The Infinite Hotel Paradox - Jeff Dekofsky 

Maybe they all stay on an infinite 1st floor.

"Oh, you're lucky. I'm staying in room 8.369304720x10^4830382075."

The lift control panel is basically a scientific calculator

@@MrSRMatthews 😂😂😂

They only need a number close to infinity to contain infinity passengers because they will die in their finite life on the infinity long way to their infinity room number.

Thats the imbrogilo!!!

well yes, but actually no.

Seagull i haven't even watched the video yet but funny

Some answer is yes and always yes. Bus driver may be driving a while to get to next open room but it is always there.

Clever :)

underrated comment

bro. Who are you? Einstein the memer coz holy cow thats a great comment!

Eh, you got an infinite amount of time to get there.

Hey are u at your room yet?

@@fmjjjjn7510 Not yet, still stuck in the elevator

And then Buddy the Elf gets into your elevator and presses all of the buttons ...

It will have infinite elevators

@@AA-ni3km :trol:

@@AA-ni3km me whenI have to wait an infinite amount of time because an elf pressed all of the infinite amount of floors buttons, slowly ticking every number that exists

"Maybe there's super mega bombastic ultrasonic fast fantastic elavator that delivers you to any floor instantly" - summer, 2 weeks ago

There's an countable infinite amount of cleaning ladies.

The lady is the 🤖

Infinity Fawlty Towers 😳 ... Guests at 3,141,592,653rd floor: "We are not satisfied!" Basil Fawlty shouting very loudly: "Well, people like you never are, are youuu?" 😂

The poor plumber is not very happy either 😂

But she gets infinite money for her job

'One night, the infinite hotel is full with an infinite amount of people' Brain: 💥

where is the numbers alabnole and Omega?

Asu howwwwwww

Who are those poor women birthing an infinite number of children?

@@LegacyCrono the mothers of the wicked

And an infinite amount of debris

Breaking news: A second infinite plane has hit the infinite hotel

@@JoseMedina-xq8mf ♾️/♾️

@@JoseMedina-xq8mf breaking news infinite planes are hitting infinite skycraper causing infinite deaths and infinite 9/11

@@ygotsvlog3762 Infinite jet fuel cant melt infinite steel beams

Swag in ohio 😩🤘

lmaooooo

down in ohio

50?

@@thanhtamnguyenthi7073 ?

What if there are infinite maids that look the same

@@TheSewDew Oi! That's jokes aside a good theory!

No

DOROTA

There's actually an infinite amount of maids

To the nth °

Then the infinite amount of passengers use an infinite amount of energy to walk up the infinite stairs in an infinite amount of time. Then I think of when they need to go to the dining room to eat an infinite amount of food LOL

Yeah that's my problem, too. If the hotel has got an endless number of rooms, it will never be full. So you can forget the whole experiment.

inifinite hotel cant be full right?

And the night manager is now in depression. *CRIES IN MATHEMATICS*

I agree

Thank you! I couldn't believe nobody else was mentioning this. It would have terrible online reviews. Infinitely bad.

It's okay, they have infinite complimentary mints as well. Totally makes up for having to move yourself and all your stuff over 2,000,000 floors a few times a night.

@@morallyconflictedtortoise6494 😀😆😂🤣

And all that because one mathematic smoked too little weed and thought only infinityth guy can go to infinityth+1 room. Just send newcomer there. You only need infinity of weed as without it he will not find his way.

you actually never get a room you move to room 3? well they actually need you in room 7. And so on

thats exactly what i was thinking but then i realized he was talking about alef 0 which is the countable infinite natural numbers.a weird concept

IT IS *ALEF NULL*

Pupper Playlist Night Manager: No it ain’t XDDD

Infinity=infinity but infinity is also an infinite times more powerful Now compare this to zero

A wild universe deletion appears!

wow same haha. this video is my childhood, it always feels nostalgic to be here again

oh wait.. but what if there are infinite nights with infinite buses of infinite people? or what if there are: infinite nights, infinite buses of infinite people, infinite rooms, and infinite elevators that only go up to floor n.

A Thanos move no doubt

You could just start from room 2 and ignore room 1

Haha! It is like...imagine that in SW: The Phantom Menace Anakin asks his mother if he can go with Qui Gon Jinn and mother says no. (Closing music starts immediately) & THE END..

*entire hotel implodes* infinitely

@@yechankim7713 You could also start from room n+1 and leave everyone where they are

Profits: *crashes* in a second

The hotel still has room, having infinite space, there will always be more room. So it can’t be full

@@ChrisHinners008 you don’t seem to understand the concept of the paradox. The hotel isn’t generating new rooms or anything like that, an infinite of rooms exist there aren’t new ones when there are new people, so when there are an infinite amount of people they fit in the infinite amount of rooms. You can run out of room if you are working with multiple infinities.

