The Banach-Tarski Paradox

Рет қаралды 43,732,723

8 жыл бұрын

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Q: "What's an anagram of Banach-Tarski?"
A: "Banach-Tarski Banach-Tarski."
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en.wikipedia.org/wiki/Countab...
en.wikipedia.org/wiki/Uncount...
Banach-Tarski on wikipedia: en.wikipedia.org/wiki/Banach%...
Banach-Tarski proofs:
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www.math.hmc.edu/~su/papers.d...
people.math.umass.edu/~weston/...
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Пікірлер: 107 000

@kedapofeng8993 4 жыл бұрын

Chiropractor: I’m just gonna make a small adjustment. *turns 90 degrees* *accidentally duplicates spine *

@dillon1012 4 жыл бұрын

Hah

@squid_god_supreme5795 4 жыл бұрын

Ok but like a Hydra

@Omega7321 4 жыл бұрын

My mans did the shift + drag

@dti6342 4 жыл бұрын

Extra flexible

@davidcroly7654 4 жыл бұрын

add bra kad add bra????

@paulcimijotti3686 4 жыл бұрын

Teacher: the test wasn’t that hard The test:

@lindseyrubenstein6028 4 жыл бұрын

Paul Cimijotti right when I read this Vsauce said “That’s not possible to do in the real world.” Lmao

@fosin3889 4 жыл бұрын

Yep

@Ryan-fosho 4 жыл бұрын

Right after I read “the test” Michael asked “what is infinity” like it was question no. 1

@zer0kelvin511 4 жыл бұрын

Same exact thing happened to me indie Jones lol

@ireviewyourcomments8071 4 жыл бұрын

Copied

@zeroclout6306 5 ай бұрын

Been watching this repeatedly for 8 years now and it never fails to blow me away. Peak KZfaq and peak Sauce content.

@tev5040 Ай бұрын

this is that one vsauce video i come back to like once a year and hope that this is the time i actually get it

@notagain3732 Ай бұрын

I watch this video again when i feel im starting to forget some of it hoping the spaced repetition affect to take place

@wet-read 22 күн бұрын

Maybe you should lay off the Sauce.

@zeroclout6306 22 күн бұрын

@@wet-read no

@tangereenclaringbold6921 7 ай бұрын

from a professor in undergrad: an anagram of "Banach-Tarski" is "Banach-Tarski Banach-Tarski"

@gamagames4311 22 күн бұрын

Lol idk why this has no likes

@bilingualistic8514 8 күн бұрын

That's goddamn genius

@the.slanging.thomas4038 4 жыл бұрын

6 year old: im infinite cooler than you Another 6 year old: im infinitely+1 cooler than you Michael popping out of thin air: actually...

@blightedcrowmain8236 4 жыл бұрын

Dunk Potato This is the most underrated comment on this comment section

@asdasd-ho3mm 4 жыл бұрын

The funniest thing is that when we were kids, we would say that. Then as high schoolers, we thought infinity = infinity + 1 and made fun of people. But actually, in terms of ordinal numbers (where omega is the smallest infinity - countable infinity), omega is smaller than omega + 1, which is smaller than omega + 2, etc. This is different than cardinal numbers, like aleph-0, where aleph-0 + 1 = aleph-0. The whole point is that people have their own ideas about how to define everything, which is pretty epic in my opinion. Mathy explanation of the difference below: When defining the ordinal numbers, we take 0 = the empty set, and S(n) = n union {n}. Thus, the nth natural number is the union of all the natural numbers before it. Omega is the union of all the natural numbers, then. And then adding one more element to the set grows it, clearly. The cardinal numbers are defined as the distinct isomorphism classes in the category of all sets. That is, if you can map every element in one set to every element in the other set, they're in the same isomorphism class. So, as it turns out, when taking about these, we could totally map a set with omega elements to an element with omega + 1 elements. So in that sense, infinity + 1 = infinity. Weird, right? It's the best part about math, that the further and further we dive into trying to explain everything, we find more and more unanswerable questions.

@hecommentswithmyhandle1698 4 жыл бұрын

😂

@3ghin5 4 жыл бұрын

*vsauce music plays*

@youraverageasian123 4 жыл бұрын

Me, an intellectual : I am cooler than you no matter what

@seniorvelez7427 4 жыл бұрын

Cop: You’re under arrest. Micheal: *Or am I?*

@rjbloxham9400 4 жыл бұрын

See what you don’t understand is...

@raydiesel6251 4 жыл бұрын

Nice...

@magnusmidjord1644 4 жыл бұрын

Michael*

@bdkroyale 4 жыл бұрын

uNo ReVeRsE cArD iN a NuTsHeLl

@nukeshine 4 жыл бұрын

Cop: Ah shit, here we go aga- *Vsauce music plays*

@morfy2581 19 күн бұрын

Most KZfaq videos are one time consumptions. Vsauce is that rare gem with rewatchability value.

@TheRayneBowe 3 ай бұрын

the hyperwebster introduction made it all click. absolutely mindblowing.

@trc__ 21 күн бұрын

There is actually a variation on the internet called library of Babel. Just search it and it can give you a string of any number of words

@reginaphalanges9428 3 жыл бұрын

Gave 1 star to Hilbert's hotel on Trivago. They kept shifting our room.

