#### Am Vor 5 years

Dauer: 24:13

Want more brain food? Want your house to become a museum? Now you're thinking: www.curiositybox.com

Q: "What's an anagram of Banach-Tarski?"

A: "Banach-Tarski Banach-Tarski."

twitter: twitter.com/tweetsauce

Instagram: instagram.com/electricpants

Kevin’s Field Day video: de-film.com/v-video-1zARMZ08ums.html

Field Day: de-film.com/ch-UCRPktNf5vnBR1J4e7t1RUVg

Deep dream animation by instagram.com/NaderMakki/

If you like it, you'll love this video also by Nader: de-film.com/v-video-fJ9j_z2kXI0.html

Chocolate illusion: mathandmultimedia.com/2014/07/22/explanation-infinite-chocolate-bars/

Chocolate illusion video: de-film.com/v-video-dmBsPgPu0Wc.html

related Numberphile videos:

sizes of infinity (includes diagonal argument): de-film.com/v-video-elvOZm0d4H0.html

infinity paradoxes: de-film.com/v-video-dDl7g_2x74Q.html

Vi Hart on types of infinity: de-film.com/v-video-23I5GS4JiDg.html

Countable & uncountable definitions:

mathinsight.org/definition/uncountable

en.wikipedia.org/wiki/Countable_set

en.wikipedia.org/wiki/Uncountable_set

Banach-Tarski on wikipedia: en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox

Banach-Tarski proofs:

math.uchicago.edu/~may/REU2014/REUPapers/Robinson.pdf

www.math.hmc.edu/~su/papers.dir/banachtarski.pdf

people.math.umass.edu/~weston/oldpapers/banach.pdf

Banach-Tarski explinations online:

www.irregularwebcomic.net/2339.html

www.kuro5hin.org/comments/2003/5/23/134430/275?pid=5#10

skepticsplay.blogspot.co.uk/2010/05/doubling-sphere.html

austinrochford.com/posts/2014-05-14-banach-tarski-paradox.html

www.math.cornell.edu/~mec/Summer2009/Whieldon/Math_Explorers_Club%3A__Lesson_Links/Entries/2009/7/28_Lesson_6%3A__Whats_an_Anagram_of_Banach-Tarski.html

rachellevanger.com/index_files/BT%20Animated%20Presentation%20Web.pdf

quibb.blogspot.co.uk/2013_03_01_archive.html

blog.computationalcomplexity.org/2011/04/what-did-banachs-wife-think-of-banach.html

geopolicraticus.wordpress.com/tag/banach-tarski-paradox/

dgleahy.com/p47.html

www.math.hmc.edu/funfacts/ffiles/30001.1-3-8.shtml

Cayley graph animated gif: twitter.com/GIFsofWikipedia/status/624202342259240960

Hilbert’s hotel on wikipedia: en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel

types of infinity: www.xamuel.com/levels-of-infinity/

set theory and quantum physics: link.springer.com/article/10.1007/BF02213427#page-1

LHC gif: cms.web.cern.ch/news/lhc-data-be-made-public-open-access-initiative

Zermelo-Fraenkel axioms of mathematics: mathworld.wolfram.com/Zermelo-FraenkelAxioms.html

Is math invented or discovered?

phys.org/news/2013-09-mathematics-effective-world.html

www.scientificamerican.com/article/is-the-universe-made-of-math-excerpt/

more deep dream images: www.reddit.com/r/deepdream/

BOOKS:

The Pea and the Sun: www.amazon.com/The-Pea-Sun-Mathematical-Paradox/dp/1568813279

The Outer Limits of Reason: www.amazon.com/Outer-Limits-Reason-Science-Mathematics/dp/0262019353

Why Beliefs Matter: www.amazon.com/Why-Beliefs-Matter-Reflections-Science/dp/0198704992

Things to Make and do in the Fourth Dimension: www.amazon.com/Things-Make-Fourth-Dimension-Mathematicians/dp/0374275653

Music by de-film.com/us/JakeChudnow and

www.audionetwork.com

США - Италия. Инаугурация Байдена. Отделяем зерна от плевел. Проколы пропаганды и оппозиции.

Aufrufe 36 208

Sie schnitt einer HOCHSCHWANGEREN ihr Baby aus dem Bauch! Ist das T0DESURTEIL nun gerecht ? |socills

Aufrufe 264 955

🔔ГАДАНИЕ НА КРЕЩЕНСКИЙ СОЧЕЛЬНИК💞ЧТО ЖДЕТ ПО СУДЬБЕ ДОРОГА ЖИЗНИ ПЕРЕМЕНЫ💥Приглашаю на ОБУЧЕНИЕ ТАРО

Aufrufe 114 714

## KOMMENTARE

## voidredstone

Me: trying to take the video seriously and learn something My brain: furry ball

Vor Stunde## click me

0 divided by infinity equals- *Physics cannot predict what this number is*

Vor Stunde## Jamie Bainbridge

If you ever think your job is pointless, some mathematician wrote a paper saying infinite numbers plus one is both a larger set than infinity and isn't a larger set than infinity. Thanks mate, really helpful, great work.

