How An Infinite Hotel Ran Out Of Room

  • Am Vor Monat

    VeritasiumVeritasium

    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., \u0026 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 Iván 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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Waail EL Aourabi
Waail EL Aourabi

I've got question here 👋 ! Any room number can be written in binary system, 0s and 1s ! Isn't that equivalent to the As and Bs in the names of the guests ? Like if the names of the guest were made of 0s and 1s instead of As and Bs, couldn't we assign each guest to a room number equivalent to the decimal writing of his name ?? Somebody answer me please !!!!!

Vor 3 Stunden
Tom Svoboda
Tom Svoboda

numbers have only finitely many digits. for example the name BBBB... would be 1111... but that's not a number, just an infinite string of digits.

Vor Stunde
Levan Katsadze - LeoKac
Levan Katsadze - LeoKac

4:34 - This logic is wrong, you can't change all of the names, because you will never change all of the names, because they are infinit, never ending, you will never reach the last name, because there IS NO last name. It is never ending.

Vor 4 Stunden
Daniel Stefanov
Daniel Stefanov

"HOW AN INFINITE HOTEL RAN OUT OF ROOMS" 0:35 "Let's say all rooms are full" Well ya done it, congrats :\

Vor 4 Stunden
Phlypour
Phlypour

It appears mind-blowing, but every time I hear a theory fighting theory... it only shows the limitations of all those theories. You cannot assume that there is an infinity hotel that is full. Infinity can't be full because it's infitit. Whatever's inside is already there making the infinity look full, but you can always expand. Just add a second floor for uncountables XD

Vor 4 Stunden
Kazper TeH_OnE
Kazper TeH_OnE

@Tom Svoboda because... infinite... However many guests that show up, regardless if they can be assigned a number or not will have a room. Number's are simply a way for us to measure and communicate the things that are being counted. There will always be a placeholder to continue that measurement if needed.

Vor Stunde
Tom Svoboda
Tom Svoboda

Why can't an infinite hotel be full?

Vor 4 Stunden
Rubia, Giechris P.
Rubia, Giechris P.

This is probably a dumb question to ask, but how does a hotel with infinite rooms get full?

Vor 5 Stunden
Iza Kast
Iza Kast

I could never wrap my head around this problem. Isnt infinity defined by it's inability to be quantified? By assigning a number to an infinity, doesnt that mean you've quantified it? and by that metric, it should no longer qualify as an infinity. No matter how many numbers, letters, or any point of quantification you use, infinity should be a greater amount than it.

Vor 5 Stunden
Iza Kast
Iza Kast

​ @Tom Svoboda Isnt this assigning a number to an infinity? 2:15 Isnt it implying that within any of those 'infinite' buses filled with 'infinite' people, there's a finite number/metric that can be written out on a supposedly 'infinte' spreadsheet? If infinite by definition means unending, wouldn't 0:41 "but all the rooms are occupied", imply a end, a countable number/metric of people/buses? 5:17 even states "Some infinities are bigger than others" isnt that quantifying it? To imply it is bigger means it's is comparatively larger than something else. The purpose of numbers/letters/words/etc is to denominate an X object compared to a Y object. If only X object exists, there would be no need for defining Y. Since you're here im just gonna ask the other questions plaguing me. 3:42 states that "there's a person with every possible infinite sequence" So why would 4:48 's combination "..guaranteed to appear nowhere else on that list" if the owner is assigning a different room to each new guest?

Vor 4 Stunden
Tom Svoboda
Tom Svoboda

Where did you see "a number assigned to infinity"?

Vor 4 Stunden
Vishi Karthik
Vishi Karthik

Okay I don’t wanna freak anyone but imagine this so your in the hotel all alone, you look all the way down the hall and since it’s infinite it’s super long but you look down the hall and see somebody there and there running towards you.

Vor 5 Stunden
FUN 4US
FUN 4US

ABABAABABABABABABA×♾️ 😂really his parents should must be proud of him.

Vor 6 Stunden
oddlynick
oddlynick

Me: ok My brain: error

Vor 6 Stunden
Austin Yu
Austin Yu

Reminds me of the comparison between the size of set of rational numbers and real numbers between 0 and 1

Vor 6 Stunden
Bobv177
Bobv177

This feels like vsauce

Vor 7 Stunden
Soda Milk
Soda Milk

Damn, this my gf make this problem? Because there's a 0% chance that it ever happened or will ever happen.

