Head over and sign up to our Patreon for some exclusive behind the scenes footage, showing how the animations and illustrations for this video were made! www.patreon.com/posts/patreon-behind-126443880?Link&
tAp-GEti-FREE-RObUIx-rizz69 well they are not outright wrong actually. The only missing squares are 16 and 17. The only one without a square (that is with a false match) is 16 and the rest have squares for f(x) = (x+1)^2
What I always learn from watching these videos is that old school mathematicians and scientists threw the craziest shade at each other. Calling someone else's paper a "grave disease" is WILD.
Yeah, I noticed that. I also noticed that the video only IMPLIES that the insult "corrupter of the youth" was because of his mathematical theories. This was his former teacher; he may have been trying to tell people he was a pedophile.
@jonathancard4466 it was the teacher that called the student a corrupter of youth. Not to say the wording can't imply what you said it could, but to say that it was possibly also/instead a means to separate himself from blame as the teacher of someone he disagrees with.
That is human nature, we all do it, internet discussions is many times someone calling someone else dumb or worse and many of us aren't scientists... And IMO what made science so successful, was this fight between scientists, sometimes vicious, but the result was that science, only got better and better over time because of it. This is because scientists police each other, some spend entire carriers trying to prove other scientists wrong (using the tools of science, is not enough to claim someone is wrong) and so obvious charlatans were easily dismissed.
"A corruptor of the youth." Little Bimmy was such a good kid until he fell in with a bad crowd and started well-ordering infinite number sets. The societal decay.
❤❤Jesus can give you happiness Hey I don't know how to describe you how much happiness Jesus can give you except saying that that is a very promise of God himself that he would never leave nor forced us and that he would be with us through every trial and tribulation in every difficulty I just wanted to say jesus loves you he's changed my life and all the better he can change yours to because he loves you and died for your sins come to him and be saved and experience his love he'll always be by your side embrace christ as he wishes to know you god bless You are valuable and your life does have a purpose God made you perfectly in his image and he is a plan for your life Jesus loves you john 3:16 fear THE lord he died for your sins so that whoever believe in him will not perish but have eternal life and escape hell no one will enter heaven by living a good life but though true faith in him we will be saved We've all sinned and deserve hell but jesus paid the pricePLEASE PRAY THIS PRAYER FORM THE HEART AND TRLUY MEAN IT AND YOULL BE SAVED Prayer for giving your life to Christ Lord I recognise I am a sinner In need of the Savoir And I trust in the Lord and Saviour Jesus Christ Who is God come in human form to die for my sins And I confess my sins to you Asking for forgiveness Asking that you would make me a new creation and fill me with the Holy Spirit Lord I want to live for you from this Day forward Asking you would guide me To live and follow your commandments So I trust you Lord in Your life death and resurrection from this Day forward In Jesus name Amen
It isn't in that sense, if you are actually being serious. Suppose your child starts trying to write all the numbers in a 'serial order' to prove something or the other. Do you think he will end up anywhere? My thoughts are same for the guys who spent years studying knots, listing all possible knots. Look I respect their work, but they weren't around to harvest the fruit of their hard work.
I like how mathematicians are like “this is what I think is true” and then other people just decide whether to bully that person or build upon his/her revelation
Maybe it's not your fault, it's a weird thing for them to say that. ∞ is not a thing that appears in this sort of "list". First come 1, 2, 3 and so on and after that come ω, ω+1, ω+2 and so on. and ω *is* greater than any natural number.
It's actually pretty simple. Take every real number between 0.0 and 1.0, that's your first set of infinity (omega), then take every real number between 1.0 and 2.0, that's your second set of infinity (omega + 1), then 2.0 to 3.0 (omega +2). You just keep doing something like that. It's just a mathematical concept that really has no practical use.