Vor 5 Stunden## Релёкс84

infinity + 1 = infinity. Nobody writes papers to explain this relatively simple fact.

Vor 4 Stunden## Oyong Santoso

If you rotate URRU to become DURRU it becomes RRU which has already been placed somewhere else in the circle. Right???

Vor 6 Stunden## Релёкс84

Yes, which is why valid paths must not back track.

Vor 4 Stunden## Neon SWitchblade

"Blah, blah, blah" is not infinite. There is exactly 873,450,316,993,444,303 of them.

Vor 9 Stunden## Brian Arbenz

Hundreds of thousands of your viewers are now tearing their dollar bills up, hoping to double their money. And wow, are they gonna be mad!

Vor 10 Stunden## Kim NANA The Artistic Masterpiece Whaley

This is just fascinating

Vor 12 Stunden## Mr. Johnson

don't try the dollar shit it doesn't work.

Vor 12 Stunden## atrimus

13:15 Red Dead Redemption!

Vor 13 Stunden## Ubaid Baig

i dont understand shit but i watch to feel smart

Vor 14 Stunden## treelongated musk

My brain hurts

Vor 17 Stunden## MagicReason

I'm only commenting here because the image for this video looks like a butthole, and I think that's what Michael really likes.

Vor 19 Stunden## Alinn

I can’t not think with common sense, what does any of this mean?

Vor 19 Stunden## Johnny Espinoza

Think the dollar will still work in a machine

Vor 19 Stunden## Λευτερης

you heard it guys no hole will be left unfilled

Vor 20 Stunden## Ryan Reyna

this has given me more brain cells than ive had in my life

Vor 20 Stunden## Mohammed Tahmid

5:46 that's a weird way to write 8

Vor 21 Stunde## Gromp

Can't you do the same with Whole numbers just like you did with real numbers on that list? Take whole numbers, just remove the 0. so the first whole number is 5032164.... the second 7829136... and so on then add 1 to each part or deduce 1 if its a 9 and you'll have 68281.... which is obviously a new number isn't that also the case here?

Vor 22 Stunden## Релёкс84

It doesn't work because whole numbers always have a finite amount of digits: an endless string of number does not generally correspond to a whole number, unless it ends in an endless string of zeros. And this is critical, because if you were to construct a string of number based on cantor's argument, it would necessarily end in an infinite string of non zero digits and therefore not desbrice a whole number.

Vor 19 Stunden## Ekata Satya

is there any practical use in this paradox, because life on Earth is practical..

Vor Tag## Jeff Bautista

VSauce: What is infinity? Gojo Satouru: 😏

Vor Tag## Ricardo Ribeiro

This isnt properly explained in the sense that the whole sphere should be all the same color, a color that would be the mix of all the colors because each sphere of points contains all the points including the other sphere's points, so each of the decomposed spheres is equal to the combined sphere because its Just all the points on top of all the points, 6 layers of the same points

Vor Tag## eggynack

No, every position on the sphere is hit exactly once. And they are thus each only a single color.

Vor 13 Stunden## Balou

Never have i had a bad customer service as now, changing people’s room everyday and stuff ... Never coming back To Hilbert’s Hotel 📌

Vor Tag## Mello Gee

Good frickin' grief, dude. Just when I thought I was starting to finally grasp the Klein Bottle concept, someone on the 8chan discussion board decides to toss this Banach-Tarski concept at me, which ultimately led me here. You're a great teacher and you explain things very well in your videos, but this Banach-Tarski thing is hurting my brain. Next up: Quantum Entanglement and the Double-Slit experiment, for those of you who are not confused enough yet.

Vor Tag## Nghiep Luu

11:53 arccoss

Vor Tag## _xiiaoyang

I watch ur video when insomnia hits me

Vor Tag## MrDes1980

Дык частицы жеж в вакууме возникают их ниоткуда и анигилируют постоянно. Похоже это явления одного порядка.

Vor Tag## CJVPlayz

Only death but live soul can pass though infinity = ∞

Vor Tag## masterpotato 120

1+1=1 I don't know any more

Vor Tag## Frances Hogg

Doesn't this paradox prove that infinity doesn't exist?

Vor Tag## ELISA MOYA

that is how cels divide right?