Vor 8 Stunden
Gourob Kundu
Gourob Kundu

Isn't this the same way we can prove that there are more real numbers between 0 and 1 compared to all the Natural numbers?

Vor 8 Stunden
Timberwolfe
Timberwolfe

So Stupid. Like a little kid saying INIFINITY PLUS ONE!!! And Let us remember that this is ALLLLLL Theroretical!!! NO REAL PROOF WHATSOEVER

Vor 9 Stunden
Timberwolfe
Timberwolfe

Why doesn't he just add the Infinite Bus to the next Infinite Rooms? No need for the chart

Vor 9 Stunden
Timberwolfe
Timberwolfe

I think the content maker RAN OUT OF IDEAS. Answer: The Manager sends them to Infinity Rooms. Done

Vor 9 Stunden
hena kumari
hena kumari

Well the definitely makes me eligible to be a manager at the plaza hotel I guess 😂😂

Vor 9 Stunden
Chul Yeom
Chul Yeom

The godly burst computationally surround because brother-in-law whitely thank but a humdrum specialist. mute, free tongue

Vor 9 Stunden
tory carlozzi
tory carlozzi

The medical mini-skirt selectively charge because tomato suprisingly suspend around a nervous taurus. complete, addicted calculus

Vor 10 Stunden
Mrdog011 -
Mrdog011 -

Me rn: 👁👄👁 huh?

Vor 11 Stunden
Steel Soldier75
Steel Soldier75

So what is the highest integer that you can't add one to? Answer that and I'll agree

Vor 13 Stunden
Tom Svoboda
Tom Svoboda

Why should there be a highest integer?

Vor 4 Stunden
FortNikitaBullion
FortNikitaBullion

What if there's a COVID-19 outbreak?

Vor 14 Stunden
OffBrandStudio
OffBrandStudio

0:14 “You are the manager” Me:ok… hold up. Why am I blue?

Vor 15 Stunden
Ron Mascarenhas
Ron Mascarenhas

Everything is infinite, except the poor lone receptionist. 1:Several Infinites. Not fair math!

Vor 16 Stunden
LittleMopeHead
LittleMopeHead

I believe The trebliH Hotel might be able to handle this.

Vor 17 Stunden
Petet Xul
Petet Xul

*Reminds me of the pullover “philanthropist” criminal Billy Gates. Invents a problem that doesn’t exist and “sells” a solution to it. For the money that exist.*

Vor 17 Stunden
Mads Baunbæk
Mads Baunbæk

Go to every room until you find a room with noone, thats yours

Vor 18 Stunden
Tom Svoboda
Tom Svoboda

You will not find a room with noone. All rooms are occupied.

Vor 17 Stunden
Mads Baunbæk
Mads Baunbæk

3:40 and thats how the ABBA band started...

Vor 18 Stunden
Nebula
Nebula

A mathematicians wet dream

Vor 18 Stunden
WolffLandGamez
WolffLandGamez

The guy with room number infinite that was just told he has to move down infinite spaces 😑

Vor 19 Stunden
Artur Styszyński
Artur Styszyński

1:40 Isn't 7x2 = 14?

Vor 19 Stunden
Unknown
Unknown

So dumb, and utterly pointless this is.

Vor 20 Stunden
Mahabir Neogy
Mahabir Neogy

what is the problem? i didn't understand.If he just tell them to knock every room and whenever they find an empty room it will be their's.

Vor 21 Stunde
Mahabir Neogy
Mahabir Neogy

@A B oh now i can imagine it.

Vor 7 Stunden
A B
A B

Then individuals have to move an infinite distance. They’ll never get there. Whereas with the other strategies each individual only has to move a finite distance. Each number is uniquely paired with one person

Vor 16 Stunden
Tushar gola
Tushar gola

The new name we generated at the last... we can just say him to move to the last room of the hotel......(infinite dead body)

Vor 21 Stunde
Preetam Priyadarshi
Preetam Priyadarshi

My brain stopped working sorry for that....and thank you

Vor 22 Stunden
Sunrit Roy Karmakar
Sunrit Roy Karmakar

this is just stupid

Vor 23 Stunden
Romarain
Romarain

Well, no : for a guy to have a name composed of the diagonal you mentioned, it would have to reach the infinity of names, wich CAN'T be reached because it's infinite. So, that supposed guy doesn't exist, it's an intellectual ghost. Infinite numbers are enough stupid¹ for us to imagine something geometrically based on it... (¹: Infinity doesn't exist, it's just a concept and an hypothesis, and it has never been verified, nor could be. However, the absurdity of the diagonal is directly comprehensible and therefore the silliness of its author verified).