@eleanorbarryjhondersey7492 3 жыл бұрын

Feels like I've learned everything but nothing at the same time

@mdriz1353 3 жыл бұрын

Underrated comment!

@peet-janissen5838 3 жыл бұрын

This comment is just a cute joke and I love it

@peet-janissen5838 3 жыл бұрын

@Eric Lee thanks spelling is not my strong suit

@madkirk7431 3 жыл бұрын

@@eleanorbarryjhondersey7492 I hate to be the a**hole, but that was stolen from one of the top comments.

@superninjahguy 4 жыл бұрын

This, is just simply how a cobblestone generator works.

@peterspiesz6739 4 жыл бұрын

This is an underrated comment.

@litmaaxg1782 4 жыл бұрын

Facts

@lexruptor 4 жыл бұрын

This just made my day.

@armironkurbalaj9343 4 жыл бұрын

u are awesome dude

@okaylow9124 4 жыл бұрын

Lol

@nicholasbradley8868 5 ай бұрын

"you cannot cut up a chocolate bar and finish with more than you started with.. or can you?" I immediately grabbed a chocolate bar because I know Michael's got me

@calebwashburn38 7 ай бұрын

This video is so nostalgic to me. May very well be my favorite on all of KZfaq

@harambe9461 7 ай бұрын

Same bro it’s been 8 years but I still look at it sometimes and feel how mind blown I was as a nerdy kid.

@muhammadkamruddin3881 Ай бұрын

@@harambe9461did you understand this

@Vertigo359 20 күн бұрын

haha same, it’s a classic

@leonvanheerden8054 4 жыл бұрын

[At Michael's Wedding] Michael: I do. Guests: Awww Michael: Or do I? [Vsause music intensifies]

@bee-ud6zu 4 жыл бұрын

Leon Van Heerden *turns to guests* Hey VSauce, Micheal here.

@fosin3889 4 жыл бұрын

Lol

@theultimatechampion154 4 жыл бұрын

Haha good one. I liked that.

@theultimatechampion154 4 жыл бұрын

Or did I?

@bggg9836 4 жыл бұрын

Legend

@firaskoukene7370 3 жыл бұрын

Whenever I feel like I'm smart, I come and watch this video to get rid of that nonsense

@josephbauer4483 3 жыл бұрын

Ever tried watching videos about space-time??? Or astronomical physics? Lol

@screamsinrussian5773 3 жыл бұрын

one 2 heist 1 cespie . = 1 despite cheeeck, while it take

@robertmetzger1753 3 жыл бұрын

Yeah ! Right ?

@robertmetzger1753 3 жыл бұрын

@@ragecentral2861 Not Very Nice Earthling ?

@robertmetzger1753 3 жыл бұрын

So What His Point! I Already Knew you cant be like Buzz Light Year and go BEYOND INFINITY !! WE ARE FINITE!!

@LegendEditz100 21 күн бұрын

Bro getting frustrated by 0's at 4:20 is HILLARIOUS

@FBarbarian 5 ай бұрын

I can't think of anyone who produces content that is more worth it to watch than Michael's. So much effort and passion are put into those videos that it's a crime not to watch them. Thank you VSause for making these.

@skittles3310 5 жыл бұрын

Sir, Sir excuse me, I only asked if you wanted cream in your coffee...

@joseomarmeza8175 5 жыл бұрын

😂😂😂

@poopfart65 5 жыл бұрын

Lmao

@popeyethe29th 4 жыл бұрын

Or did you?

@pranav3866 4 жыл бұрын

Sauce?

@MrChilliGaming 4 жыл бұрын

Oh sorry sorry, yes i would like cream in my coffee Or do I? What even IS cream?

@jarvingviolin6027 3 жыл бұрын

“countable means you can count them” is the only part i understood

@memama4389 3 жыл бұрын

same

@dougb9348 3 жыл бұрын

ditto

@elinel9658 3 жыл бұрын

:))))))

@RickGrimes807 3 жыл бұрын

Lool

@TuddecBMW 3 жыл бұрын

it means there exists a bijection between the set you're looking at and N (the set of natural numbers)

@deepro2499 3 ай бұрын

I could watch any Vsauce video 20 times in a row and still learn something new every time.

@elidavarela8113 4 ай бұрын

Michael's mom: Micheal its bed time Micheal: Or is it?

@Zenyx64 13 күн бұрын

Michael: Does time even exist? According to a research paper done by Harvard University, a conclusion regarding sub-atomic particles shows that time- Michael's mom: Honey, please, you know you need sleep to function.

@pisulolol 3 жыл бұрын

dude imagine you’re in a argument with Michael and all of a sudden he says “or can you?” at that point you know you’re done

@BobOnSteam 3 жыл бұрын

Yep

@Nyromen 3 жыл бұрын

“You can be alive. Or can you?”

@oliviawilson4806 3 жыл бұрын

Omg this comment is genius

@iiReTr0Z 3 жыл бұрын

@@oliviawilson4806 Or is it?

@omega4379 3 жыл бұрын

@@iiReTr0Z or are you?

@jeremiahnoar7504 4 жыл бұрын

Every time Micheal says “or can you” the universe reluctantly has to rewrites the laws of physics.

@velcro3105 4 жыл бұрын

@@alexandramarberry1023 Or is it ?

