An Infinite Hotel Can Be Fully Booked, Here's How
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- Опубліковано 23 лют 2023
- Imagine you have to find a hotel room for yourself last minute. The receptionist starts by saying all the rooms are booked. The infinite number of rooms are all filled by an infinite number of guests. But wait, the manager might have a solution to still check you in. To see why and how it's possible, let's look at David Hilbert's infinite grand hotel mystery.
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To the people claiming that this video copied content from Veritasium or TedEx or some other channel: no. This is a very famous thought experiment, Hilbert's "paradox of the grand hotel", dating back to the 1920s. It is not at all surprising that there is more than one video on youtube about a well known and interesting bit of mathematics.
After rewatching the Veritasium video and looking at some of the other "content" on this channel... yeah this was almost certainly just a shameless ripoff of Veritasium's video, down to the use of the phrase "party bus". However my point still stands that the actual content is common knowledge and the hotel idea does not "belong" to any one person (except perhaps David Hilbert who originated it).
I know but who actually made it first lol
He literally does the same thing and says the same exact words. Sorry if I’m wrong
When ever I hear this solution I imagine how hard it must be for the first person to walk out of the hotel, because their room was changed so many times…
When the hotel is infinite, you get kicked from your room an infinite number of times as well.
If I was a guest in this hotel, I'd be super annoyed that I'm being asked to change rooms every 15 minutes!
But you are saying that there is going to be always another combination of X and Z which is why it is an infinity the combination you get is just a part of the infinity and its an infinity with infinite number of different combinations with X and Z. So its just a normal infinity with the solution in the begging or move to a room with an odd number. Because with this logic I can say that even with the first bus I can always say that there is going to be a bigger number.
'But you are saying that there is going to be always another combination of X and Z which is why it is an infinity the combination you get is just a part of the infinity and its an infinity with infinite number of different combinations with X and Z. So its just a normal infinity with the solution in the begging or move to a room with an odd number'
Firstly, 'infinity' is a meaningless word. The actual term that you are trying to think of is 'infinite set'.
Secondly, the fact that the resulting name is in the set of named guests is the point. We prove that the name that belongs to a named guest doesn't belong to a named guest who got a room.
'Because with this logic I can say that even with the first bus I can always say that there is going to be a bigger number'
Incorrect. You will not be able to find a seat number that would belong to a guest that did not get a room.
There is no such thing as infinity.
Ted Ed posted this ober 9 years ago
Veritasium a year ago
Most explanations of this paradox follow the problem of including a finite number of new guests with the problem just one infinitely-long bus with a countably-infinite number of passengers, in which the proprietor of the hotel relocates the existing guests to the room number that's their starting one doubled, leaving all the infinitely many even-numbered rooms occupied and the infinitely many odd-numbered ones available for the passengers, who could, if you'd like, be assigned room 2n-1, n representing their seat number on the bus. Then the explanations go to the infinite amount of that type of bus mentioned earlier. You skipped that problem I explained myself.
Also, there are explanations that don't use the table with the zig-zagging line, but utilize prime numbers as proven by Euclid that there was an infinite quantity of during 300 BCE. The existing guests would be reassigned room number 2^n, the passengers on the first bus: room 3^n. Bus 2: room 5^n. This solution houses all existing and all new guests of all those buses alike, though rooms will be left vacant as long as the numbers they're labeled with aren't pure powers of any of the prime numbers.
Man I love this animation style so refreshing 😁
In the current era, the ability to focus well will really help us in completing all our work.
Practice Your Focus Every Day On Our UA-cam👍
if there was infinite people then he would also have infinite money, he could just quit in 1 day of the job and live his life.
Veritasium's idea but in a different style
But what’s a strategy for it if there’s an infinite amount of floors on every infinite bus?
If there are countably many floors on every infinite bus, then it makes no significant difference.
I'd rather not.
???
@@aboukeita6117 check myself into one of those hotels.
Kinda, kinda not
Indeed
I’d rather book room 841374230297461837482939471725 so I probably won’t have to be moved any time soon
This dude never run out of contents. Danm it.
its stolen.
