to the room all the way at the end of the hotel. they would never get there because it would take an infinite amount of time.
@StarSupernova59
@StarSupernova59 2 роки тому
"What would happen if infinite of infinite buses with infinite of infinite passangers show up?" Show them the 2nd floor.
@the_jingo
@the_jingo 2 роки тому
Good one
@trevorbeatz5741
@trevorbeatz5741 2 роки тому
lol
@StarSupernova59
@StarSupernova59 2 роки тому
*THATS ALOT OF ROOMS*
@1tzL1t
@1tzL1t 2 роки тому
Lol
@HaLKer5
@HaLKer5 2 роки тому
Big brain time
@faizanquraishi4126
@faizanquraishi4126 2 роки тому
Infinite hotel: "nobody can beat me" Infinite party bus: "hold my abbbababbbbaaaaa...."
@ZoyoYEP
@ZoyoYEP 2 роки тому
Ok
@yawn74
@yawn74 2 роки тому
Infinite hotel: Ok guys group yourself into starting As and starting Bs. Press the negative infinite room button
@sugoiikizza8384
@sugoiikizza8384 2 роки тому
Lmao
@nathanalexander305
@nathanalexander305 2 роки тому
@@yawn74 lmao
@pushkar31
@pushkar31 2 роки тому
I'm the 1000th like
@user-rm8qu5yp1o
@user-rm8qu5yp1o 26 днів тому
Could you imagine if you just got to room 500 quadrillion and you had to go to room 1 quintillion
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