@Zengo38 4 жыл бұрын

But can you?

@zebedeoiiiganado9312 4 жыл бұрын

or can they?

@MrT8T3R 4 жыл бұрын

"Ye canny change the laws of physics!" -Montgomery Scott

@obiwan8972 4 жыл бұрын

Or will it 🤨

@niczim123 2 ай бұрын

11:32 Wow, I'm very impressed with your freehand circle drawing abilities!

@killmaster8312 3 ай бұрын

This is mind-blowing! It took me a while to understand all of this. Thank you for making this knowledge more accessible to everyone. I appreciate your effort. Keep going😉

@nickitachu9290 3 жыл бұрын

I've watched this like 5 times now, I'll get it eventually...

@orange2894 3 жыл бұрын

I don't think I'll ever understand this...

@BurgoYT 3 жыл бұрын

@@easterlake I think I’ve watched this 5 or 6 times since it came out and I finally get it omg I guess I was just too young before lmao

@dairhat 3 жыл бұрын

It's my 6th or 7th time watching now and I just got it! :)

@arijitdubey2282 3 жыл бұрын

If u watch it infinite number of times, the information u find is gonna keep increasing, as every time you watch it, your brain gets somethings that it didn't get the last time. Eventually, you will end up with infinite knowledge wtf It's 1:00 am. Don't you dare say I'm wrong. Actually..It maybe a hyperwebster... Caus' infinite knowledge can be divided into two parts: 1. Infinite knowledge 2. Infinite knowledge. Basically, U have infinite amount of infinite knowledge. I need to sleep.

@Adam_5291 3 жыл бұрын

lol

@_username Жыл бұрын

Michael could go clinically insane and no one would notice a difference.

@lore644 Жыл бұрын

maybe a little bit

@Trevor123abc Жыл бұрын

Already is

@JohnDoe-my5ip Жыл бұрын

Same goes for all mathematicians really

@PeterDB90 Жыл бұрын

Please! Someone explain this part to me 13:50 Why is it that "UP" does not end at the same point as "RIGHT, UP, LEFT"?

@pecareca6735 Жыл бұрын

Fr dude

@electroq2368 19 күн бұрын

It is truly interesting and impressive when Michael tries to guide us into some easier topics before delving into such of a beast. Can't find any other channels that can do this.

@BesmirAlia 10 күн бұрын

Except vsauce2 and veritasium

@jarodlokrantz8655 2 ай бұрын

So crazy that I watched this video 8 years ago while procrastinating homework and now I'm watching this today while procrastinating homework. Very nostalgic to come back to this with much more time invested in higher level maths classes and fun maths videos and actually understand the explanation Michael gives.

@archaven7783 4 жыл бұрын

"Countable means you can count them" michael you are so wise

@morpher728 4 жыл бұрын

Or is he

@JetFalcon710 4 жыл бұрын

@@morpher728 ...Hey, wait a minute!

@HastelloyC276 4 жыл бұрын

Ngl he spittin striaght fax

@michaelpartridge1381 4 жыл бұрын

My name is Michael

@althaia8348 4 жыл бұрын

Lmao idk why I needed this, but thanks

@definitelynotasquid 8 жыл бұрын

you know you boutta learn some shit when michael says "or can you?" and the music starts

@RunItsTheCat 8 жыл бұрын

And you see that the video is 24 minutes long xD

@TheForsakedAngel 8 жыл бұрын

Daniel Grosch He should put x-files music on when he says that xD

@tim213455 8 жыл бұрын

Daniel Grosch You know that the shit is about to get real when he says "or can you?".

@frzferdinand72 8 жыл бұрын

When he says that, just know... YOU GON LEARN TODAY

@YujiUedaFan 8 жыл бұрын

Daniel Grosch Yeah, I even mouthed along to it! BTW, this Paradox reminds me of how people used Key Black on cartoons, so they didn't have to use use too much Magenta, Cyan and Yellow. They took away colours, yet ended up with the same thing!

@nikoforsyth514 5 ай бұрын

It is so cool coming back to this video every few years. I remember when I was in middle school and I could only keep up for a little bit, but now that I am in 3rd year pure math, and it all makes perfect sense.

@pedrobertonhasodre5564 2 ай бұрын

Man I wish Michael would be my college professor it would be so cool to grasp all these profound things directly from him in a class

@pinkelpie1 8 жыл бұрын

you know shits about to go down when he pauses and says "or can you"

@user-xo2ts7ob5r 8 жыл бұрын

😂

@Sepharig 8 жыл бұрын

LMAO

@karldinglasan9551 8 жыл бұрын

yeah

@jamestaylor1118 8 жыл бұрын

You just go... "Fuck. He's off again, isn't he?" *Sighs*

@demonshaz 8 жыл бұрын

I love that part

@cystock3696 4 жыл бұрын

Imagine having enough brain cells to understand this.

@Eulers_Identity 4 жыл бұрын

Imagine having a brain cell.

@Pallid3 4 жыл бұрын

Lol

@castrucciocastracani0 4 жыл бұрын

@@MikeSmith-vz6nnI'm a man of taste

@oliviaocasain9980 4 жыл бұрын

You don't want them. Now all I'm going to do for the rest of the night is lay here and stress about this. You can have mine. Please take them.

