The Banach-Tarski Paradox 

Hah

Ok but like a Hydra

My mans did the shift + drag

Extra flexible

add bra kad add bra????

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

Yep

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

Same exact thing happened to me indie Jones lol

Copied

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

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

Maybe you should lay off the Sauce.

@@wet-read no

Yep

“You can be alive. Or can you?”

Omg this comment is genius

@@oliviawilson4806 Or is it?

@@iiReTr0Z or are you?

maybe a little bit

Already is

Same goes for all mathematicians really

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"?

Fr dude

thats a huge achievement! congrats!

Same! I'm revisiting this video after learning about this paradox in my functional analysis class today

@@anthropomorphicpeanut6160 Isn't this part of measure theory?

Congrats bro, you are no longer a human🎉

We know we're grown up when Vsauce's tangents start making sense...

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

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.

😂

*vsauce music plays*

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

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

Underrated comment!

This comment is just a cute joke and I love it

@Eric Lee thanks spelling is not my strong suit

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

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

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.

​@@harambe9461did you understand this

haha same, it’s a classic

Or is he

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

Ngl he spittin striaght fax

My name is Michael

Lmao idk why I needed this, but thanks

See what you don’t understand is...

Nice...

Michael*

uNo ReVeRsE cArD iN a NuTsHeLl

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

And you see that the video is 24 minutes long xD

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

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

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

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!

same

ditto

:))))))

Lool

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

@@alexandramarberry1023 Or is it ?

But can you?

or can they?

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

Or will it 🤨

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

Lol

Haha good one. I liked that.

Or did I?

Legend

It won't be that easy either.

Right😂

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

420 likes niceeeee

The test: deconstruct this test and make two tests

😂😂😂

Lmao

Or did you?

Sauce?

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

*groovy music starts playing*

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

It's how Jesus duplicated bread

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

Reals are Aleph_null to power of Aleph_null

Ha. *Yes*

Michael written the laws of physics !

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

SamTheMa'am you stole this didn’t you

Or do they

This is an underrated comment.

Facts

This just made my day.

u are awesome dude

Lol

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

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

Yeah ! Right ?

@@ragecentral2861 Not Very Nice Earthling ?

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

>rent is due >OR IS IT?

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

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

😄

Like 667, saved you all from the devil.

Mostly makes me angry.

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

@@n0denz 😤

@@stealthis 😤= 😠 + 😔 + 🙁 + 2 x 💨

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

impactofredemption r/im14andthisisdeep

That's maths for you.

that's called life

Vsause? More like Vegie sause! ! !

that's why it is called paradox

Micheal: disappears

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

😭😭😭

@@lore644 🎩🐇

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

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

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

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

Maybe you should try it 👍

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

Lol

We need 1 more like till 100

Technically he isn't Vsauce, He's Micheal. We're Vsauce.

When did this get 289 likes wtf

Saw this when he said it.

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

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

haha yup

omg yes 😂😂😂

Yeah I love it

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

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

And some fuckin dollar bills

2015*** my dood

2015*

😂

LMAO

yeah

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

I love that part

Imagine having a brain cell.

Lol

@@MikeSmith-vz6nnI'm a man of taste

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.

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

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

The aliens would give up

Lmaooooo best comment so far

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

MELT THEIR BRAIN

sounds like my honey moon

Except the potholes in my home state!

@@arakbmt2379 Michigan?

The words my dad muttered on my 7th birthday party

@@arakbmt2379 sweet home Alabama?????

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

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

@@larswalzberg8486 9 divided by zero is infinite :D

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

@@larswalzberg8486 I know

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

You're not helping.

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

Tom Powwell z

Lol! Great comment!

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

HEHEHE I AM A SUPASTAR WARRIOR lmao

Shailesh Rana o

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

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

lol

That’s exactly what I was thinking lol

Imagine, you will move out of your room infinite times in a day.... ow sheet

Or like just give him the last or infinity+1th room which is infinity

Infinite numbers of Aw shit, here we go again

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

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.

Stop copying veritasium bro

@@sameerbiswas2662 who?

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

Aren't those the best videos? haha

Yep, my second coming. Still dont get it.

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

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

lol

5 months in 👍

I’m here by year 8 😏

Oh you are also time travelling?

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

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

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

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

@@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

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

@@friedec3622 smol brain ;)

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"

why Yes?

@@paulscottfilms because yes

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

Who the **bruh** is Hilbert lol

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

@@farr2600 or did he?

I just learned how to hack chocolate

Mum be like wtf

Cool pfp

pkcaleb Your 100th like your welcome 💯

Abstracted mathematics must be one of the dumbest, most pareidolia type of activities in the history of mankind. The number of atoms and the degree of force in a dollar bill and in a rotating unit is exactly the same before or after math nerds start their rants

same

I literally stayed home from school ND watched alot of his vids n took notes ND learned it went back to school taught my teacher den used this all in my reason why I dont need to go to school to learn

The only thing I understood from this vid

Or can you?

Michael playing Gta San andreas: Or do we go again?

Or do we?

haha😂😂🤣 btw thanks for 130 now lets reach 140 pls 🙏😀😀

It’s more like forget everything you think you know from doctor strange

Lmao same though

😂😂🙌🏼♥️

😂😂😂

Graveyard That's where you belong

*Micheal Scott intensifies*

Lol same

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

Hos Delgatoes 3344 you got me there

Alec Ryan oh word

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

And about time, too!

Banach-tarski :*explained the paradox Thanos : impossible

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

🔥😂🔥

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]

Literally the most big brain comment

I cant stop laughing lmao

i think that’s what did happen

What didnt happen "ZZZZZZZZZZZZZZZ"

Ross: "The woman just vanished!"

Same lmao

AYE JUNGKOOK I SEE YOUUUU

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

ARMY

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

+kamui Cage No shit Sherlock !!

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

@@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

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

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.

lol

How does rotating create new points?

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

@@cryingkiller1179 *inserts: fam*

Cue music*

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

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

we will divide until we cover the earth’s surface

CHOCOLATE IS NOT EVEN MY FINAL FORM

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

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

In a theory by Buttock Tarski? Why ever not?

( ͡° ͜ʖ ͡°)

This my friend is called MathPorn...

@TheFakeyCakeMaker 📸

9:16 yw