@Soulsphere001 That explanation really isn't "pretty simple" at all, and I wager it isn't accurate either. I knew that cuz it just sounded so incomplete and wrong. Throwing it into AI, it confirmed your description isn't accurate at all. It had a section for each of your sentences, including the part where it has "no practical use." It noted that the very video you watched mentioned its use: It is essential in all of modern mathematics. Does that not sound useful to you? AI reply for proof: Based on the video's explanation of mathematical concepts, Soulsphere001's description is incorrect.The user's comment confuses ordinal numbers (order) with cardinal numbers (size) and misidentifies the nature of the real numbers. Here is the breakdown of why the description is wrong based on the transcript: 1. $\omega$ is not the set of Reals between 0 and 1 The Comment's Claim: "Take every real number between 0.0 and 1.0, that's your first set of infinity (omega)." The Correction: The video explains that $\omega$ (Omega) is an ordinal number used to describe the order of the natural numbers ($1, 2, 3...$) once they are exhausted 14:01. It represents a countable infinity. In contrast, the set of real numbers between 0 and 1 is uncountably infinite (a "bigger" infinity), as proven by Cantor's diagonalization argument 05:45. You cannot fit all the real numbers into the label $\omega$. 2. $\omega + 1$ is not the set of Reals between 1 and 2 The Comment's Claim: "...then take every real number between 1.0 and 2.0, that's your second set of infinity (omega + 1)." The Correction: In set theory, $\omega + 1$ simply means the next step after you have counted all the natural numbers. It is the order type of a set like $\{1, 2, 3, ..., \text{last}\}$.The video explains that when well-ordering the reals, you assign indices: $X_1, X_2... X_\omega, X_{\omega+1}$ 14:21. $\omega + 1$ is just the index of the single number that comes after the infinite sequence of natural numbers; it is not an entire interval of real numbers. 3. These concepts are practically useful The Comment's Claim: "It's just a mathematical concept that really has no practical use." The Correction: The video explicitly states that the Axiom of Choice (which relies on these ordinal concepts to well-order sets) is "incredibly useful" 31:22 . It allows mathematicians to shorten proofs from 20 pages to half a page and is "essential" for modern mathematics, such as in the fields of topology and functional analysis. The video concludes that without it, you are "working with both hands tied behind your back" 32:28 . Summary: The commenter is trying to describe a way to stack infinities, but they are incorrectly applying countable labels ($\omega$) to uncountable sets (intervals of real numbers).
They did not even cover Cantor's power set theorem proof, which shows how to create an infinite hierarchy of infinite sets with different and ever-increasing cardinalities. I kept expecting it to come up, but it probably deserves a whole video of its own.
The key to understanding infinite is, to me, to look closely at the word: in-finite, in other words not finite. It's an adjective. Same as "red". We get in trouble when we try to use it as a noun. The same as we'd confuse ourselves if we tried to treat "red" or "loud" as a noun. Are there different kinds of red things? Sure. In the same way, there are different kinds of things that are not finite, that are infinite.
This is kinda true in almost any fields of study. And there is a reason for this. Like, take any field of study and imagine someone coming and telling everyone that everyone are wrong and they made a discovery that shows everyone are indeed wrong. Okay... what is their proof? Well, they don't have a proof but they know that they are right and everyone else is wrong. Imagine how that would grate at everyone's nerves. So much so if that said person keeps talking about it and goes on youtube and social media. They have made a revolutionary discovery, without any proof that they are right mind you, that shows everyone, even the greatest minds of the past, are wrong!
Imagine if back then some kid corrected us and said it's not infinity PLUS one but rather next number AFTER infinity?!?! Ah the endless arguments that would have followed after :)
@iconicmessi123 Yeah who ever thought that when your sibling would say, "That's impossible, you can't have more then infinity," we didn't know we were having a mathematical argument of the ages.
Nah, 'power level' is very clearly a cardinal (a number that measures size) and 'infinity plus 1' only makes sense for ordinals (numbers that define an order).
Mathematically speaking sorting a set only requires you to be able to say whether a number is bigger or smaller than another one. They don't actually come after infinity, but you may decide that any negative integer is bigger than any positive integer and that's it. What you lose is the capability to reach every number starting from zero in a finite number of steps, that's why they "come after infinity".
@Marcos_ateu_espiritual The first number in the well-order is 0, then we get 1 then we have 2 and so on, all the positives in increasing order, after those we place -1, then -2, then -3 and so on. This is a well defined order on the sense that if I give you any pair of numbers you can tell me which comes first in this particular ordering. E.g. 100 and -7, well 100 is first and -7 comes later. -17 and -5, here -5 first then -17 later. Try it, give me any pair of numbers and I'll tell you their order. In fact give me any subset and I can tell you the order. So they are well-ordered. To give them each a position or rank (or ordinal) though we have to make up a new type of number since we can give 0 rank 1 as it is first, then 1 is second so rank 2, and so on labelling all the positives numbers with a normal natural number. But what rank do we give to -1, -2 etc. well we just make up a new symbol say w (should be omega but I don't have that on my phone 😢). Then give -2 the rank w+1, and -3 w+2 etc. Because we want the order to have 100 before -7 then the rank w+6 must come after rank 101, in fact w must come 'after' every normal natural number. It's strange I get that, but it also makes sense. But please don't try to count up to w, you'll be there a while 😊.
Is this video a "META" post? cuz i feel i already seen this video before or at least the part of mapping all real numbers between 0 and 1 to natural ones.
Ask your doctor if The Axiom of Choice is right for you. Side effects may include unmeasurable sets, self duplicating objects, getting publicly slammed by your favorite professor, and bouts of insanity. Do not use The Axiom of Choice if you get paid based on the length of your prof or if you live in a reality that does not contain The Axiom of Choice. If you experience any of these side effects while using The Axiom of Choice, stop writing math papers immediately and become a philosophy major.
i mean parallel lines has a similar story that theory still haven’t been proven to my knowledge so than come in non euclidean space cause apparently lines might not actually be able to be parallel 😂 it confuses my brain and i love it
tbf, pretty much everything new is labeled that way up until today, be it changes in how things are being viewed, new media (music genres, games and so on) or maths - as soon as something changes or something new is being made it's automatically bad all while people go on to ignore actual bad things going on.