@user-pp1cx6zh5v 4 жыл бұрын

But don't think to hard because you don't have that many

@dennisthenothing5139 2 ай бұрын

I love how vsauce's videos stay nearly same as they were aswell as being just as entertaining as they were almost a decade ago.

@willgiles-tz8it 6 ай бұрын

This is extremely interesting and I can explain infinity now. Due to your experience with science, physics and mathematics, you have combined my understanding and knowledge with yours and it has created a new subscriber for you. Thank you for putting your time and effort into this video.

@g_g... 6 ай бұрын

Explain what he explained in the video, cuz I don't get it at all

@willgiles-tz8it 6 ай бұрын

@@g_g... I study in my free time about things I don’t understand

@g_g... 6 ай бұрын

@@willgiles-tz8it I guess we're in the same boat then 😂

@willgiles-tz8it 6 ай бұрын

Maybe you should try it 👍

@g_g... 6 ай бұрын

@@willgiles-tz8it I like to learn random stuff too. I should try to improve my habitual skills.

@jekimoh 6 жыл бұрын

Feels like I've learned everything but nothing at the same time

@HilbertXVI 6 жыл бұрын

impactofredemption r/im14andthisisdeep

@theviniso 6 жыл бұрын

That's maths for you.

@stanleymizerski1065 6 жыл бұрын

that's called life

@maxwellli7057 6 жыл бұрын

Vsause? More like Vegie sause! ! !

@ashleydabas7612 6 жыл бұрын

that's why it is called paradox

@carsongraham2192 8 жыл бұрын

when michael says "or can you" you know it's about to get real

@sorinnoctis652 8 жыл бұрын

every single time "my mind is about to be blown..."

@Elvalley 8 жыл бұрын

Or as is usually the case with his videos, about to get theoretical.

@hasankh4n 7 жыл бұрын

haha yup

@nicolasboissiere 7 жыл бұрын

omg yes 😂😂😂

@isakglerupjakobsen5388 7 жыл бұрын

Yeah I love it

@guidomuzzin9209 2 ай бұрын

Cant stop watching it, I never get bored of listening the same explanation over and over

@BornConfused630 3 ай бұрын

The Banach-Tarski paradox is like a mathematical magic trick

@professionalgarbage2893 3 жыл бұрын

Michael: “Or can you?” The laws of physics: *sighs*

@spikynwm4292 3 жыл бұрын

Ha. *Yes*

@skoviozgamer7436 3 жыл бұрын

Michael written the laws of physics !

@sofijagorovenko6288 3 жыл бұрын

In future they will say Vsauce the god of Or can you

@joemomma6414 3 жыл бұрын

SamTheMa'am you stole this didn’t you

@ivosirakov1278 3 жыл бұрын

Or do they

@thecoolestdogonearth7913 3 жыл бұрын

Michael: Obviously you can’t cut up a chocolate bar and have more than you had before. Me: don’t say it Michael: or can you

@CieloDehaz 2 жыл бұрын

*groovy music starts playing*

@rodh1404 2 жыл бұрын

I can. (Because I'll steal yours too. And Michael's, now that I think about it).

@kagemushashien8394 2 жыл бұрын

It's how Jesus duplicated bread

@manioqalegram5396 2 жыл бұрын

Once You know lyrics, You can't sing along! Toom aroom, pam pom pam

@manioqalegram5396 2 жыл бұрын

Reals are Aleph_null to power of Aleph_null

@hydrohomiee 5 ай бұрын

I come back to this video every few months, the idea fascinates me deeply

@Kyuubiiiiiii 6 ай бұрын

This video never fails to make me sleep. It’s really helpful with my insomnia. This is why I never actually understood the video topic.

@meend6456 4 жыл бұрын

youtube man solves world hunger by giving everyone chocolate squares (2019 colorized)

@wrongparadoxscience1485 4 жыл бұрын

Dude do you know if they are relatives? I meant Vsauce,Vsauce2,Vsauce3?

@bdkroyale 4 жыл бұрын

@@wrongparadoxscience1485 a mystery only god could solve..... *or is it?*

@Stre55ed1 4 жыл бұрын

And some fuckin dollar bills

@MoreLikeCappuccino 4 жыл бұрын

2015*** my dood

@UhOhTheStoveIsOn 4 жыл бұрын

2015*

@Dravignor 18 күн бұрын

I love this video for introducing me to the complex rabbit hole that is higher-level Math

@capanser9756 7 ай бұрын

One of the best videos in KZfaq history

@CosmiKazie 4 жыл бұрын

Everybody gangsta till Michael says “or is it?”

@emmersonhollenbaugh4397 4 жыл бұрын

CosmiKazie legit😂

@jupiter8711 4 жыл бұрын

CosmiKazie or are they

@halfofabucket1346 4 жыл бұрын

AHH! THE CASTRAISTS ATE COMI- _or is it?_ *madness stops* ah, phew

@input3471 4 жыл бұрын

Or does he??

@halfofabucket1346 4 жыл бұрын

@@input3471 *more maddness intensifies, causing magma to leak from the crust* OMG MY FRIEND MICHAEL SAY IT! *or is it?* *magma cools down*

@arsiarskila Жыл бұрын

Doctor: "You are in a mental hospital sir" Michael: "Or am i?!" Doctor: "Yes you are."