Vor Tag## Miroslav Daniel Roshal

yutub be lik: twenti fiftin: nyet twenti sextin: nah twenti sebuntin: never twenti eiteen: not twenti neinteen: no TWENTI TWENTI: OKIE DOKIE LETS RECOMEND DIS TO EVERYWHUN!!!1 (P.S. Comment made in 2021) (P.S. This comment is a joke)

Vor Tag## Koji

I've watched this video maybe 25 times since I was 12 years old and I still don't understand how this works

Vor Tag## Samuel Magi locusts

I stoped believing after the rip up a dollar gain 2 dollars thing. You can’t get something from nothing.

Vor Tag## Mr. Johnson

@Samuel Magi locusts my exact thoughts when i saw the dollar thing

Vor 12 Stunden## Samuel Magi locusts

@Klejnot Nilu check out 1:54 of the video. You can clearly see that he ripped those two bills differently than the one in his hand.

Vor Tag## Klejnot Nilu

Pls say you're baiting

Vor Tag## Klejnot Nilu

Wait wtf

Vor Tag## Jason Boyle

I lost him at "hey guys"

Vor Tag## Samuel Magi locusts

It’s so hard to tell when he’s giving facts or making something up lol

Vor Tag## Roguewindow 758

Him: literally does a duplication glitch in real life Gta player: I’m listening

Vor Tag## Market Socialist

The gerog contour diagonal argument is proven incorrect via the true statement that there are as many even numbers as whole numbers, infinite will always match up with infinite for infinity contains all even the things infinity doesn't contain is contained in it... Otherwise it isnt infinite ;)

Vor Tag## eggynack

Why would that prove the argument incorrect? There are as many even numbers as whole numbers, prime numbers, integers, rational numbers, and infinite others. There are more real numbers than any of those.

Vor Tag## Bashir Weheliye

9:15 no hole will be left unfilled

Vor Tag## unaura

1 fuzzy ball = 2 fuzzy balls

Vor Tag## Kunwar

What I learnt from genius people in these videos : *To become a genius one needs to write with a marker instead of a normal pen*

Vor Tag## tecHow

The chocolate thing was easy

Vor Tag## Alexander Bozhilov

The circel's name is Bob

Vor 2 Tage## cash man

Watch this guy if u want a big brain

Vor 2 Tage## Shirley .R.

guys i have a shower thought: how much is flat? or - how flat is flat

Vor 2 Tage## Loop Innovation

Am I the only deranged by how he write the 8 number ? 5:46

Vor 2 Tage## C-moon and Pucci

fun fact: none of fun fact is a fact then does that mean this fun fact is a fact?

Vor 2 Tage## Minecrafty Cam

Wait... Wut

Vor 2 Tage## Keana Dianne

the fuck

Vor 2 Tage## Farras Alghazy

my brain:kaboom? me:yes rico kaboom

Vor 2 Tage## Zeke Korte

isnt the money thing illegal?....

Vor 2 Tage## Ar707x

THX MY BRAİN HURTS

Vor 2 Tage## Ar707x

he waste a dolar

Vor 2 Tage## Akash Krishnan U

@Legend oh ok my bad

Vor 12 Stunden## Legend

@Akash Krishnan U No its a literal crime to destroy US currency. it doesn't matter if its "his"

Vor 19 Stunden## Akash Krishnan U

@Legend no it is not,it is his money,he can do whatever he wants with it

Vor Tag## Legend

@Akash Krishnan U it’s a crime to destroy currency

Vor Tag## Akash Krishnan U

Bruh ,he gets a lot of money from these type of videos A dollar isnt really a big thing for him

Vor Tag## Prometheus

ive watched this video many, many times, and i never quite understand it, i guess part of it is the trouble i have connecting infinity to the real world. this problem, imo, only works when you assume that infinity is truly infinite, but that's sort of impossible for shapes outside mathematics i hope im wrong and something lights up in my head one day and suddenly i understand everything! that'd be better

Vor 2 Tage## Chili Ghost

So.. If it's possible to collide particles and get more particles, couldn't that mean it actually may be possible to build a machine that produces more energy than it uses?

Vor 2 Tage## Monti McShan

Watching this while baked is a trip ..

Vor 2 Tage## Judah Speece

You lost me at, “There’s a famous way to...”