Beefs between geniuses are way more vicious than those between dumb people. Newton spend considerable amount of energy on trying to destroy Leibnitz for example
I learned about the diagonalization proof in one of my first college math classes. I said something like “this doesn’t seem like math to me, he kinda just found some creative logic to prove his point.” The prof whipped around, the most excited I’ve ever seen anyone be, and said, “my friend! That’s what mathematics is!!” ❤
@Bluebloods7no no no, "cool story bro" is for when someone makes an obviously false or irrelevant story for manipulative purposes, not just when you don't care: did you not cover this in your internet classes?
unless talking about real gifted mathematical minds, it's all about exercising a certain language, the math language. i can read and write in a few languages but understand nothing in others :)
I live only a stone-throw from Cantor's resting place and have workrelated ties to him. He is one of the unsung geniuses of our time and I'm really glad to see his work celebrated here. Thanks Veritassium.
My father was a mathematician and he would have loved this. He'd yap abt math history and I'd just nod and listen and not understand a word. I miss him so much.
Same thing with my grandfather and the history of world affairs. I was too young and naive to understand or even take interest in the things he knew. Now not a week goes by where I don't at least once wish I could pick his brain.
The moment Derek said (omega) the flash back hit me about the time Vsauce was counting past infinity i really missed this kind of videos about pure math
@gastfaremis1136 why is this such a common theme in these comments? is this not beautiful to you? is math not beautiful? how is it mentally distrubing to do math?
Now I know that Buzz Lightyear wasn't overexaggerating when he said "to infinity and beyond!" ...and maybe "overexaggerate" isn't really redundant after all...
@noonehere6994 I had the same question but I found something, look up "veritasium 37", he's made a video on this number , that it is very often chosen randomly
My wife is a math and chemistry major and watching stuff like this makes me glad I stuck to chemistry. It's interesting but also makes my head hurt and makes me appreciate my wife even more. Celebrating 25 years today and looking forward to many many more.
May God bless your twins, wife, and you. I don't have the answers, life is too short to know everything, But I believe there's a creator to everything, and everything in the infinite it has conscious understanding of Even if you created a time machine, and studied everything, I do believe you'd only find God at the center of everything. I do believe God came as a human named Jesus, to reach us 1 on 1. I don't have an understanding to everything, but I believe there is power in the name Jesus. Through Jesus everything was created, and everything is for Jesus. When you start looking at every dot on your body, every color, every sound, every thought, dream, everything It goes on infinitely... I believe Jesus was there before the big bang Before the beginning of everything And I hope in the end of our lives we get to see God. I trust God loves us, and there's no knowing if anything is real, so I want to believe God loves you, and I pray he watches over you. In Jesus name amen
you could say she used her axiom of choice to find you out of infinite possibilities. Technically, kids are the duplication factor; if you want to look at it in a more biological frame. I'm a 3D artist and I had no idea what I was getting into, since the strong foundation needed is both creative and mathematical (at least logically;) but out of those two I found a happy joy in quantum physics studies. My husband is a news producer; almost my complete opposite. Where Im stoic he's incredibly emotional. He's tall, I'm short. We also seem to follow patterns of change that flip certain traits between the both of us. After 17 years I'm convinced people are just as able to be considered physical representations of inverse kinematics. I'm happy to hear about your marriage. May it stay strong an your life be graced by love as long as exitance is true.
One of the favourite microblogging posts I've made was: "My favourite anagram of Banach-Tarski is Banach-Tarski Banach-Tarski." No engagement, but at least it made me laugh.
@borovitinshund Well even in Medieval times certain knights on a certain quest knew the Earth's is not in fact flat or spherical but is in fact Banana shaped so that makes perfect sense to me!!
Bro published a paper saying that you can divide out 1 infinitely, and then immediately started getting death threats. "The Georg Cantor situation is CRAZY"
Victorian mathematicians are ridiculously over-dramatic. Cantor: "I have this esoteric mathematical theory that I haven't been able to prove yet and that almost nobody outside of higher mathematics understands. It also has almost no application in the real world, and almost no one will ever hear about it because it is so advanced." Kronecker: "THINK OF THE CHILDREN!!!!!!"
Victorian? Cantor, Zermelo, Tarski, Banach, Kronecker, non of them english and non of them vassals of the british empire. Nineteenth-century mathematicians is the appropriate term, even Belle Époque mathematicians is more appropriate since they were continentals.