@@zackschaefer my brain is kinda crashing now

imagine infinite amount of karens

Hey person on the first bus in seat 7, another infinite set of infinite busses has arrived. Please move to room 22521666186739810716017129863546474247925813985186306383480395759255528226899398031271474259176472311138130302909797370563984143657840869015723623128208458564711932390036470899999940399003451938771468124775412134017692556582989981820657376622292117781429636251681663364133246565240603802421309871873386179061056683850002592550658912005406539073633368208169912295100765107813056035892005304712416817301893705332191267615274619407764899319819287315641053762034009508858938727147166108668063720886082155921552955435591503022900749768195878181491707144967461286550140023171580051111358071521188926359524314904062599527129957121490685127011258936786658012354838528. It's on the 2252166618673981071601712986354647424792581398518630638348039575925552822689939803127147425917647231113813030290979737056398414365784086901572362312820845856471193239003647089999994039900345193877146812477541213401769255658298998182065737662229211778142963625168166336413324656524060380242130987187338617906105668385000259255065891200540653907363336820816991229510076510781305603589200530471241681730189370533219126761527461940776489931981928731564105376203400950885893872714716610866806372088608215592155295543559150302290074976819587818149170714496746128655014002317158005111135807152118892635952431490406259952712995712149068512701125893678665801235483853rd floor.

FAX 🤣🤣

Impossible.

There is no roof since there are infinite rooms

lol!!!😂😂😂

@@ajaymahajan3890 the roof is still there just infinitely high

Oooooooooo fluck

they switched rooms infinity amounts of times

Even worse, they have to walk infinite amount of stairs

they tell different people to switch rooms

Its an Infinite hotel. Not a five star infinte hotel. You get what you pay for

@@Noah-Runge Sounds like a hotel with negative infinite stars.

Something's wrong, I can feel it.

Infinite confusion

this theory is wrong the hotel is already FULL with infinite numbers of guest which are = to infinite numbers of rooms he said

@@arslanakram043 Yes, but just if you are considering only the countable infinity. But according to absolute infinity, not.

@@moisesggomes Ahhhhhh right, just clicked, of course, should have spotted it *frantically googles 'countable infinity'*

Fun Fact: it is impossible to jump off the top of this building since it is infinitely high so there is no top.

A: Suicide is impossible B: Flying is now possible

"What happened to him?" "He died of thirst"

I mean u can never go that high , eventhough u did and jump u will fall and not fall at the same time.

@@martonferenczi7894 There is a top. it just takes an infinite amount of time to reach it.

same

Underrated

~infinity~

Wait wouldint it get destroyed by the sun or it will stop at the max build high

Back Huat Lee lol I never thought of that

:)

:)

:)

:)

:)

Nice

Don't copy MrBeast (reply to me)

For a moment I thought you were one of those fake Mr. Beast bots

R U REAL? I LOVE MR BEAST PLS

You misspelled “fathom”

@DaFragileTomato yes it is

@DaFragileTomato its infinitely underrated

Best comment ever

You got me there 😂

bendydick cumonmyback best username ever

😂😂😂😂

I only have 2 though so that’s impossible

@@Lyenati you saying that actually makes me believe you.

Your Kyckling No, it makes sense. You can’t loose an infinite amount if there’s a finite amount.

@@Lyenati Then why did you specify that you had 2 IQ?

Are you talking about the guys voice? I think his voice is the best Ted ed has.

Damn! You a mind reader?

It doesn't make any sense. If it was an infinite hotel it couldn't be full

Infinity isn’t a measurable quantity, it’s only a hypothetical idea. To put it simply, infinity does not exist in real life, as everything can be quantified and infinity by definition cannot be quantified. There are extremely large numbers, like the number of atoms in the universe, but no infinity, it only exists in our heads.

literally

Sheepy. Exactly what I done! 😂

This hotel has infinity maids

@@arnold8248 who work an infinite number of shifts for an infinite amount of time. Also no retirement.

I’m feeling like the maid being like 🤬🤯👺👹💩

Infinite maids!

I think that it’s only relatively full. From that initial perspective. When there comes more than one infinite of people that are already booked the space is automatically generated to fit the people that arrived. If that infinity that is full cannot fit more people it wouldn’t be infinite. (I will contradict myself: if you have an infinite big water bottle that is filled, can there be added more water to it? Can that water bottle be stretched to be able to contain more water? If it’s full then that means that there shouldn’t be more space without deforming the first reference system……) This is how I’d imagine a closed infinity system…..