@lore644 Жыл бұрын

Micheal: disappears

@arkosilaura Жыл бұрын

@@lore644 Stop right there, criminal scum! You have violated the laws of physics.

@slikognito Жыл бұрын

😭😭😭

@slikognito Жыл бұрын

@@lore644 🎩🐇

@flunxyofficial Жыл бұрын

No I’m a finite amount of time I can turn this place into a party Doctor: Yeah he’s definitely high

@dustinsoodak8954 5 ай бұрын

The part of the definition of the hyperwebster dictionary which no one seems to state explicitly is that it is simply what happens when you use standard alphabetization on a list of every combination of letters of any (finite) length. I assumed it was something more complicated and didn't figure it out till several hours later when I decided to try reverse engineering it from the recursive description suggested by the next part of the proof. Every time I watch this video I figure out a bit more...

@gabe_1971 3 ай бұрын

This video is such a VSauce classic

@sk3llyb0n3zz7 2 жыл бұрын

Imagine pulling up to an infinite hotel and being told “we’re full”

@itsBLX 2 жыл бұрын

yeah that would be crazy especially if it involved infinitys being bigger then other infinitys and stuff

@user-iq7mk3gb9w 2 жыл бұрын

en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel Coincedentally, your thought is similar to a mathematican who lived in the 20th century. It goes like this : If the hotel is already full, and guest (from room) 1 move to room 2, guest 2 move to room 3 and so on, every guest will have a room to move into, and somehow from a full hotel you manage to create an empty room (room 1) out of thin air. Now you have a room. Even if an infinite guest show up and the hotel is already full, guest 1 can move to room 2, guest 2 to room 4, guest 3 to room 6, guest n to room 2n. There will be an infinite number of empty room (room 1, 3, 5, ,7 ,9, etc) appeared for those new guest. But, it does not just stop there. If you host a pyramid scheme in that hotel, everybody will gain and nobody will lose their money, because there are always more people to be involved in the scheme.

@sameerbiswas2662 2 жыл бұрын

Stop copying veritasium bro

@sk3llyb0n3zz7 2 жыл бұрын

@@sameerbiswas2662 who?

@sk3llyb0n3zz7 2 жыл бұрын

@ChrisGD¹³ but what if an infinite amount of people go into the hotel and then you go in

@TheSuperNick1134 8 жыл бұрын

1:05 - 1:14 "or can you..."" Me - ...And so it begins.....

@primeninja2357 8 жыл бұрын

I love this mystery sound that comes when he asks questions like this ^^

@Yarblocosifilitico 8 жыл бұрын

Prime Ninja me too, one day they'll use it in schools

@Lyraniah 8 жыл бұрын

Deadeyes especially when it comes down to more chocolate :D

@rawstarmusic 8 жыл бұрын

Lyraniah ...yeah I also want to know the chocolate secret. How to do it at home. Buy one bar then start move them around and consume the leftovers. A chocolate 3D printer wouldn't be so bad either, starting with a 3D printer that makes chocolate 3D printers.

@_Uhtcaru 8 жыл бұрын

Deadeyes *inception noise*

@Upper-Moon Ай бұрын

Do we know yet?

@chambo4645 3 ай бұрын

I’ve watched this video like 15 times over the years, and every time it’s recommended I’m intrigued

@smartaIec 7 жыл бұрын

all I wanted was two bars of chocolate

@angeloakley2764 7 жыл бұрын

Lol same

@Mike-xp8zc 7 жыл бұрын

Alec Ryan but they wouldn't give it to me!! Tell me you where quoting Suicide tendencies

@smartaIec 7 жыл бұрын

Hos Delgatoes 3344 you got me there

@Mike-xp8zc 7 жыл бұрын

Alec Ryan oh word

@yves5400 7 жыл бұрын

you can have a countable infinity amount of chocolatebars by simply rotating the chocolate into the right

@shaileshrana7165 5 жыл бұрын

Kindergarten teacher: 1+1=2 Michael: or is it?

@heheheiamasuperstarwarrior9281 5 жыл бұрын

Collage teacher: ok so class i have a question. What is 1+0? Class:*laughs* 1 Collage teacher:* pulls mask off * Michael: WRONG ITS 2 CLASS DISMISSED

@legendarylightyagamiimmanu1821 5 жыл бұрын

HEHEHE I AM A SUPASTAR WARRIOR lmao

@CommanderSpaceDog 5 жыл бұрын

Shailesh Rana o

@aspiringcloudexpert5127 5 жыл бұрын

This was actually a real problem that mathematicians faced when trying to define the foundations of mathematics.

@SG-ix3ly 5 жыл бұрын

Well, it could be IIIV or 01 or even impossible to solve...

@RealKidNamedFinger 7 ай бұрын

i always come back to relearn it

@I_also_like_tally_hall Ай бұрын

This has to be one of my favorite vsauce videos

@SilentWalker 4 жыл бұрын

Teachers: The test won’t be that hard The test:

@timothyfreeman7913 4 жыл бұрын

It won't be that easy either.