I swear I heard this exact same thing on a different channel years ago
same
BECAUSE THIS VIDEO IS STOLEN
@@duckinsaneguy6102 No, the content of this video was not stolen. The infinite hotel is a very famous mathematical thought experiment first devised in the 1920s. This video and the others that you have seen before are no more "stolen" than a youtube video about Schrodinger's cat.
its veratasium search veratasium infinite hotel you will find it
Probably veritasium
Fun fact: Waffles are pancakes but with abs.
Are crepes anorexic? Lol
mmmmmmm.. Pancakes.. couldn't care less if pancakes had abs.. don't care how suggestive it looks as I'm drizzling syrup all over 'em.. lol.. sounds fruity AF.
I'm f'c'kin hungry now! THANKS!! :(
@@gueits8586 lol..possibly.
@@gueits8586😂😂😂
@@mrmagoo.3678 No problem lol. Since I made you hungry, I’m basically saving you from starvation, so typing that low effort fun fact actually paid off. 😅
This is like life .... confusing.
In physical world there is nothing infinite, it's a mathematical expression when something is very big compared to another thing.
We can consider earth size an infinite to human size and sun size the same, and sun is bigger than the earth.
0:00 - Hi BS. 8:19 - 488th like from me. Cheers.
WHAT? YOU COPYED AN OLD VIDEO? BUT WILL SOME CHANGES?
Hi
How come it says the names only consist of X and Z but you can clearly see there is a Y
🤣 man imagine typing those names into a computer
Bro literally copied Veritasium
Yes
ARGH So confusing bruh. But still pretty nice
It makes no sense. There is no such thing as an infinite amount of rooms. Even if there was, why not put people directly into the infinite amount of EMPTY rooms?
It's a thought experiment, so the hotel is not meant to be considered as a real place that exists in our universe. Limitations like lack of material to build an infinitely large hotel or only finitely many people in the world are irrelevant.
As to why you can't put people directly into the empty rooms: there are no empty rooms. The premise, as stated in the video, is that the hotel is initially full. This is perfectly fine if there are also infinitely many people to fill the rooms. Assuming we can label the rooms with natural numbers (R1, R2, R3, ...) and similarly for the guests (G1, G2, G3, ...), then we can just assign guest GN to room RN, for each natural number N. Think of any possible room number: there must be a guest with the same number already assigned to it.
@@extravagantpanda7962 You missed the point entirely. Of course this is a mental experiment, and the actual place does not exist. However, if rooms are available to move the existing patrons into, then wouldn't it make more sense to just place the new patrons directly into the new rooms as they materialize, instead of moving old patrons into the new rooms?
The room assignment is a moot point. if there are 3059 filled rooms, and 6 new customers arrive, assign them to rooms 3060 to 3066 instead of moving over 3000 people to different rooms, just so that the new patrons could be placed in rooms 1-6. In either case, someone has to be assigned to rooms 3060 to 3066; either the new, or the existing patrons. Its not that difficult to understand.
Not to mention, how can an infinite hotel be full? You can't have it both ways.🤔
@@asher6657 I think you have missed my point entirely, buddy. Please re-read my previous comment, it already addresses all of the concerns you raised in your latest comment.
You said "if rooms are available to move the existing patrons into, then wouldn't it make more sense to just place the new patrons directly into the new rooms as they materialize". There are not any rooms available for new patrons to move into, that is the premise of this thought experiment. I explained how this is possible in my previous comment.
As for your example about the 3059 filled rooms, I really do not understand what you are trying to say. Every room is initially filled. It doesn't matter how many new guests show up, there are initially _zero_ vacant rooms for them. If the set of guests has the same cardinality as the set of rooms, then it is possible to re-arrange the existing set of guests in such a way that infinitely many rooms are left vacant so that we can accommodate the new infinite set of guests. If they do not have the same cardinality, then we cannot do this. This is very basic set theory, please look into the concept of "cardinality" and Cantor's diagonal proof, you will hopefully understand that, despite being quite simple, it is very unintuitive and your intuition regarding infinity in the context of mathematics is often wrong.
@@extravagantpanda7962 You said "As for your example about the 3059 filled rooms, I really do not understand what you are trying to say". That is pretty obvious. If this 'thought experiment' is supposed to work, then we should be able to give an example of HOW it works.
