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The Banach–Tarski Paradox

Vsauce August 1, 2015 Poledance 39 Comments 500 Views

Q: “What’s an anagram of Banach-Tarski?”
A: “Banach-Tarski Banach-Tarski.”

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39 comments

Mitsugiri Playz
November 21, 2017 at 4:43 pm

Im a 12 yrs old learning algebra …why am I here…

Reply
starcrafter13terran
November 21, 2017 at 4:51 pm

If antman retains his mass but can shrink to a microscopic level (or smaller), will he become a black hole?

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Alex Burov
November 21, 2017 at 5:19 pm

stupid paradox. If you delete some point clouds, its density always tends to <1

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Bortify
November 21, 2017 at 5:59 pm

The real question… what does IS mean ? What is IS?

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Daphne
November 21, 2017 at 7:18 pm

Infinity is always one more, it's moving always.

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ニア • Near
November 21, 2017 at 9:38 pm

why
did
you
rip
the
money
?????

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再见我不喜欢学中文
November 21, 2017 at 10:08 pm

Pay attention, Sarthak.

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Verina Flame
November 21, 2017 at 11:30 pm

Google is that uncountable infinity dictionary

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Rockemsockem Gaming
November 22, 2017 at 12:24 am

Destruction of us currency

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Andres Pascal
November 22, 2017 at 2:26 am

One question: that can be possible if the sphere has infinite "elements", but physically it is supposed it has a huge number, but a finite number of atoms… so, how this could be possible?

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Jeff Carpenter
November 22, 2017 at 2:47 am

What is infinity minus infinity

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Peoples KarmaSquad
November 22, 2017 at 4:43 am

My brain hurts.

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henry8smallwood
November 22, 2017 at 5:44 am

Wow, phenomena ARE empty. And simultaneously infinitely full.

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sunwolf87
November 22, 2017 at 6:44 am

Has Vsauce discovered the secret to infinite procedural generation? I know he didn't discover the paradox, but I love his analysis.

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Coshmaster
November 22, 2017 at 7:37 am

I just wanna know if the chocolate thing works

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diego da dealer
November 22, 2017 at 9:35 am

I'm way to high for this shit

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Pinapley
November 22, 2017 at 1:23 pm

If u r too lazy to count ,write infinity.

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Bob Bina
November 22, 2017 at 4:25 pm

Part of our physical world coinsidinces with something familiar here. After having two spheres, can we take one and perform the same operation to know have 3 spheres? Maybe not.

As we list the infinite points we need to add poles. The final trick to snatching out a duplicate sphere involves studying what would happen if at the very last step, a set of points changes it's direction of spin for one step, negating the final point listed in the set thus creating a similar infinite set which appears to be much of the sphere.

A particles in space is a point, not a sphere, but it does smoothly generate a sphere of effect.

As anyone would, Wolfgang Pauli assumed each "unit" in space time couldn't hold more than one particle, until he realized the that energy levels hold two not one. Two particles with all identical quantum identifier except one binary property, spin right or spin left.

If we only allowed moving up and right we could complete the same task without accidently producing a second identical sphere.

A point object is thought to be infinite and cannot spin, however, it's affect on spacetime is a sphere.

It seems that only non-spin defined spheres could appear as more spheres or two spinning spheres. This means that two spinning spherical objects of opposite spin could explain one infinite 1d non rotating point.

We see things in reality like this.

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kyutoreru
November 22, 2017 at 4:45 pm

This video skips an important point. It relies on an irrational step size to make sure that points are not encountered twice, and a proof that this works on the sphere. But the same basic construction can work even without this. Even if the same point can be reached with an infinite number of different paths, the Axiom of Choice allows us to pick exactly one of those paths to use as the color label. This can be an uncountably infinite number of choices made from countably infinite sets.

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Gunnar Nottmeier
November 22, 2017 at 4:46 pm

how to end Infinity: Infinity x 0

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swedesam
November 22, 2017 at 5:11 pm

In this case, just do it by weight….problem solved.