Vor Tag
A B
A B

The limit as x approaches infinity of 1/x is zero. Infinity applied, a useful concept. It’s defined much more rigorously than it is in this video in pure mathematics. So it has been proven (to use your language)

Vor 16 Stunden
Tom Svoboda
Tom Svoboda

You're confusing the existence of the name with our ability to write it down.

Vor 17 Stunden
Dark Soul
Dark Soul

Fun fact: Infinity is not a number but rather a Definitive Constant that's why we don't include Infinities in any Domain/Range

Vor Tag
Nicholas Colombo
Nicholas Colombo

But infinity could be a number.

Vor 11 Stunden
FalloutJack
FalloutJack

You can't have a complete infinite set. You can hand me a big box marked "Everything", but you can't tell me you know the limits of what Everything is, regardless of whether or not the box filled with Everything actually includes its own box, the box of a different universe's Everything, whether it's a multiversal Everything, or even if it's just the *concept* of Everything, as in to say that anything that can be conceived exists in that box. The imagination has no limits, and numbers themselves don't really have an upper-limit. Why should conceptual infinity? Besides...in your theory of many infinite buses of people, you didn't count on my having infinite Hilbert Hotels.

Vor Tag
FalloutJack
FalloutJack

@A B Math doesn't really limit itself. In fact, if anything should be less limited than potentially the universe (which we can't measure at this time, but know that it's constantly expanding, so it's generally regarded as effectively infinite until better answers come in), it's the math. Put simply, you may run out of *names* for numbers, but you won't actually be able to stop counting up if your goal is to reach the end. If you ask a computer to start counting, it will never stop until deprived of the ability to do so. And that doesn't mean that it stopped, only that it *was* stopped by an outside force. The set of infinity is just a placeholder for 'An ongoing forever number'. You can assign a meaning and a category to it, but it's still a forever number, much the same way a letter-assaigned variable - like X - is a stand-in for an unknown number. Basically, if you're trying to define a finite infinity, you're working too hard and not getting paid enough for it. The argument will go on forever because you're trying to say that the concept of no limit has a limit. Eliminating the concept would destroy the meaning of the question, and therefore render the whole thing moot, so you can't have it that way.

Vor 14 Stunden
A B
A B

@FalloutJack nothing in this universe is infinite (at least not in the observable universe). Not in a mathematical sense. There are different sizes of infinities, countable, uncountable, and other orders

Vor 15 Stunden
FalloutJack
FalloutJack

@A B Oh no, that bit was just an aside. The main point is that arguing infinities literally has no end. I was removing whether it can self-reference itself from argument there because it wouldn't be relevent.

Vor 15 Stunden
A B
A B

@FalloutJack no, I’m saying you define that a set cannot contain itself. So a set of all sets does not contain itself. An axiom of modern set theory.

Vor 15 Stunden
FalloutJack
FalloutJack

@A B So, you're saying my infinite Hilbert Hotels can be stored inside my Hilbert Hotel? Neat.

Vor 16 Stunden
Precious Baldon
Precious Baldon

Who even thinks of this

Vor Tag
JCCyC
JCCyC

Sorry, if you want to dance, jive, and have the time of your life, you gotta stay in the bus.

Vor Tag
Vargub Lahkar
Vargub Lahkar

I think the question itself is inherently wrong, since we know the some infinitys are bigger then other infinity, but the hotel owner nor us have a way to calculate is the number of infinite people is bigger then the infinite number of rooms, if the room infinity is bigger then people infinity, the lack of room does not exist

Vor Tag
A B
A B

We know how many rooms there are, a countable infinite of them since they’re numbered with all the positive integers. And the different groups of people have different infinity sizes assigned to them, culminating in an uncountably infinite group

Vor 16 Stunden
Himadri Barad
Himadri Barad

Some infinites are bigger than other infinites ..well it made sense in TFIOS !

Vor Tag
Bethany Tjaden
Bethany Tjaden

???