@Irishgal420 4 жыл бұрын

Right😂

@fetendo8291 4 жыл бұрын

Correction: Teachers: The test won’t be that hard The test: *Video*

@ninjachris2344 4 жыл бұрын

420 likes niceeeee

@Dougiewoof 4 жыл бұрын

The test: deconstruct this test and make two tests

@christianjeffreys6588 Ай бұрын

Idk how many times over my life I have to watch it before my feeble mind will grasp. I return every year or so to check

@CallMeThyme Ай бұрын

Same lmao

@jaykerzp3643 4 ай бұрын

I love this video. Can't remember how many times I've watched it, but I feel like I'm getting close to understanding what he's talking about.

@pawekrychowiak4435 5 жыл бұрын

-Michael stevens, do you take this women to be your wife -i do -... -or do i?

@cryingkiller1179 5 жыл бұрын

and for that i tip my fedora to you my kind "insert here what you identify as"

@ReverseJuxtapose 5 жыл бұрын

@@cryingkiller1179 *inserts: fam*

@Desert_guy 5 жыл бұрын

Cue music*

@Environs112 5 жыл бұрын

*clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap**clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap**clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap**clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* *clap* 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@harryb7505 5 жыл бұрын

*vsauce music begins playing as he goes off on a tangent about the concept of marriage*

@InfernalGarish 7 ай бұрын

Very epic Micheal

@codg3484 5 ай бұрын

this is by far and not even a contest, his best video

@ultrabaltard1479 4 жыл бұрын

“What happened to Amelia Earhart” “AAAAAAAAAAAAAAAAA”

@chillingwhitenoise4903 4 жыл бұрын

Literally the most big brain comment

@vayroxayp7331 4 жыл бұрын

I cant stop laughing lmao

@betsy3096 4 жыл бұрын

i think that’s what did happen

@bartman8876 4 жыл бұрын

What didnt happen "ZZZZZZZZZZZZZZZ"

@chris-vv1nt 4 жыл бұрын

Ross: "The woman just vanished!"

@ithinkimconfused 7 ай бұрын

we found the infinite money glitch

@gamerxp1887 6 ай бұрын

its 8 years later and i wonder if they have new solutions to the problem

@dekardandrew1067 6 ай бұрын

Me too

@AndresFirte 6 ай бұрын

Solutions to what problem?

@gamerxp1887 6 ай бұрын

@@AndresFirte the mathematical Problem mentioned in the Video

@AndresFirte 6 ай бұрын

@@gamerxp1887 the video shows a counterintuitive theorem, but it’s not a problem. It’s solved, proven. It is called a “paradox” because it’s counterintuitive, but it is known that the theorem is completely correct

@vakeiniux321 5 жыл бұрын

"No hole will be left unfilled" -Vsauce

@BermanTV 5 жыл бұрын

sounds like my honey moon

@arakbmt2379 5 жыл бұрын

Except the potholes in my home state!

@kiraholzhausen9936 5 жыл бұрын

@@arakbmt2379 Michigan?

@bluecicada9904 5 жыл бұрын

The words my dad muttered on my 7th birthday party

@Canose 5 жыл бұрын

@@arakbmt2379 sweet home Alabama?????

@justakid1238 5 жыл бұрын

Landlord: Alright Michael, rent is due Michael: *proceeds to explain to them why rent isn’t due until next century*

@pickle3641 5 жыл бұрын

>rent is due >OR IS IT?

@itsflyde 5 жыл бұрын

Krakeon “michael please you do this every month give me the money and let me see my family”

@voicemint 5 жыл бұрын

No problem for Michael as this video has probably paid for his house -- no more rent.

@purewater3177 5 жыл бұрын

😄

@PR0TEGE 5 жыл бұрын

Like 667, saved you all from the devil.

@vaiolat1480 7 ай бұрын

I will come back and change my comment in 10 years

@zuhaibzahoorx Ай бұрын

5 months in 👍

@cjwag5 Ай бұрын

I’m here by year 8 😏

@videos_not_found 25 күн бұрын

Oh you are also time travelling?

@zuhaibzahoorx 24 күн бұрын

@@videos_not_found That's aging! Not time Travelling💀

@videos_not_found 24 күн бұрын

@@zuhaibzahoorx Nevermind, young man: Row, row, row your boat Gently down the stream. Merrily, merrily, merrily. Life is but a dream.

@josephjackson1956 15 күн бұрын

I think the most applicable the Banach-Tarski paradox could be is to break down complex problems and see what is and isn’t necessary. Also maybe use an actual finite number of points to use in a more tangible way.

@monarchblue4280 5 жыл бұрын

Start: INFINTE chocolate End: THE UNIVERSE IS A LIE AND WE ARE ALL FAKE

@earlhollar1906 5 жыл бұрын

The universe is a thought and everything that is seen or touched is Just Energy vibrating at different frequencies!

@johnthebrave97 5 жыл бұрын

we will divide until we cover the earth’s surface

@kuliimjulischreiben 4 жыл бұрын

CHOCOLATE IS NOT EVEN MY FINAL FORM

@monarchblue4280 4 жыл бұрын

@@kuliimjulischreiben I will destroy this planet in five minutes.. OR WILL I

@borge7403 4 жыл бұрын

He’s technically just saying theoretically our world is infinitely small and that we could duplicate things if we got the technology and if it was plausible

@Thebrebeee 7 жыл бұрын

Micheal: I mean, come on, obviously you cannot cut up a chocolate bar and rearrange the pieces into more than you started with... or can you? *proceeds to challenge my common sense*

@junehya 7 жыл бұрын

AYE JUNGKOOK I SEE YOUUUU

@0o.anubis.o036 7 жыл бұрын

The rule is, whenever he says "Obviously", it's somewhat followed up by him saying, "Or can..."