Other esoteric mathematical theories of the time include the theory of algebraic curves, which can now be seen in computer graphics, robotics, and guided missiles. All math is theoretical until it isn't
The resolution to the Axiom of Choice paradoxes is the most mathematician thing imaginable: "the validity of the axiom has been left as an excercise for the reader"
Andrew Tate Hears About the Guy Who “Broke Math and Himself” It started as a casual conversation-Tate sitting in a podcast studio, legs wide, mic too close, ranting about how men “need to reject weakness” and “wake up at 3 a.m. to bench their fear.” He was mid-rant about how algebra is useless for millionaires, when one of the interns casually mentioned: “Yeah, but what about that one guy who broke math and himself? You know, the one who solved some equation that didn’t exist and then just… collapsed emotionally?” Tate froze. “What?” “Yeah, he like… disproved something? Invented a new number or dimension? I dunno. But he cried for 8 hours and now he teaches part-time in Vermont.” Tate’s eye twitched. His lips parted. His sunglasses slid down slightly-the alpha’s version of cardiac arrest. “You’re telling me… a man… broke math… and wasn’t celebrated?” “Nah, he kind of broke himself too. Shaved half his head and gave his cat power of attorney. Total collapse.” Tate stood up. “That’s not masculine. That’s not logic. That’s chaos in socks.” He paced. “Real men conquer math. They don’t let numbers defeat them. Math is for discipline. For bank accounts. Not… emotional collapse.” The intern shrugged. “He rewrote three laws of physics, though.” Tate turned toward the camera. Face flushed. Voice shaking with rage. “Any man who breaks math is a man who was never strong enough to multiply. Real men divide pain and subtract weakness
i just absolutely love the narrative of a man who went insane because he knew he was right, he just couldn't explain why he was right until someone came later to explain why he was right
I'm autistic - I have this problem some times. I explain a really simple thing to a person and they totally don't get it. Then they will get another person and I will explain the super simple thing and they will not get it. I can only assume the words coming out of my mouth do not match the thoughts in my head.
@piccalillipit9211 I think it is the opposite. The words coming out of your mouth do not match the thoughts in the other person's head. Do not assume that your explanation is wrong. It could be as simple as a matter of two persons talking two different languages. The difficulty relies on discovering a common language, which is something rather difficult to do, no matter if you are autistic or not. Just try not to get frustrated by the lack of common ground, if it happens.
With natural numbers and square numbers, what happens when you do it the other way? Every square is a natural number, so match every square number to it's natural number. Now you have matched an infinitely many square numbers, but have not matched every single natural number. That seems to lead to the idea that infinity does have differences in size.
Every time I see something about infinity I'm always like "please stop trying to do definable operations using indefinable concepts" it frustrates me to no end.
@Ethan-uf4jp I made a much larger set of comments but essentially, infinity is undefined, if you were to define it it would no longer be infinite and you can't do any math using undefined values where the result isn't also undefined.
I can’t understand it. Here is what I don’t get: you can indeed make a new number by serialization that is different from every other by one. But why can’t we do that with natural numbers? Why does “0.” matter? I can’t agree with this proof just based on my likely naive logic that by removing that ‘0.’ prefix from the new real number we will create a new natural number
This reminds me when I was a child and I used to play imagination battles with my brothers and friends saying things like: "My shield has infinite protection", and they would go: "Oh yeah?, my sword has infinite + 1 strenght" and so on
Even more remarkable is, that Chuck Norris counted to both the end of countable infinity as well as the uncountable one. Both TWICE! He would break all your infinity shields and swords!
😂 yeah, I also compete my friend on elementary school about something infinity, I thougt I win when I claim something infinity, but he revenge with 2 times infinity 😂 until I start think about infinity time infinity, but he answer with 2 time infinity of 2 time infinity which is became more absurd and nonsense
I've thought exactly about almost everything stated in this video. Literally. I believe I shall come up with the Infinite Energy Equation one day. It's always been something that has constantly bothered me and very very little things bother me for such a long time. I've had dreams about uncovering it. If I do, hopefully, I will come back to this post. I will try and publish the equation to the whole world, though it will be really hard for everyone to know about it before I'm killed. You all should just know that if this equation is used to create weapons because of the way you crazy beings like to kill each other, it will be the end of everything.
Buahahhaha infinited E don't existing or you treat whole E changes as once and conservation of E as constant and termination and death not existing but not in a Buddist way, some worms eat you, than birds eat worms, than maybe plants benefit from a pop and create some rocks which will be flushed by water or create oil and deliver E to planet than maybe you became part od volcan ground for some plants.... I just don't see a way to became a human again.... Sorry Buddists
This video gave me flashbacks to old Vsauce videos on Banach-Tarski and counting past infinity. I’m so glad you’re still posting videos, please continue
Right after his intro where he described what we were about to learn about I thought this would be about Banach-Tarski and thought about that Vsauce video
You now have a little more detail about what you don't know, and you are now familiar with the name Cantor and the fact that he showed infinity is a lot more complicated than we once thought. Small gains maybe, but gains nevertheless.