Vor Tag
Stefany Del Toro - Paz
Stefany Del Toro - Paz

im so confused, if the hotel is infinite but you run out out of rooms, a new person shows up and you tell everyone to move down one, then you obviously had more rooms ?? Can someone explain am I just dumb?

Vor Tag
A B
A B

There’s always another number. To put it in a mathematical sense, you can match every whole number to another whole number, and you can list them. 1, 2, 3, … on the other hand you can’t list the decimals between zero and 1. 0, 0.0000…. What’s the second term?

Vor 16 Stunden
Knightly Ishaan
Knightly Ishaan

Start learning math

Vor Tag
Sumit Kumar
Sumit Kumar

You would need an infinite amount of money funded by infinite number of owners and an infinite number of workers to make a hotel with infinite number of rooms and an infinite number of staff to run the hotel and infinite amount of mathematicians to deal with infinite amount of money . Find the mistake and you'll get the infinite amount of profit made by the hotel with..... "repeats again" 😂😂

Vor Tag
yan wu
yan wu

Bruh, I spent 6 minutes of my life watching a video, hoping I would understand so I can teach my friends but I didn’t

Vor Tag
Jaewon Cheon
Jaewon Cheon

카운터에 한글이 있네

Vor Tag
Eleanor Conway 2!
Eleanor Conway 2!

Ababbabaabaababababbababababababababaabbababababababababbababababababababababaabba

Vor Tag
Vung Muan Ching
Vung Muan Ching

wtf ;_;

Vor Tag
Jaime L
Jaime L

Welcome to The Hotel California!🤪

Vor Tag
Speed Junkie
Speed Junkie

I understood the logic, but I still don't understand the logic

Vor Tag
Jyoti Prakash Das - 08
Jyoti Prakash Das - 08

U could again assign the name of all the people with the seats infinitly and give them the room

Vor Tag
eggynack
eggynack

Changing all the names to match the rooms is just as impossible as putting all the people into rooms. The same proof functions for both.

Vor Tag
Harshita gupta
Harshita gupta

Wait will someone tell me what purpose this vdo serves..... P.S- I'm here for the frst tym

Vor Tag
Stifler2277
Stifler2277

Look "infinity" is a concept and not a number. For instance, how many numbers is between 1 and 2, you get 1.0000000......infinity...1 up to the number 2 ( 1.0000001, 1.0000002, 1.0000003.........) So are there more numbers between 1 and 3, than between 1 and 2? It makes sense that there must be more numbers between 1 and 3 than between 1 and 2, but theoretically there is not, since infinity is a concept and not a number since: n+1> 1 So in conclusion infinity + infinity is not > than infinity, you cant count infinity and you can neither assign a character (x) in it.

Vor Tag
Brien831
Brien831

We are not talking about numbers, but sets and their sizes. You can determine, if two sets are the same size if you can find a bijection between them. A bijection is a map, that maps one element of one set to exactly one element of the other set and vice versa. For example there is a bijection between the natural numbers, and the rational numbers, wich means they have the same size. However for every open interval in the real numbers, for example (0,1) there exists no bijection to the natural numbers. In mathematics we say the set of all real numbers in (0,1) is uncountable, and for the rational numbers we say they are countable. Now in fact the set of all numbers in (0,1) has the same size as the real numbers as there exists a bijection even though the real numbers cover (0,1). If you want a more intuitive definition about set sizes, you may want to look into measure theory.

Vor Tag
Andrew Ye
Andrew Ye

infinite can not be "complete"

Vor Tag
Andrew Ye
Andrew Ye

One thing I am confused on. When describing infinity, we are still giving it a finite set amount, not an infinite. This still doesn't work. Infinite isn't something we can do/explain.

Vor Tag
eggynack
eggynack

It's a set amount, but it's not finite. The natural numbers are always just the natural numbers. Unchanging, solid, very much infinite.

Vor Tag
Rishabh Raj XB 39
Rishabh Raj XB 39

Our mathematics teacher once tried to explain the concept of infinity to us, but he ended confused himself.😂 I'm gonna share this video to him.

Vor Tag
Anakin Skywalker
Anakin Skywalker

After watching this video, you made me believe that infinity is finite ☹️

Vor Tag
MONEYBOY512
MONEYBOY512

This is not even a realistic situation

Vor Tag
MONEYBOY512
MONEYBOY512

How does this help me

Vor Tag
Hm
Hm

"Just go in an empty room"

Vor Tag
Steve Newcombe
Steve Newcombe

I just got my head around the hotel then these freekin huge busses start rocking up; loads of em. Just how big is the car park?!