Reply
ImadeThisTo CommentOnTheDabShit
November 22, 2017 at 6:20 pm

UP LEFT DOWN LEFT UP RIGHT UP LEFT DOWN RIGHT RIGHT DOWN DOWN LEFT UP LEFT LEFT UP LEFT DOWN LEFT UP RIGHT UP LEFT DOWN RIGHT RIGHT DOWN DOWN LEFT UP LEFT LEFTUP LEFT DOWN LEFT UP RIGHT UP LEFT DOWN RIGHT RIGHT DOWN DOWN LEFT UP LEFT LEFTUP LEFT DOWN LEFT UP RIGHT UP LEFT DOWN RIGHT RIGHT DOWN DOWN LEFT UP LEFT LEFTUP LEFT DOWN LEFT UP RIGHT UP LEFT DOWN RIGHT RIGHT DOWN DOWN LEFT UP LEFT LEFTUP LEFT DOWN LEFT UP RIGHT UP LEFT DOWN RIGHT RIGHT DOWN DOWN LEFT UP LEFT LEFTUP LEFT DOWN LEFT UP RIGHT UP LEFT DOWN RIGHT RIGHT DOWN DOWN LEFT UP LEFT LEFTUP LEFT DOWN LEFT UP RIGHT UP LEFT DOWN RIGHT RIGHT DOWN DOWN LEFT UP LEFT LEFTUP LEFT DOWN LEFT UP RIGHT UP LEFT DOWN RIGHT RIGHT DOWN DOWN LEFT UP LEFT LEFTUP LEFT DOWN LEFT UP RIGHT UP LEFT DOWN RIGHT RIGHT DOWN DOWN LEFT UP LEFT LEFTUP LEFT DOWN LEFT UP RIGHT UP LEFT DOWN RIGHT RIGHT DOWN DOWN LEFT UP LEFT LEFTUP LEFT DOWN LEFT UP RIGHT UP LEFT DOWN RIGHT RIGHT DOWN DOWN LEFT UP LEFT LEFTUP LEFT DOWN LEFT UP RIGHT UP LEFT DOWN RIGHT RIGHT DOWN DOWN LEFT UP LEFT LEFT MY HEAD EXPLODED

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sergio salvador
November 22, 2017 at 6:21 pm

blown my mind….

Reply
Matthew Thomson
November 22, 2017 at 6:30 pm

At what point do you think he relised he was going to draw a swastica 12:13

Reply
ＫＥＮＮＹＥＵＳＯＵ＃ＬＯＬＩＣＯＮ
November 22, 2017 at 6:37 pm

5:46
7+2=8
:v

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lars 7500
November 22, 2017 at 8:19 pm

I'm going to be such a showoff tomorrow.

Reply
gespilk
November 22, 2017 at 9:49 pm

'Countable infinity' is oxymoron!
Infinity can not be counted because it is infinite i.e 'without a finish' !

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Sundaes are Nice
November 22, 2017 at 9:54 pm

I GOT I GOT IT… Wait what the heck what is he doing I don’t understand )))):

Reply
Nathan Darker
November 22, 2017 at 10:00 pm

With the hotel thing, you run out of rooms if you have infinity rooms AND infinity people. To keep it simple, we'll keep counted instances low, 0-10. You count 3 hotel rooms, and 3 people. Then you want to add an extra person to the already infinity people. You can not just count another hotel room, for with counting each instance of infinity, you must count all other instances of other infinite quantities at the same time, so when you count hotel room 4, you gain a new person with it, already in it. Count 5, 6, 7, 8, 9, 10, etc. You will never have an empty room for that extra person. Take infinity minus one, and the answer is infinity minus one. Say you subtracted the one person from hotel 6, hotel six just nolonger has a person inside, BUT all future counted instances of hotel rooms still come with a person inside. It's infinity, with one counted/defined instance vacant. Infinity mins one, is infinity minus one. Infinity plus one, is infinity plus one. Infinity divided by two, structure is not defined but we could say that every other counted instance, has a person, and doesn't have a person, then has one, then doesnt, and so on, forever. That's the only default way to guarantee it is halved, each counted instance must be counted in pairs. OR, a structure could be defined with it, like 1-5 are empty hotels, and 6-10 have people, and so on. Also, for uncountable small numbers, I'd say the smallest measurable units of distance, would be the smallest countable number, then theoretical numbers beyond that that are uncountable. Significance of this, I guess is unrelated, but, pi, they say it's infinite. But, having the smallest measurable number, we can have a sort of end to it, where anything else that continues, is theoretical. And the banach-tarski thing, i got lost lol and it takes too long for my millennial instant gratification needs, but I imagine it'd be similar to the superwebster thing, just subtracting from infinity and displacing everything else to fill in the gap.