I was 13 when Michael from Vsauce released his video about the Banach-Tarski Paradox… now seeing this almost 10 years later has brought back so many memories… but the fact that I remember so much goes to show how important this kind of educational content is. Amazing job 👏
Oh come now, you can't reasonably hold someone to their subtitles when 99.0000001% of subtitles on RUclips are inaccurate. But yeah, roast them on the graphic. Get em! 😂
@Ayelis Not to harp on this point, but auto-generated RUclips subtitles are different. In this case, I believe Derek himself uploaded the subtitles and simply didn't count the zeroes. :P Of course, my objection is tongue-in-cheek, but it's something I noticed!
When I watch a Veritasium video that is more focused on science, I follow along quite well. When it's maths-heavy, my brain in minute one is "yes!", then "yes." then "...yes" until about halfway through when my brain politely asks me to rewatch the first half again. This is just bonkers.
@PhilipBarkley It's not just you. Cantor's math was so mind fuckery (endearing), that his teacher called him a corruptor of the youth. I really hope that sentence doesn't get misunderstood.
There is no thing as a truly random number or occurence, we live in a deterministic system, it only appears chaotic because we aren't aware of all the variables
As a german mathematician myself (focussing on differential topology) this story makes me proud. All these men contributed to my passion so much and seeing this story presented sparks my hope, that more people learn that math can be so fascinating and is even material for a captivating plot.
Hi, I am interested in learning advanced mathematics. Are there any books you recommend for self study, or would you say doing a bachelor at a university is the better choice?
@Leandery9i Well, I would say if you have the opportunity for a BA at a university, I would go for it any day. Math is so broad and this way you will gain insight into everything on a high level. Find out what exactly it is that fascinates you and cherish it! :)
Implies ultrafinitism - likely nothing is infinite in the actual universe, and human invented infinites-involving math might simply be contradictory in the end
@ReverseDominion How so? If the axiom itself is indeterminate until used or observed, does that mean choice doesn't exist until it's used or observed? The axiom is only an illusion if you decide it is an illusion, meaning choice / free will or lack thereof is itself a choice... this again implies choice must exist, but can be ignored.
"Saying that infinity drove Cantor mad is sort of like mourning St. George's loss to the dragon: It's not only wrong, but insulting" -- David Foster Wallace, _Everything and More_
No. 3-4-5-6-7 - you can make a straight. I believe unsuited 3-8 is the next worst hand, but then I’d have have to check the chance of a runt coming to high card vs a straight. But given that 2-7 is worst, I would assume so, otherwise 2-6 would be worse than 2-7.
When my wife says “what would you like for your birthday present?”, the problem isn’t even that I don’t have an axiom of choice - within a set or sub-sets, it’s rather that what I want doesn’t fit into any pre-existing ser or sub-set.
Wow, what a video. Making the connection between the "axiom of choice", and the "axiom of parallel lines" in geometry, absolutely blew my mind in the best possible way. Beautiful.
I agree. People started by arguing whether these axioms were true or not, or tried to prove them. Then models were found in which they are true, and models in which they are false. For the parallel postulate, the debate is long over, but for AOC, it is still controversial, but we are heading towards a more mature view.
3 things that fast-tracked my financial growth: 1. Taking action NOW instead of waiting 2. Reading Encoded Abundance 3. Focusing on consistency over motivation
A small piece of advice in animations: use mild (doesn't even have to be noticeable) hue shift in large gradients across the screen. This will avoid banding in low data frequency areas, especially at lower resolutions.
@lonestarr1490 Banding happens because there are as many as 2160 pixels of width, but only 256 possible values for each color, meaning each color happens for bands between 8 and 9 pixels wide. Adding a hue shift improves this banding (though it doesn't fully eliminate it) by adding an additional color that can break up the banding by blending in its own banding pattern.
@lonestarr1490 Just to add, that 2160 divided by 256 values math works out only in perfect uncompressed conditions. In practice, with typical video compression, it can be even worse, due to quantization and color space conversions, chances are you'd get even fewer than 256 bands (or even some unwanted colors around transitions), thus increasing the need for doing hue shifts, or steeper gradients, or dithering, or something else, to mask the issue.
I don't see a way to add this unless you have custom texture for each gradient and not using any built in ones from the editor. But I don't know his workflow.
I’m actually working on Axiom of Choice² about choosing whether or not to include the Axiom of Choice in your system. Well, I’m not actually working on it. I should. But it’s lunchtime. And I’m hungry.
Likely not random numbers. 37 is a reference to one of his previous videos, and 42 is the number of his channel logo. You can spot it on his channel banner,for example.
I took biology for 1 semester then I switched into chemistry then I switched into physics then finally I switched into math. Looking back, biology is like for kindergartners
@reptileandad The need for people in a science field to insist that their particular science field requires one to be much smarter than people in other, unrelated science fields is usual the best proof to have that the person you're talking to is, in fact a childish buffoon.