Vor Tag
A S
A S

We all know "Uvuvwevwevwe Onyetenyevwe Ugwemuhwem OSAS" aint getting a chance at this hotel.

Vor 2 Tage
Balaji MD
Balaji MD

This is really entertaining but conceptually wrong.. We can better understand the concept of infinity by the Indian word 'Purnam'.. Below is a famous verse which can make you realize the absolute.. Term 'Infinity' is a cheap version and has lost the value overtime.. FYI: 'OM Purnamadah Purnamidam Purnat Purnamudachyate Purnasya Purnamadaya Purnamevavashishyate'

Vor 2 Tage
Chip Vos
Chip Vos

"You pull out an infinite spreadsheet of course" - of course 😅

Vor 2 Tage
olgierd ogden
olgierd ogden

I’d like to comment but my answer is to long)))..

Vor 2 Tage
Archie Areopex
Archie Areopex

This is... mind blowing..

Vor 2 Tage
Derek Nereida
Derek Nereida

The good meat byerly scold because list demographically obey till a equal work. accidental, last encyclopedia

Vor 2 Tage
Rob Gibson
Rob Gibson

When you have infinity + 2 guests. Duh.

Vor 2 Tage
Zander Leslie
Zander Leslie

Its infinite cause they break there legs on the way there

Vor 2 Tage
Chloe Chong
Chloe Chong

I lost all my braincells when watching this entire video

Vor 2 Tage
Nico Pauly
Nico Pauly

I’m glad I now know what to do if I’m ever put in this situation. Thanks!

Vor 2 Tage
Jada Lydia
Jada Lydia

I think people aren’t going to like to be moved

Vor 2 Tage
Global warming is hot
Global warming is hot

Could they not just accept everyone and have them walk until they find an empty room?

Vor 2 Tage
A B
A B

They’d need to walk an infinite distance, not one would find a room over an infinite amount of time.

Vor 16 Stunden
Hannah K. V.
Hannah K. V.

I know the YouTube comments section is a stupid place to ask a question like this, but I'm going to ask it here in case anybody knows: At the very end, there is 1 creature that has a different sequence of A's and B's than the infinite amount of other creatures. It can't be more than 1, since there are only 2 letters to choose from, and you've already switched 1 of those in each other creatures' to come up with this one that is different. But since this is only infinity + 1 + infinity (those already at the hotel), couldn't you put the 1 first, and then arrange the rest according to even and odd numbers? I've seen the ABBA thing done with decimals in other videos, so let's do it with those as well. For numbers, you could add 1, or 2, or 3, or subtract 1, 2, 3, etc. as well. Let's say you could subtract/add/whatever to these numbers to produce an infinite amount of decimals that are different from the original infinity. Well, in this case, you'd have infinity (original) + infinity (those you just found that are different from the original) + infinity (those at the hotel). So couldn't you just put each person in a room in multiples of 3? There are infinite number of them, just like the multiples of 2. Wouldn't that mean that all infinities are the same, and countable/uncountable infinities don't exist? Obviously there are different infinities, so why wouldn't these work? Please help, I've had this question for months now and I still haven't found an answer.

Vor 2 Tage
eggynack
eggynack

@Hannah K. V. It's not that they're infinite together. There's no need to combine anything with anything else. The set is simply uncountably infinite unto itself. The point of the proof isn't that you have this infinite list and then you can add one to it, or add infinity to it, or even add uncountable infinity to it. The point is that, no matter what list you produce, it will always be incomplete. It could be some specially designed list, or a completely arbitrary list, or anywhere in between, but it will always be missing something. A list of the evens, the odds, the naturals, the integers, all of these are very possible. Nothing missing. The reason why what I did above was interesting was because it demonstrates something we already knew, that an attempt to list an uncountably infinite set will always, always, be missing an uncountably infinite set's worth of elements.

Vor 2 Tage
Hannah K. V.
Hannah K. V.