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gespilk
November 22, 2017 at 10:22 pm

'countable' implies 'finish',
'infinity' implies 'no finish'.
therefore 'countable infinity' is oxymoron!
There is no paradox just fallacious use of words.

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SGDeGalvez
November 22, 2017 at 11:25 pm

There is no such thing as an 'infinite set'.

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Termi Nation
November 23, 2017 at 2:31 am

NO NO – you are using conceptual slight of hand. First slight of hand is this "countable" infinity verses "uncountable" infinity. You first act like its a requirement to count how many numbers in a set linearly. But that is not so. In a set of whole numbers from 1 through 9 I don't have to start at 1 and then linearly to 2 and so on to "count" the amount of numbers in a set. I can go to 8 first and say that's one number, cross it off so I don't recount what is already counted and then go to any other number in the set, say 3, and say that is a second number of the set, cross it off, and continue… third then fourth, irrespective of it's linear placement til l have counted up to the ninth crossed off, regardless of which ends up being the last number in the set to be counted, and I counted the set to contain nine whole numbers. If I had a set of [ 6 8 2 4] counted that would be a set of four even numbers. Doesn't matter if it's linearly arranged [2 4 6 8] or scrambled [4 2 8 6] it's still counting the numbers in a set. And that would be the same for an infinite set of whole numbers. Now lets go to your so called 'uncountable set of 'real' numbers. It's only uncountable when you apply that phony rule of a starting point and linear counting from that point. But as shown in the whole number counting that linear rule is PHONY. I don't have to count from a starting point and linearly from there. I can go to the half point, .5, and that's one 'real number' counted, then the quarter point, .25, and that's a second 'real number' counted, etc. etc. and I'm counting an infinite set. It's not an "uncountable" infinite set it's a countable set as the infinite whole numbers is a countable set. It's just that your phony rule conceptual slight of hand that causes an APPEARANCE, a false impression, of un-countability.
I can show the use of conceptual slight of hand in that 'points on a sphere' "math" you are pulling that debunks your whole "paradox" of something appearing out of nothing also.

Reply
psycronizer
November 23, 2017 at 2:40 am

do I EVER have a problem with this ! this whole business about higher infinities is such utter crap…and here's why. We all know what the definition of infinity is-anything at all that has no no end, ie, ongoing, perpetual, non stop, no big deal…BUT ! any further extrapolation of that immutable concept is SIMPLY an anthropic distortion of the simple reality of infinity, what I mean by that is it's just kind of metaphysical. It's like saying what has a higher value, infinity or infinity plus one, mathematicians would argue that the later has a higher value, but in reality that's just semantics, a human failure, because if infinity is the absolute then trying to add to it is meaningless, in exactly the same way that you can't add any value to the speed of light, because it's an absolute, although the VALUE of units is not infinite, the CONCEPT is…ie, 300,000 kM per second versus light as the highest possible velocity. I think it's just a silly thing that some pencil neck came up with one day whilst day dreaming about an infinite amount of pencil sharpeners….

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Ender Donovan
November 23, 2017 at 4:02 am

Ima not skip count 0.000000000000000000 (infinity years later) 001 0.0 (infinity years later 0002 0.000000000(infinity years later)
003 etc.

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famaz
November 23, 2017 at 5:15 am

There's an infinite number of rational numbers in a fraction.
Thinking is hurting.
y u do dis

Reply
Waste Basket
November 23, 2017 at 5:18 am

whats the outro music

Reply
Ryan Powell
November 23, 2017 at 5:29 am

takes about 4 watches to really understand everything

Reply
StormEL
November 23, 2017 at 6:36 am

My first vsauce vid. I'm scared to like it. Memes make me fear I'll un ironically like it

Reply
Robert C. Smit
November 23, 2017 at 11:37 am

I lost track in the middle, but got back from 19:00 m/s: There it all becomes infinitely important. Vsauce says that the universe isn't strange, but we are strange. And here for me, the Astavakra Gita comes in:
Last chapter, last words:
"For me who am blessed and WITHOUT LIMITATION, there is no initiation or scripture, no disciple or teacher, and no goal of human life.
There is NO BEING OR NON-BEING, no unity or dualism. What more is there to say? There is NOTHING OUTSIDE OF ME."
INFINITY CAN NEVER BE KNOWN, IT CAN BE LIVED.

Reply

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The Banach–Tarski Paradox

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