😭😭😭I can't

Um that would take infinite time? 💀

AAAAAA

this hotel has no final floor because there are infinitely many :D

Do you know what infinity is?

But he makes infinity dollars a night who cares if he loses his job

@@user-ws5ei9zf8p no job means no profit means no money means no infinitu dollars

@M. Woller have you read the fault in our stars, "Some infinites as bigger than other infinites" #)

He's just on an infinite amount of weed

After one paycheck he can retire

Omg

A maids Nightmare for sure :) Peace

There are infinite cleaners

Naw it’s cool, they got an infinite wait staff

@@jimiplayscobo5877 I can imagine smile ✌️

Except it doesn't exist in that hotel because all the rooms are natural numbers, therefore integers 1 and up.

Wouldn’t Room 0 just be the lobby

u would get kicked out at the n+1 and the cycle continues

That’s the lobby!

Its the lobby!

underrated

i'd rather drop out

This is not complicated 😅

No caps, this is actually my homework.

@@mish4272 Same, BA1 MT at EPFL and this is part of my Computer Science homework

No matter how you rate the hotel, it will always be a 3-star hotel because average

@@rhamzellibay4098 That's not true, everyone could rate it 1 and it would have an average of 1. Just because there's infinite people doesn't mean that there's infinite possibilities of ratings.

@@ctleans6326 probability assumes infinitely many samples, such as in a dice with 6 faces that has a probability of ⅙ for each face if rolled infinitely many times. It means that in a hotel with a 1/5 chance of choosing numbers from 1-5, all numbers appear infinitely many times. Therefore, all 5's and 1's average to 3, and 4's and 2's average to 3. There's no way you can make infinitely many samples follow the same probability of 1/5 of choosing 1 since (1/5)^∞ = 0.

​@@rhamzellibay4098 People rating a hotel isn't exclusively random, some may rate it 5, and some may rate it 1, but every rating isn't equally likely to occur, unless you treat people as dice.

@@ctleans6326 There's no way you can predict how will people rate a hotel because that's their personal preference. There are infinitely many guests so all numbers 1 2 3 4 and 5 rating will also appear infinitely many times, making them equally likely. I'm assuming a more probabilistic scenario lol.

+Jess Express why wouldn't it? there's an infinite amount of guests the hotel room is infinite, and each room is occupied. therefore, the number of hotel guests is infinite hilbert hotel is basically another way of saying that infinity +1 = infinity

+Jess Express IMO, the first problem is assuming that a hotel with infinite rooms wouldn't take up all the space in the universe to accommodate space to build roads so that buses can bring in more guests. A hotel with infinite amount of people would automatically contain all people as the video introduces the paradox that the hotel is "full" while at the same time not. In the video's final solution, the hotel also has an infinite number of empty rooms as only multiples of primes are filled, so why couldn't the hotel be in that state from the beginning? The video's argument defeats its own premise for its argument and all the math involved is nullified.

+Jess Express No it wouldn't, and that's the point behind the hypothetical scenario of the infinite hotel, there are so many technical loopholes; essentially making the point of how hard it is to really grasp the concept of infinity.

+clock san It seems to me that since infinity+infinity+infinity...etc=infinity, he doesnt need any new solutions for more infinite numbers of guests. Infinite rooms are enough for an infinite amount of buses with each infinite amounts of guests.

Sayuas nope, it doesn't work that way. infinities interacting with each other in the basic mathematical operation is a big no no. that means, infinity plus/minus/times/divided by infinity can't work. you have to use another solution. well, at least in calculus. i've no idea how it is in a more advanced mathematics. did you know that some infinities are bigger than the other? yup, it's confusing. and that is the entire point of hilbert hotel. infinity is such a hard concept to grasp because of how counter intuitive it is

That is clever.

Underrated.

Ah, I see what you did there.

Watch this comment be the first one with the most likes

I don't get it :(

Incorrect. Every room is initially full, we did not magically forget any. And there isn't always more room for new guests - if the set of new guests is sufficiently 'large' (i.e. has a greater cardinality than the set of rooms; for example, if there is one guest for every real number), then we can't fit all of those guests.

oh she's not pissed because of the infinite number of room she has to clean by 3pm. she enjoys her job and is thankful to have it. no, she pissed her young and irresponsible but infinitely gorgeous niece called in sick yet again this week. and she knows for damn sure her niece is not sick; she's going out again with her going-no-where boyfriend of her's who says he is a "day trader".... whatever that is! good for nothing so-and-so.