@eggynack What I don't understand is why the second infinite list of numbers is the same as the first, but together they're uncountably infinite. Why doesn't infinity x 2 = infinity? Earlier in the video it was mentioned that when you have 2 infinite sets, you can match 1 with the evens and 2 with the odds. So why can't you do that with the original set of infinity and the new, different set of infinity? I hope this makes sense it's difficult to explain lol

Vor 2 Tage
eggynack
eggynack

The amount of numbers you're missing isn't simply one, or even infinite. It's uncountably infinite. What's left over is exactly as numerous as the set you started with. There's actually a pretty cool way to do create such a set of missing numbers via the diagonal argument, though I dunno how to do it offhand with the binary set presented here. Just with the base 10 representation. But check it. Consider a list of the reals between 0 and 1. .4987891234... .1972304802... .7171717171... .9999199999... .3141592653... and so on. So you do the standard diagonal trick, adding one to each of the digits along the diagonal, getting you .50806... But, as you note, you can also add two to each digit, getting .61917... Or, y'know, you could alternate between 1's and 2's, getting .60907... Or, and here's the cool part, you could use literally any combination of 1's and 2's and you'd get a new number. And we can represent these as decimal numbers, with, for the sake of argument, the 1's replaced with 0's and the 2's replaced with 1's. So the ones so far are like .0000... .1111... .1010... and so on. Except what do ya got when you have literally any combination of 0's and 1's after a decimal point? You got the set of all real numbers between 0 and 1 in binary. Which, y'know, that's just the set of all real numbers. In other words, in attempting to list the set of all real numbers, you missed literally all of them. 100%. And you can't do any better than that. Any attempted list will miss as many numbers as were in the original set. It is a far greater infinity than the infinity of the list, or the hotel.

Vor 2 Tage
Trexy Lemur
Trexy Lemur

is anybody gonna talk about how ted-ed did a video similar to this also im not saying he copied their video but it was a really good ted-ed video

Vor 2 Tage
A B
A B

It’s a famous thought experiment thought up before both of them

Vor 16 Stunden
Daniel Röder
Daniel Röder

But there is a way to fit all guests into unique rooms. Just tell them to treat their name as binary instructions to find their room, A = 0 and B = 1. For example, if their name starts ABBA... then they add 1 ( as offset because first room is called 1) + 0*1 + 1*2 + 1*4 + 0*8 ..... so after the first 4 letters that guest would stand before room 7 and then calculate his next step. Everyone is guranteed to have a unique room this way. The guest at room 1 would have all As in his name, the guest in room 2 would be named B followed by infinite As. Every guest would have a unique room to himself after infinite calucations for the room number (which might be slightly annoying for the guests but gives you enough time to write the guestlist...). If there is another person at that room, that guest would have the exact name so that can't happen as we know. Your room list would look something like this: AAAAAAA.... BAAAAAA.... ABAAAAA.... BBAAAAA.... AABAAAA.... and so on. The argument with the name that doesn't appear on the list: If you start writing out the first letters of the first names of the list you will see that the technique of switching the letters on the diagonal will generate a string consisting out of all Bs. Because on the diagonal there will only be As going down the list. Otherwise it would mean that the two graphs Y=f(2 to the power of X) and Y=f(X) )intersect for a number X > 0. "All Bs" happens to be in the last room and at the end of that infinite list, because by definition it is on the opposite end of "All A", the guest who has to add every 2 to the power of X term.

Vor 2 Tage
Tom Svoboda
Tom Svoboda

which room does BBBBB... get?

Vor 2 Tage
Mechros
Mechros

There's so much that doesn't make sense. For example there are an infinite amount of people on an infinite amount of buses. It could also mean you could fit an infinite amount of people in one infinitely long bus. This would create another "Hilbert's hotel" but on a bus. If all values are not finitely set but are infinite (including the rooms), it would quite literally never end. Though I do understand that this video's point was to try and prove different sized infinities.

Vor 2 Tage
Mechros
Mechros

@Brien831 yeah I had a look into it after watching this video. I read something similar but with numbers. It made a lot more sense than the hotel. Comparing sets of natural numbers and decimals, and when you get a number from each decimal in each decimal place it creates an entirely new number that didn't exist on the list. It was done in this video when they sorted the names but it makes more sense with plain decimals.

Vor Tag
Brien831
Brien831

Yes his explanation is a bit sloppy there. If you want some further explanation look into countable and uncountable sets. Sometimes abstraction is easier to understand than simplification.