Let's take it step by step. I will use smaller numbers, as the larger numbers seem to have frightened you. Today. there is ONE filled room. There are NO empty rooms.
Here comes a patron requesting a room. Somehow, somewhere, a room has to be created, made available, or materialized, or the experiment ends here. Somehow there now has to be 2 rooms. There is no way around this simple concept. The premise of the experiment is that the way we fill this room is by moving patron #1 into room #2 thus creating a vacancy room #1. If that is the case, then it is also possible to leave patron #1 where he is, and instead, assign patron #2 into room #2. Again, there has to be a room #2 created or materialized, or else this experiment is a moot point .
So you are saying that the only possible way to give patron #2 a room, is by moving patron #1 into room #2 to create a vacancy in room#1, but NOT by assigning patron #2 into the newly created room #2? If that is your point, I will have to recognize the fact that your understanding of logic is ...poor.
'There is no such thing as an infinite amount of rooms'
The hotel is just an analogy for the set of natural numbers, and there are infinitely many natural numbers, so that is incorrect.
'why not put people directly into the infinite amount of EMPTY rooms?'
Because there are no empty rooms initially.
'However, if rooms are available to move the existing patrons into, then wouldn't it make more sense to just place the new patrons directly into the new rooms as they materialize, instead of moving old patrons into the new rooms?'
No new rooms are being created, so we can't do that. All of the rooms that we are working with already exist.
What is happening is that the initial arrangement of guests represents the choice of function f(n)=n for natural n, and then we choose a different mapping from the set of natural numbers to itself, which is represented by us relocating the guests. For example, f(n)=n+1 shifts the guests by one room. f(n)=2*n shifts the guests to the room that has twice as great of a number.
'if there are 3059 filled rooms, and 6 new customers arrive, assign them to rooms 3060 to 3066 instead of moving over 3000 people to different rooms'
There are infinitely many filled rooms, so we can't follow your proposal.
However, the fact that we are working with infinite sets is what allows us to do the tricks with relocating the guests.
'how can an infinite hotel be full?'
Every room is occupied.
'You can't have it both ways'
Yes, you can.
For example, the aforementioned function f(n)=n is defined on all natural n, and its image covers the entire set of natural numbers. There are no natural numbers (i.e. rooms) in the complement to the image of f within the set of natural numbers (i.e. among the unoccupied rooms) - N\Im(f) = {}.
'If this 'thought experiment' is supposed to work, then we should be able to give an example of HOW it works.
I will use smaller numbers, as the larger numbers seem to have frightened you. Today. there is ONE filled room. There are NO empty rooms'
Your example with finitely many rooms is irrelevant, however, as working with infinitely many rooms is the point. That is what allows us to free rooms without evicting people by just rearranging the guests.
'Here comes a patron requesting a room. Somehow, somewhere, a room has to be created, made available, or materialized, or the experiment ends here'
Incorrect. No new rooms are created.
In a hotel with finitely many rooms we cannot free any rooms merely by relocating the guests, we have to evict somebody. This is because finite sets, unlike infinite sets, can't have proper subsets of the same cardinality as the sets themselves.
'So you are saying that the only possible way to give patron #2 a room, is by moving patron #1 into room #2 to create a vacancy in room#1, but NOT by assigning patron #2 into the newly created room #2? If that is your point, I will have to recognize the fact that your understanding of logic is ...poor'
That is not their point, so, you don't have to hold what you imagined of Panda's skills as fact. Your accusation is especially amusing given your prior claims of an infinite hotel not being able to be filled.
Both room 1, and room 2, and so on - they are all occupied. You can't just assign a free room to the new guest, as there are none. You have to free some up. Which we do by shifting everybody by one room in this case.
no way infinite rooms
Isn't this video same from the video of Veritasium😅😅😅😅😅😅 Love the video tho!
@@TheChessCommunity I never said its a copycat I just said that I seen it before
This is a copy from veritasium
My head is spinning
Quantum Physics is my JAM!
Roblox rooms be like:
Rooms by nicorocks right?