I have a tractor. It has a throttle and a hydrostatic drive which increases and decreases speed, depending on the RPM. It is listed as having infinity speeds. Someone asked me how many speeds it has (since some tractors have numbered speeds, and only have, say 5 speeds). I say it has infinite speeds. He says "yea, right. So you can go 100 miles an hour?" I say no, I can't go ALL of the speeds, I can just go infinite speeds. There is still a minimum and a maximum. He stares at me and rolls his eyes. He walks away.
It doesn't have infinite speed It has infinite number of possible speeds Although due to quantum mechanics its probably a very small number like 10 to the 35 or something
Very happy that Cantor was able to see his work taken to the axiom so after his mental breakdown his hard work and thoughts were asserted and respected.
I need to ask, is the origin of your name the same meaning as the word quoted on the video or is there another story and you just happen to be here watching a random video which quotes a word ridiculously close to your name by coincidence? This stuff intrigues me
I’ve always had the outlook that the mathematical axioms we create to describe things that happen in the universe aren’t actually the rules that the universe follows, but frameworks that characterize our observations of how things happen. It’s like finding an expression that properly matches an experimental data curve. As such, I think this extends to logic itself. Our deductions about what should make sense are based on the patterns we observe, but the universe isn’t actually bound by those patterns, it just tends to follow them.
Head over and sign up to our Patreon for some exclusive behind the scenes footage, showing how the animations and illustrations for this video were made!
www.patreon.com/posts/patreon-behind-126443880?Link&
Ok
Hopefully not AI
tAp-GEti-FREE-RObUIx-rizz69 well they are not outright wrong actually. The only missing squares are 16 and 17. The only one without a square (that is with a false match) is 16 and the rest have squares for f(x) = (x+1)^2
This was a lame explanation of the axiom of choice it didn't have any mathematical reasoning to it at all.
After this video I promise to close axioms of Goedel. within a week. I will prove unprovable. Like I have proved my ToE.
What I always learn from watching these videos is that old school mathematicians and scientists threw the craziest shade at each other. Calling someone else's paper a "grave disease" is WILD.
Yeah, I noticed that. I also noticed that the video only IMPLIES that the insult "corrupter of the youth" was because of his mathematical theories. This was his former teacher; he may have been trying to tell people he was a pedophile.
Corrupter of youth famously was the accusation that got Socrates killed is was 100% a reference to teachings and not anything else.
Considering Cantor was trying a proof by God, they were right
@jonathancard4466 it was the teacher that called the student a corrupter of youth. Not to say the wording can't imply what you said it could, but to say that it was possibly also/instead a means to separate himself from blame as the teacher of someone he disagrees with.
That is human nature, we all do it, internet discussions is many times someone calling someone else dumb or worse and many of us aren't scientists...
And IMO what made science so successful, was this fight between scientists, sometimes vicious, but the result was that science, only got better and better over time because of it.
This is because scientists police each other, some spend entire carriers trying to prove other scientists wrong (using the tools of science, is not enough to claim someone is wrong) and so obvious charlatans were easily dismissed.
"A corruptor of the youth."
Little Bimmy was such a good kid until he fell in with a bad crowd and started well-ordering infinite number sets. The societal decay.
They said the same thing about Socrates too...
Everyone knows that the axiom of choice is a gateway axiom for more harmful things like getting addicted to set theory paradoxes.
It was more like jealous
❤❤Jesus can give you happiness Hey I don't know how to describe you how much happiness Jesus can give you except saying that that is a very promise of God himself that he would never leave nor forced us and that he would be with us through every trial and tribulation in every difficulty I just wanted to say jesus loves you he's changed my life and all the better he can change yours to because he loves you and died for your sins come to him and be saved and experience his love he'll always be by your side embrace christ as he wishes to know you god bless You are valuable and your life does have a purpose God made you perfectly in his image and he is a plan for your life Jesus loves you john 3:16 fear THE lord he died for your sins so that whoever believe in him will not perish but have eternal life and escape hell no one will enter heaven by living a good life but though true faith in him we will be saved We've all sinned and deserve hell but jesus paid the pricePLEASE PRAY THIS PRAYER FORM THE HEART AND TRLUY MEAN IT AND YOULL BE SAVED Prayer for giving your life to Christ Lord I recognise I am a sinner In need of the Savoir And I trust in the Lord and Saviour Jesus Christ Who is God come in human form to die for my sins And I confess my sins to you Asking for forgiveness Asking that you would make me a new creation and fill me with the Holy Spirit Lord I want to live for you from this Day forward Asking you would guide me To live and follow your commandments So I trust you Lord in Your life death and resurrection from this Day forward In Jesus name Amen
It isn't in that sense, if you are actually being serious. Suppose your child starts trying to write all the numbers in a 'serial order' to prove something or the other. Do you think he will end up anywhere? My thoughts are same for the guys who spent years studying knots, listing all possible knots. Look I respect their work, but they weren't around to harvest the fruit of their hard work.