Vor Tag
Isaac Rock
Isaac Rock

Anybody else's brain full after 2 min

Vor 2 Tage
TheRealRB3902
TheRealRB3902

5:56 anyone know where I can get a wallpaper like this? This looks so nice. Even if I can't get a premade one, could anyone at least tell me how to make something like this if they know? thanks so much in advance edit: by wallpaper i mean like a wallpaper for my macbook

Vor 2 Tage
TheRealRB3902
TheRealRB3902

@Red Panda ohhh yeah that looks amazing ty :D

Vor Tag
Red Panda
Red Panda

I don't know where to find a wallpaper that look exactly like that but maybe you will like vaporwave grid wallpaper. You can search it on google.

Vor 2 Tage
Liam -
Liam -

I just lost thousands of brain cells by watching this one video 👁👄👁

Vor 2 Tage
Petru-Mihai Petrenchi
Petru-Mihai Petrenchi

I think I saw this first on vsauce a couple of years ago

Vor 2 Tage
Rexanious
Rexanious

the problem isnt infinity or sth its how they will walk to their room lmao, "yes sir your room is 7252846 please walk $down the hall"

Vor 2 Tage
Puar XI
Puar XI

Instead of making everyone goes to the next room. Why don't just let the new guest taking the room that the last person would take anyway?

Vor 2 Tage
Just a HKer
Just a HKer

Because, when dealing with infinity, there is no "last" person.

Vor 17 Stunden
flare
flare

This is called The Banach–Tarski Paradox. It was the topic of a VSAUSE Video a while back which used the Hilbert Hotel example.

Vor 2 Tage
flare
flare

@Tom Svoboda I KNOW

Vor 2 Tage
Tom Svoboda
Tom Svoboda

@flare banach tarski paradox is the theorem about reassembling a ball into two balls. this video is way more basic stuff (different sizes of infinite sets), but it's a needed ingredient for banach tarski, so it was covered in the vsauce video. but the banach tarski paradox itself is something different. pythagorean theorem is about triangles, but not everything involving triangles is the pythagorean theorem.

Vor 2 Tage
flare
flare

@Tom Svoboda oh wait it isn’t?

Vor 2 Tage
Tom Svoboda
Tom Svoboda

this is unrelated to the banach tarski paradox (even though it was mentioned in that vsauce video)

Vor 2 Tage
Ayush Patil
Ayush Patil

This video is already there on Ted channel uploaded 2014.he just told the same

Vor 2 Tage
Lordlouckster
Lordlouckster

Ted-Ed used powers of primes. bus-th prime ^ seat

Vor 2 Tage
eggynack
eggynack

This way is better, cause it actually fills all the rooms. The power of primes thing leaves infinite rooms empty.

Vor 2 Tage
Flávio
Flávio

Me watching: Hey, that's not allowed ✋🏼

Vor 2 Tage
Atapd
Atapd

COPY FROM TED-ED

Vor 2 Tage
Muazzam Hazmi
Muazzam Hazmi

I don't understand this but I agree

Vor 2 Tage
HyperBlade 93
HyperBlade 93

the most interesting part of this whole thing is wondering how much money is being raked in from all those guests.

Vor 2 Tage
Bitfire31337
Bitfire31337

That's easy: An infinite amount. Depending on the net profit per guest and night it might be a bigger or lesser infinity though 😅.

Vor 2 Tage
MegaMrblackguy
MegaMrblackguy

This is dumb.

Vor 3 Tage
Jiri Valek
Jiri Valek

you can compare the amount of members of an infinite group only if you simplify it by using a finite group...but than you are comparing our number systems rather than the actual number of members.

Vor 3 Tage
Tomor Inferno
Tomor Inferno

wouldn't infinity mean that no matter how many Infinity are filling that infinity it would never be full? Due to Infinity not being like 1+1 but more like everything+everything+everything=everything

Vor 3 Tage
D. Dillon Duffield
D. Dillon Duffield

Surreal! No I mean, do a long video on Surreal Numbers! 👌😸

Vor 3 Tage
Guhan SEN
Guhan SEN

Thats y i took Biology over maths

Vor 3 Tage
MisterSaur
MisterSaur

She: How much you love me? He: Infinite.. She: Will you buy that dress for me? He: Infinite also has limits.

Vor 3 Tage
schotte
schotte

Infinite number of rooms, maybe - but I’d hate to imagine the breakfast buffet.

Vor 3 Tage
Barty
Barty

What did I just watch

Vor 3 Tage
Surekha Veer
Surekha Veer

This is hard as dark season 3😂😂got it

Vor 3 Tage

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