@@Invertedspearofheavenfromohio yes
@@plokenv ok
Tbh I learned something today
Is Everything infinite ? ♾,
I guess, Maybe 🤔
Maybe 🤔
interesting
🤣 ack I thought this was an actual hotel seriously imagine that they'd be pretty confusing yet funny
bro stole vesterite
@Chess Community ik
Bro this guy just stole this video from someone else unshamefully and the original is used as its thumbnail
Blud copied Veterasium 💀💀💀💀💀
This is just a copy of veritasium's Hilbert hotel video, and I don't mean the solution is the same, the articulation andpresentation is too, pathetic effort.
Btw this vid is based by vetalusuim
W8 but.... still the hotel has infinite rooms....
Im trying to be more smart so that is why i am watching this:)
Wonder how much IQ bright sode has:)
Stolen? Wow
I seen this
I think this video has been posted before...i remember the infinite hotel
Yeah same.
Verastium posted it a long time ago
@@ElectroBlade-jm3jl yess... I think i saw that one...
@@ash2NT I couldn't remember it but i'm guessing it was veritasium who posted it first from all the other comments
The infinite hotel is a very famous and interesting mathematical thought experiment, so it is not surprising that there are lots of youtube videos about it.
🤣 man I imagine in the infinite dimension everyone is not only xz xz xz xz but I also imagine the movies are rated the same way
Ooh,I'm third..
Veritasium already made that
Veritasium already made this bruh
this is almost the exact replica of another UA-cam vidio I saw
this is stolen from veritasium, exactly like that video
🤩🤩🤩🤩🤩🤩🤩🤩🤩🤩🤩🤩 lol
But moving each costomer from one room to another will take infinite time which is impossible
I don’t understand why they move them. Why not just put the new person in the next available room???🤓🤔
They can leave at the same time.
@@gwen8859 just to save the time needed by the first guy to walk.
⚽️
Doesn't sound like the 50 year old guy who sound like 20 or does it hmmm
§
I have 20 friends
Mmm very original
Œ
Fun fact: This video is copied from veritasium which was posted about a year ago😆😆
Fun fact: the infinite hotel is a very famous thought experiment from about a century ago, not the intellectual property of Veritasium. There are plenty of videos about it on this platform that predate Veritasium's.
Is this how hackers flood servers?
Bro stole veritasium’s video ideas
No this is a paradox written by someone
stolen idea
No
There is no such thing as infinite. 🤦
Except for CaseOh
@@NerdBoiVR huh
@@drummerhq2263 you don’t know who caseoh is?
@@NerdBoiVR sorry, I don’t
One person per room? That's a bit much.
It appears I have a arrived a tad bit earlier than most others
copy cat , you stole it from Veritasium he uploud this a year ago
And then there was also a TED video years before Veritasium's.
300th like
Yeah no thanks!
Ps There’s only 8b people in this world!
Is that 8b even or approximate
Approximately 8 billion
hold on.. so you're gonna harrass a INFINITE amount of People just to fit the new guests in?.. will you have to do that EVERY time a new guest walks through the door?.. and there's not a infinite amount of people on planet earth...but I'm just being picky there..BUT THE FIRST BIT?..YEAH..You gotta stop a infinite amount of guests doing whatever they're doing to move..and not EVERY guest will be in their rooms at the same time, and when you're dealing with these numbers?.. you'd need a infinite amount of call center staff just to inform the guests to move so you can fit ONE guest in?..hmmmm...methinks there is another way, but I'm not telling YOU!!
You stole this video
Yep saw this video but worded different a couple years ago
Yes!!!! FINALLY SOMEONE NOTICED
@@tom-ks when I watched the original I saw this so I also noticed
AND THEY COPIED EVERTHING expect for the name
And they just made it a little diffrent BUT ITS NOTICEABLE
not first
Literally copied from Veritasium!!! Unsubbing. 😠😠😠
12th
I'm the 10th
Brain broken.
Mind herty
TED-ED
8 billion room hotel
Doors floor 2
K I didn’t ask or care
Congrats to Everybody who is here in time to find this comment 🏅
Stolen concept @veritasium
I heard this EXACT same thing off of another channel as well, I cannot remember it because it was years ago, but it could be from that person
TRUE!!! I am gonna say this on most of the simillar comments
Listen to ths wording then. I did my research, and I knew this was an experiment. I am not taking any more videos from this youtuber.
Hi