* angry cleaning lady noises *

Cause we left you for that

You must be talking about consuela

We need infinite number of ladies for cleaning job

That would be horrible

Same imagine being in room 100

how would the elevator work if it had infinie buttons

@@felixjaphygaming9115 You would just go to your room. 🙄

with an elevator, of course

@@TJYuh32 expenses: infinite $ per hour

@@TJYuh32 Additional requirements: Must be capable of sorting out an infinite number of people within 24 hrs.

@@jasonchiu272 8-12* seriously suggested:: ability to complete supertasks

Lmao

@@TJYuh32 per nano sec

Every room has a guest, so it' s full.

Its funny how the "infinite" hotel only has one employee

Hidde Lekanne Deprez but then they move to the next room, which apparently didn’t exist

@@epicgaming7813 I admit that this video does a terrible job at explaining the problem and is basically one big inside math joke for the people who already know the problem. It's a mapping problem, if you map person 1 to room 1, aka n to n then you know every room will be full. but if you map person 1 to room 2, aka n to n + 1 you know that room 1 will be empty (since there is no person 0). Intuitively you would eventually run into a problem: since both sets are infinite, thus equally large, that when the mapping is unequal (n+1) you run out of rooms before you run out of people. But that's where infinity comes in, both sets don't have an ending so this problem can't occur. Thus as long as you can find a mapping which assigns each person an unique room number you're allowed to fill whatever rooms you know won't be mapped to with whatever you want :p To give an advanced example: I can say person 1 gets room 2, aka n to n * 2, and I have 1 free room for ever empty room, but the set is still infinite, meaning I have both infinite amount of full rooms and infinite amount of empty rooms. Intuitively I just created a "bigger" infinity with this mapping but mathematicians didn't find this distinction useful so we use other methods to compare infinities in size.

Hidde Lekanne Deprez I’m sorry I’m too lazy to read all that oof

When you come in with an infinite amount of others, each with a infinitely long name consisting of a and b.

Binary: Allow me to introduce myself

AAAAAAAAAAAAAAAAAAA.................= 11111111111111111111111............. BBBBBBBBBBBBBBBBBBBBB..............=0000000000000000000...........

Ahahahaha true

because it's countably Infinite

淼淼 8 Billion is countable

Yes, i really don't understand the first problem

it's one-to-one and onto, so that's why an infinity hotel can be full, one person for one room each

Infinity time

No tension! The hotel has infinite numbers of elevators 😉

There should be infinite number of elevators

Its fast as light

@Chim Chim Genie maybe it's not a button for each floor but rather one keypad where you input floor numbers?

This thought project is invalid if "every" room is full. If every room is full then no room is empty and therefore the newcome will by no means rightly receive accommodation without evicting someone else.

@@sola2943No one needs to be evicted, you do not get it. The idea is that because this is a hotel with infinite rooms you can just *make* infinite empty rooms by moving your guests to the next room(according to whatever strategy). The reason why the next room would be empty is because the guest in that room would move to the next room; leaving the room they were just in unoccupied. This process is the same for the guest in the next room and guest in the room after that and so on. This goes on infinitely, countably infinite. If you do not understand, research countable infinity and what exactly its existence means. I recommend watching “Infinity is bigger than you think-Numberphile” on RU-vid.

SIKE THATS THE WRONG NUMBER

Renewin Celestian 😂

Or 1.6055465e+61

How do I read this?😂

Technically it could still be way worse

Yes

Builder : how many floors would you like ? Manager : how many bread did you eat in your life

666 likes

Legend says they are still building to this day

minus 111 likes please

ö

Ö

The 999.999.999.999.999 people: "I'll just take the stairs."

Jump™

*ö*

Because everyone works for the manager .

Donovan Reynolds whatever country this is both has a GDP of infinity, a GDP per capita of infinity, and a GINI of 100.

Because he has cheats on

Manager

@@abrahampowell6792 HESOYAM

nah, they hired an infinite number of cleaning works for their infinite cleaning crew

@@themanguy2110 Should've hired Infinite Managers

@@themanguy2110 An infinite number of cleaning ladies is clearly too much, while a finite number is ridiculously low. I guess the Head Manager is having a hard time too

@@jeanllup6150 I think we should hire half of infinity (before you say anything I know what that means)

@@clairdeloona how do you get half of something that isn't countable

Yeah and that's making the assumption that only one person can stay in each of the countable Infinity amount of rooms but instead if the limit was 5 people in a room out of the accountable Infinity amount of rooms then the hotel would store about countable Infinity 5 amount of people

Hotel?

Trivago

😁

Hotel? Trivago.