Vor 2 Tage## Matthew Song

I totally wasn't fooled by the infinite chocolate bar trick... i hope

Vor 2 Tage## scott turner

Yes I'm retarded this proved it

Vor 2 Tage## Trevor Sabinson

I feel personally offended by all of this

Vor 2 Tage## Akash Krishnan U

@Trevor Sabinson he didnt draw it tho- Wtf is wrong with you

Vor Tag## Trevor Sabinson

Look how close he came to drawing a full blown swastica at 13:46

Vor 2 Tage## Louis Hazelwood

Who on earth would give this 20K thumbs down :(

Vor 2 Tage## vx vx

This is how Blender UV spheres works

Vor 2 Tage## Zendusi

S w e l l

Vor 2 Tage## Zeli Mitchell-Hopmeier

I just shat myself

Vor 2 Tage## John Marston

My brain stopped functioning

Vor 2 Tage## Dr Silverium

1+1 equal 1 lol

Vor 2 Tage## Doug Steel

There's no demonstrable relationship between maths and physics. That might sound crazy, but a relationship is stricter than tolerant correlation. On a practical level, I say practical, objects can't be closer together than the planck length the way they can in maths

Vor 2 Tage## Larry Pugsley

For anyone who watches vsauce, there’s hope. Every one of his videos are amazing!

Vor 2 Tage## Midnattsol

The doublicating sphere is an example of the difference between math and physics. While the description can be doublicated, not every described point contains matter. The matter of the object is not infinite, only the mathematical description of it is, as the description is an approximation, not an accurate representation. The more you zoom in, the bigger in relation will the distance become between described points which represent something real.

Vor 2 Tage## Panzerkampfwagen VI

1:18 ohh yeah, that is the good shit

Vor 2 Tage## CoolSkeleton95

1:40 : Mean while michael: *internal suffering*

Vor 2 Tage## John0693

So, mathematical points are bullshit.

Vor 3 Tage## xaralampis_

Me watching this video for the 5th time hoping that I am smarter enough to understand

Vor 3 Tage## J_Wolf_Cuber

bruh just use the bundle dupe glitch in the snapshots of 1.17 XD

Vor 3 Tage## Teodoro Marques

OMG THE SONG ON THE END, LOOKS LIKE A COMMON OPENING OF A BRAZILLIAN NOVEL

Vor 3 Tage## Keelan Thornton

Makes me think of Cellular mitosis.

Vor 3 Tage## javed ansari

Hey Michael, Do you think atoms and molecules or cells reproduce themselves like that

Vor 3 Tage## Yo The Profit

I’m running out of dollars are you sure I can make two dollars from a dollar lolololol

Vor 3 Tage## IVO

Música brasileira pra encerrar foi perfeita

Vor 3 Tage## robert bennett

Maybe it was through this process sub atomic particles multiplied during the big bang and began our universe.

Vor 3 Tage## JasonSpeeber

I spose the flaw of the whole theory here is that we can't even measure infinity (countable or not). So trying to base any kind of functional mathematical or physical model on it is kinda moot.

Vor 3 Tage## Bob Forrest

the dollars Michael ripped apart have different letters, try again

Vor 3 Tage## ok ok

Infinite money glitch but chocolate

Vor 3 Tage## Evan McDonald

Out of all the vsause videos if ever watched this one is by far my favorite. It gives me chills every time.

Vor 3 Tage## martin chagra

Me suffering when he cuts a dólar knowing that with that I could buy Tucumán

Vor 3 Tage## Asher Mastera

"Existence exists... or does it?". I promise you, that will be the next video.

Vor 3 Tage## Biscuit Tasty

17 paradoxes later

Vor 3 Tage## Case McDonald

This is nothing but a demonstration of why mathematics is limited.

Vor 3 Tage## SpartanKnights DAD

So if you believe in a Multi Universe then I believe this concept could be applied in the real world. If applied maybe a Universe/Dimension can exist on its own or within another Universe / Dimension to an Infinite degree.

Vor 3 Tage## Shogun FPV

Are we not going to talk about how he wrote the number 8?!

Vor 4 Tage## TEMPU

I AM WATCHING THIS VIDEO OR AM I ???

Vor 4 Tage## Aileen Laurel

The rural direction unusually pretend because dress assembly question until a successful authorisation. precious, burly sugar

Vor 4 Tage## MESS

so what about the chocolate again?

Vor 4 Tage## Cynthia Estrada

Whaaat?

Vor 4 Tage## CellGames2006

I don't think it's a good idea to annoy an infinite number of hotel guests by asking them to move to the next room... you might run into problems down the line.

Vor 4 Tage## Raw Hide

Is this how we’ll be able to teleport ourselves to other planets?

Vor 4 Tage## DEVESH MORE

If this banach tarki paradox applies to real world, we can create atoms and we can call ourselves God

Vor 4 Tage## Panders Person

Henry stickman: *breaks the bank* This guy: *breaks my brain*

Vor 4 Tage## Rik Raunaak

https://youtu.be/mUraYXBwrk8

Vor 4 Tage## freeflight 42

He could have used a pease of paper a stick a cloth but no he used money

Vor 4 Tage## Cool Bob

Okay I can’t be the only one whose brain literally hurts right now

Vor 4 Tage