I like how mathematicians are like “this is what I think is true” and then other people just decide whether to bully that person or build upon his/her revelation
Mathematics is a school playground of scholars.
Or Both
`
I dont like it🤪
It’s not mathematicians, it’s society. Anyone who goes against the grain from what society believes will be ostracized.
THEN THE WHOLE WORLD IS A SCHOOL PLAYGROUND!!
"omega numbers aren't bigger than infinity they just come after infinity"
my head hurts
Maybe it's not your fault, it's a weird thing for them to say that. ∞ is not a thing that appears in this sort of "list". First come 1, 2, 3 and so on and after that come ω, ω+1, ω+2 and so on. and ω *is* greater than any natural number.
It's actually pretty simple. Take every real number between 0.0 and 1.0, that's your first set of infinity (omega), then take every real number between 1.0 and 2.0, that's your second set of infinity (omega + 1), then 2.0 to 3.0 (omega +2). You just keep doing something like that. It's just a mathematical concept that really has no practical use.
@Soulsphere001 I finally understood, thank you
@danielasanchez3512
You're welcome.
@Soulsphere001 That explanation really isn't "pretty simple" at all, and I wager it isn't accurate either. I knew that cuz it just sounded so incomplete and wrong. Throwing it into AI, it confirmed your description isn't accurate at all. It had a section for each of your sentences, including the part where it has "no practical use." It noted that the very video you watched mentioned its use: It is essential in all of modern mathematics. Does that not sound useful to you?
AI reply for proof:
Based on the video's explanation of mathematical concepts, Soulsphere001's description is incorrect.The user's comment confuses ordinal numbers (order) with cardinal numbers (size) and misidentifies the nature of the real numbers. Here is the breakdown of why the description is wrong based on the transcript:
1. $\omega$ is not the set of Reals between 0 and 1
The Comment's Claim: "Take every real number between 0.0 and 1.0, that's your first set of infinity (omega)."
The Correction: The video explains that $\omega$ (Omega) is an ordinal number used to describe the order of the natural numbers ($1, 2, 3...$) once they are exhausted 14:01. It represents a countable infinity. In contrast, the set of real numbers between 0 and 1 is uncountably infinite (a "bigger" infinity), as proven by Cantor's diagonalization argument 05:45. You cannot fit all the real numbers into the label $\omega$.
2. $\omega + 1$ is not the set of Reals between 1 and 2
The Comment's Claim: "...then take every real number between 1.0 and 2.0, that's your second set of infinity (omega + 1)."
The Correction: In set theory, $\omega + 1$ simply means the next step after you have counted all the natural numbers. It is the order type of a set like $\{1, 2, 3, ..., \text{last}\}$.The video explains that when well-ordering the reals, you assign indices: $X_1, X_2... X_\omega, X_{\omega+1}$ 14:21. $\omega + 1$ is just the index of the single number that comes after the infinite sequence of natural numbers; it is not an entire interval of real numbers.
3. These concepts are practically useful
The Comment's Claim: "It's just a mathematical concept that really has no practical use."
The Correction: The video explicitly states that the Axiom of Choice (which relies on these ordinal concepts to well-order sets) is "incredibly useful" 31:22 . It allows mathematicians to shorten proofs from 20 pages to half a page and is "essential" for modern mathematics, such as in the fields of topology and functional analysis. The video concludes that without it, you are "working with both hands tied behind your back" 32:28 .
Summary: The commenter is trying to describe a way to stack infinities, but they are incorrectly applying countable labels ($\omega$) to uncountable sets (intervals of real numbers).
Before watching this video, I knew what Infinite was, now I don't. Thank you.
They did not even cover Cantor's power set theorem proof, which shows how to create an infinite hierarchy of infinite sets with different and ever-increasing cardinalities. I kept expecting it to come up, but it probably deserves a whole video of its own.
Infinite means never ending. It's not a number.
The key to understanding infinite is, to me, to look closely at the word:
in-finite, in other words not finite. It's an adjective. Same as "red".
We get in trouble when we try to use it as a noun. The same as we'd confuse ourselves if we tried to treat "red" or "loud" as a noun.
Are there different kinds of red things? Sure. In the same way, there are different kinds of things that are not finite, that are infinite.
You still. Just because a mentally ill person found logic in nonsens. Dont listen to people who define themself as intelligent
The set of sane people who look into infinity without going mad is the null set.
math beef is so funny like “oh you can’t find a way to match some number sets? i’m going to bully you so bad you need to go to a psych ward”
new torture method unlocked: muffin
My wife has a Ph.D. in math, and let me tell you, these people take this stuff SUPER seriously. It's basically their religion.
This is kinda true in almost any fields of study. And there is a reason for this.
Like, take any field of study and imagine someone coming and telling everyone that everyone are wrong and they made a discovery that shows everyone are indeed wrong.