@charlottewiltshire1838 7 жыл бұрын

ARMY

@KamuiCage 7 жыл бұрын

he didnt! all those little missing pieces in the middle adds up to the piece of chocolate removed

@jaykenley8677 7 жыл бұрын

+kamui Cage No shit Sherlock !!

@bluecreeper6161 2 ай бұрын

13:50 the coincidences of you choosing red and that direction being the same starting letters for a games’ title, Red Dead Redemption, it makes me slightly happy for some reason

@CastellZord Ай бұрын

8:50 this haunted me for a couple days, because a was surprised that there are a countable infinite number of points on a circumference. Matter of fact, it's false. If this statement was true then it would follow that the cardinality of the interval [0,2π] is aleph zero, but that's clearly false since you too stated that the cardinality of the interval [0,1] is more than aleph zero. With your method you'll never reach the point that's √2r from the starting point on the circumference

@AndresFirte Ай бұрын

I don’t understand, are you saying the video is wrong? Or are you saying that you misunderstood the video? (The video doesn’t say that a circumference has countably many points)

@error7263 3 жыл бұрын

Start: Can you multiply a chocolate bar? End: The Universe is both infinite and finite.

@phoenixjamirazucena5672 3 жыл бұрын

hah when u know why theres choco trick but u cant explain

@larswalzberg8486 3 жыл бұрын

You don't have to be smart to get its relative point, i gues :D

@DaSilverBackz 3 жыл бұрын

@@larswalzberg8486 9 divided by zero is infinite :D

@darshanjain6707 3 жыл бұрын

@@phoenixjamirazucena5672 lol he spent a great deal explaining how you can make two spheres

@error7263 3 жыл бұрын

@@larswalzberg8486 I know

@vamasiya 5 жыл бұрын

If aliens ever show up we need Michael on the negotiation table.

@logann6615 5 жыл бұрын

Aliens: we want 1 million dollars Micheal: but there are infinite numbers in between a million?!

@macbrns1438 5 жыл бұрын

The aliens would give up

@FF-qj5se 5 жыл бұрын

Lmaooooo best comment so far

@jonasmangonon4237 5 жыл бұрын

Vsauce : hey V- Aliens : we surrender we are now your cattle allknowing being

@puzzlepiece2502 5 жыл бұрын

MELT THEIR BRAIN

@pookiewookie1837 2 ай бұрын

Watching vsauce vids while being miserably sick is a fever sick. And i can feel my headache getting worse and worse

@yashodhanbarve3581 Ай бұрын

Why does he keep calling me vsauce

@angelakonan438 4 жыл бұрын

Me: 'mum i just learned something new' Mum: 'what' Me: ...

@farr2600 3 жыл бұрын

Or did you? ***Vsauce theme plays***

@cracked_nebula1479 3 жыл бұрын

@@farr2600 or did he?

@pepermint787 3 жыл бұрын

I just learned how to hack chocolate

@Insigneon 3 жыл бұрын

Mum be like wtf

@waterwolf982 3 жыл бұрын

Cool pfp

@personmanthing 2 жыл бұрын

“Hilbert’s Hotel can be applied to a circle.” Thats it I’m officially lost

@friedec3622 2 жыл бұрын

No, I still not lost it. The moment he said about left right on sphere is I lost it.

@Theguywhoasked001 2 жыл бұрын

I lost it when he started talking about why up down something didnt work so we had to move some parts of the sphere somewhere or something

@TheFagerlund 2 жыл бұрын

@@friedec3622 if you move you move inside a sphere because the earths atmosphere is round contrary to the earth itself that is slightly larger at the middle point if you lost it at that point you have smol brain

@friedec3622 2 жыл бұрын

@@TheFagerlund What? Does the video talking about Earth? I think it's about geometry and placement.

@segmentsAndCurves 2 жыл бұрын

@@friedec3622 smol brain ;)

@cord2706 3 ай бұрын

I see this video in my reccomendations more than once a day for years. Why. I have watched it many times, but I have seen this goddamn thumbnail so many times it’s ingrained in my brain

@quantumdevil5147 3 ай бұрын

It's tough to wrap my head to this concept at once. I gotta to again and over again in order to comprehend it😊

@marcoreale02 4 жыл бұрын

Michael: "I mean, come on, you can't obviously cut up a chocolate bar and rearrange it to get more pieces than you started with" Me: haha yeah of course Michael: *long pause,* *stares into camera* Me: oh no michael you didn't Michael:

@devyns1969 4 жыл бұрын

@Top.commemt.god

@chrls5559 4 жыл бұрын

69 noice

@marcoreale02 4 жыл бұрын

@Neco everything is ruined. not nice.

@jeremiahperko6071 4 жыл бұрын

@@marcoreale02 just make 68 accounts and dislike it

@leoschmude8263 4 жыл бұрын

This was my exact reaction

@tompowell3380 6 жыл бұрын

Therapist: how did your existential crisis begin? Me: Hey Vsauce Michael here

@glick5601 6 жыл бұрын

Tom Powwell oh I thought therapist said " the rapist" lmao

@littlebrain4482 6 жыл бұрын

You're not helping.