😂😂😂😂😂

omg this comment is gold why doesn’t it have 10k likes sksksksskskk

@@axlychee3113 shut up

The engineer : had a stroke and died

@@CJ-ow2ld Imagine the elevators!

Elevator: I can get you to your room in 3-5 business days

Wyatt you would move to room 68.719.476.736

maybe the elevator is infinitely fast

@@caiooctavio yes, but with infinite floor you could never reach anywhere

*You could never reach the truth**

@@thebookless3381 ohshitthat'sdeep

you can watch my maths videos.

I always hear "on crack" but never "on weed" 😂

Hahahaha

Rincoglionito, if he loses his job, he'd lose an infinite amount of money

exactly, he has an infinite amount of money so that doesn't matter it's not like his Boss is going to take his money back if he quits

By this logic, infinite sets aren't a thing, and the sets of natural numbers and real numbers are both finite. That's obviously false.

Technically, an infinity is unlimited but the only limitation is our thinking about the limitation…. That doesn’t make the infinity less of an infinity if we cannot comprehend it….. 😅

Ali Raza why not Negative Infinity?

@@raynerfr How to losing your braincell

Ice Pumpkin I’m sorry, what?

@@raynerfr can u count negative in finity to infinity?

Ice Pumpkin uhhhh, no? It’s literally impossible to count to negative/infinity

HAHAHAAHA

Just add infinite amount of newcomers. It will result in making +1 operation every time new guest arrives, but due to newcomers being infinite number of operations would be infinite.

Math says so to

Yes R, they r

they need to be

Lmao me in the infinite hotel

Lmao

I like that you actually calculated the numbers instead of putting in random numbers.

Well the thing is only if there is infinite people in the hotel

Omicron Force who cares

Who said the cleaner's a lady?

Who says there's not infinite of her?

@@Cuzjudd even an infinite amount of cleaning ladys is not enough to clean an infinite number of rooms. Partially because they all exist in overlapping space and cant move because of that. Edit: There is actually an infinite amount of cleaning ladys on any mm^3 but there is still infinite space without any cleaning lady at all. Welcome to infinity ;)

@@derfzgrld but if we have infinite cleaning ladies, we can just assign a cleaning lady for every floor, now each lady only has one floor to worry about.

JeraJera01 they show her

calculator

Instructions unclear, I got stuck on an infinite bus with nobody.

Where’s the elevator

Money INFINITE!!!!!

Muichiro Tokito teleport. It’s magic, don’t stress it.

CactusJupiter i am the 690th like now bow down to me

You can always go to 2 pi... but after that you'll probably start running between those 2 rooms for infinity, as well as other guest, who were asked to go to room pi... so... everyone would be on corridor- switching rooms

I don't think so, because pi 3.14159265359 etc... A decimal. Therefore its real value is just a little over 3, the more numbers after the decimal point, the smaller the decimal. It you were to round it, it would just be 3. You couldn't even round up to 4 because in order to do that, you need a five in the 10s place ie. 3.5159265359.

First of all, you can, like you would with any number. And why pi, specificly? There is a number of real numbers equal to Aleph 1, which can all be used in normal operations. Yes, pi has infinite digits, but even 1 has (1,0000000000000000000000000...), so I don't see the problem.

Man u r right. Pi is having an infinite numbers of digits after decimal, which means that pi will never end and you will never be able to go to the next room but one thing u missed my boy is that all the rooms in hotel are having natural number as their room number.

Also it's shaped like a circle.

lmfao 😂

DrDoomsday Fck the hotel, i'll just go home

DrDoomsday how it's like to chew five gum

You don't even know what a "BIG" number is(me neither). Google "Grahams Number"...

Bread NoLastName Maybe there are infinite elevators in the hotel.😁

same

Opposite

@@andrewcheng1948 *B I G* *B R A I N* *T I M E*

One thing. Imagine being on the bus. Just came back from a exhausting flight, "everyone check your seat number. *Looks at seat *Reads seat number, 1,368,075,146 "Ok mom were staying here forever"

Top 25 Most ? Video's aaahhhh

'The problem is that you considered infinity as a definite number' Nowhere in this video is infinity considered a number. '"there are infinite number of people in infinite number of rooms" the above line itself is a paradox' Yeah, they should have instead said something like 'infinitely many'. However, the reasoning showcased in the video is correct.

If it was a definite number they wouldn't be able to move up one, as it would follow a standard hotel's rules. You are saying the video is wrong because of the equivalent of a typo.

ColmMcK lmao

Yes, every 60 seconds in Africa a minute pass

*LMAO!😂😂🤣🤣*

@@nokukichimoybm8212 I was born at a very young age

infinite times