@trojan_otter583 6 жыл бұрын

Mine started when i began existing, or was it before i was existing? Could i have known of existence before existence? Impossible. Idk where i was going with this

@avomanavoman 6 жыл бұрын

Tom Powwell z

@JizzoCalrissian 6 жыл бұрын

Lol! Great comment!

@Monalisa-cr8sr 4 ай бұрын

Man I wish I could watch Michael's videos for the first time again.

@shailpatel3841 4 жыл бұрын

*1st grade teacher*- so kids 1+1=2 *Michael in 1st grade* - umm not really see if you take a 3-D sphere and mark every point.......

@debisz_ 4 жыл бұрын

@Accursed Nature but he's pretty fucking smart for understanding that lol...he lost me at "Hey Vsauce"

@watcher190 4 жыл бұрын

@Accursed Nature everything is based off of at least one small thing, so you are saying that everyone is stupid and can't do anything

@LeadSalad99 4 жыл бұрын

If you substitute the word "Michael" in the example to "person who understands this", would that make you happy? Accursed nature

@watcher190 4 жыл бұрын

@Accursed Nature i geuss i added the part where you call him stupid, but what you said was that he didn't come up with this information by himself, he just researched it and repeated the topic which he read. Im saying every piece of info is based off of something though, physicists and teachers didn't just do experiments and figure out stuff all by themselves, they go through years of schooling, so you could say they don't know anything and are just repeating what they saw in a textbook.

@badmouserising9859 4 жыл бұрын

KZfaq THE SUBREDDIT IS "r/Whoooosh, jesus christ

@starmc6130 6 жыл бұрын

you know what else infinite? winrar free trial

@Ok-wb2jb 6 жыл бұрын

Star MC true that

@justlucky_0 6 жыл бұрын

Very True.

@UltraCyborggaming 6 жыл бұрын

ikr

@jerrythepotato1919 6 жыл бұрын

Star MC big if true

@nishikoi6789 6 жыл бұрын

Yup, just click close when they tell you to buy it

@CamiloalejandroRojas Күн бұрын

1:07 top 10 best clips of history

@jonahb6580 6 ай бұрын

This is the first time that I haven’t even come close to understanding what Michael is talking about. I lost him the second he started making rotations on the circle.

@danzgalliwag 2 жыл бұрын

i feel like the reason this is one of vsauce's most popular videos is because so many people come back to it every now and then cause they don't get it.

@neilmacdonald6637 2 жыл бұрын

Aren't those the best videos? haha

@ogrim0 2 жыл бұрын

Yep, my second coming. Still dont get it.

@ExquisiteSquid 2 жыл бұрын

This one is reallly hard to understand if your brain is not accustomed to thinking in infinites and using assumptions to make other assumptions. Like I bet math majors would be able to follow this quite a bit easier than most people for that reason

@christallee2660 2 жыл бұрын

@@ogrim0 my 5th, and I'm still clueless

@user-dc8sj9np9g 2 жыл бұрын

lol

@TheRealJeff2 4 жыл бұрын

Hotel designer: so how many rooms do you want? Hilbert: yes

@susq_345 4 жыл бұрын

7:42 " u n l i m i t e d s u p p l y o f g u e s t s"

@paulscottfilms 4 жыл бұрын

why Yes?

@TheRealJeff2 4 жыл бұрын

@@paulscottfilms because yes

@d.pickal6672 4 жыл бұрын

He gonna have a hard time filling that hotel during this pandemic

@EternalFinity 4 жыл бұрын

Who the **bruh** is Hilbert lol

@KyngMark 3 ай бұрын

Cheat codes be like:

@Misteribel 16 күн бұрын

I like how you write the digit 8. I've never seen someone doing it that way (as disjoint zeroes on top of one another).

@ashtabarbor3346 Жыл бұрын

This is true pure mathematics. The kind that makes you feel smart, stupid and insane at the same time

@n0denz Жыл бұрын

Mostly makes me angry.

@henkebenkebankpress27 Жыл бұрын

That is the perfect way to describe it, thank you!

@stealthis Жыл бұрын

@@n0denz 😤

@asheep7797 Жыл бұрын

@@stealthis 😤= 😠 + 😔 + 🙁 + 2 x 💨

@Ins1gn1f1c4nt Жыл бұрын

@@asheep7797 Me when 1 + 1 = 2: 🥵 = 😰 + 😡 + 😊 + 😛 + 💧 Me when 1 + 1 = 1: 🤬 = 😡 + ➖ + #$!@

@giftedpotato5138 4 жыл бұрын

Thanos: The universe is finite, its resources finite. Banach-Tarski has entered the chat.

@silkeecks5047 4 жыл бұрын

And about time, too!

@yewdontnomi643 4 жыл бұрын

Banach-tarski :*explained the paradox Thanos : impossible

@faye_isc 4 жыл бұрын

OSCAR!!!! THIS shit is funny af😂😂😂😂😂😂😂😂 👌👌👌👌 gg man

@SidPil 4 жыл бұрын

🔥😂🔥

@Abracastabya 4 жыл бұрын

Banach-Tarski K/D = infinity. Thanos = half of the universe/0.5 (referring to when he almost died by the hands of Thor)[haven't watched end game if it's even out, don't spoil anything for me fags lol]