Okay... what is their proof?
Well, they don't have a proof but they know that they are right and everyone else is wrong.
Imagine how that would grate at everyone's nerves. So much so if that said person keeps talking about it and goes on youtube and social media. They have made a revolutionary discovery, without any proof that they are right mind you, that shows everyone, even the greatest minds of the past, are wrong!
@SamplePerspectiveImporta-hq3ip Same, but I am a high school asian
@Mech3126 "sAmE, bUt i aM a hIgH sChOoL aSiAn" 🤓
nicca go prepare for JEE or something
“Yeah? Well my guy’s power level is infinity PLUS ONE.”
So what you’re saying is 8 year old me was a genius..
infinity raise to infinity. Mahn, I miss those...
Imagine if back then some kid corrected us and said it's not infinity PLUS one but rather next number AFTER infinity?!?! Ah the endless arguments that would have followed after :)
It's not that your power level is infinity plus one, it's that the other kids has rank infinity, and you're ranked one above them.
@iconicmessi123 Yeah who ever thought that when your sibling would say, "That's impossible, you can't have more then infinity," we didn't know we were having a mathematical argument of the ages.
Nah, 'power level' is very clearly a cardinal (a number that measures size) and 'infinity plus 1' only makes sense for ordinals (numbers that define an order).
0:37 37 at 37 seconds while 37 is the most randomly picked number.. i see what you did there 👏
Was going to comment this. Thank you
No joke I said 37
Immediately thought the same thing and came to the comments.
Knew he was going to say 37 the moment he said random number, 42 is the cherry on top.
And 37 likes on your comment
37 is a number that we use most in our lives. He has a video on this
“…they come after infinity.” This is where I leave the room.
Mathematically speaking sorting a set only requires you to be able to say whether a number is bigger or smaller than another one. They don't actually come after infinity, but you may decide that any negative integer is bigger than any positive integer and that's it. What you lose is the capability to reach every number starting from zero in a finite number of steps, that's why they "come after infinity".
Well but they you can't say that both sets (negatives and positives) are begining from a precise point because *infinite* is not a number.
@Marcos_ateu_espiritual The first number in the well-order is 0, then we get 1 then we have 2 and so on, all the positives in increasing order, after those we place -1, then -2, then -3 and so on. This is a well defined order on the sense that if I give you any pair of numbers you can tell me which comes first in this particular ordering. E.g. 100 and -7, well 100 is first and -7 comes later. -17 and -5, here -5 first then -17 later. Try it, give me any pair of numbers and I'll tell you their order. In fact give me any subset and I can tell you the order. So they are well-ordered.
To give them each a position or rank (or ordinal) though we have to make up a new type of number since we can give 0 rank 1 as it is first, then 1 is second so rank 2, and so on labelling all the positives numbers with a normal natural number. But what rank do we give to -1, -2 etc. well we just make up a new symbol say w (should be omega but I don't have that on my phone 😢). Then give -2 the rank w+1, and -3 w+2 etc. Because we want the order to have 100 before -7 then the rank w+6 must come after rank 101, in fact w must come 'after' every normal natural number. It's strange I get that, but it also makes sense. But please don't try to count up to w, you'll be there a while 😊.
They came after infinity, but little did they know infinity was ready for them.
Is this video a "META" post? cuz i feel i already seen this video before or at least the part of mapping all real numbers between 0 and 1 to natural ones.
I love that math was seen as so widespread in its importance that they thought a mathematical theorem would corrupt the youth lol.
I imagine he meant young people studying to go into mathematics, but it's still a pretty funny thing to say.
You missed the point. If a falsehood is believed true, the resulting generations will pay the penalty
No it's actually through. A friend of mine started studying elementary school calculus and then ended up getting addicted and getting divorced
Imposible is corrupt youth by math, because they must benefit from it
i would have loved to see a battle between euclid and diogenese LMFAO
Ask your doctor if The Axiom of Choice is right for you.
Side effects may include unmeasurable sets, self duplicating objects, getting publicly slammed by your favorite professor, and bouts of insanity. Do not use The Axiom of Choice if you get paid based on the length of your prof or if you live in a reality that does not contain The Axiom of Choice. If you experience any of these side effects while using The Axiom of Choice, stop writing math papers immediately and become a philosophy major.
proof*
@JorgetePanete (using measuring tape on prof)
This is my favorite comment today.
Try point-free Topology?
What does this so-called “reality” have to do with anything in mathematics?
"And before you know it, you have infinite balls" -Veritasium
I know a couple of guys who have infinite balls.
It’s just an item duplication glitch, that’s all
You can either have unlimited bacon but no balls, or balls, infinite balls, but no balls
I love how after 30 years of mystery, the answer was "well it depends" 🤣🤣
i mean parallel lines has a similar story that theory still haven’t been proven to my knowledge so than come in non euclidean space cause apparently lines might not actually be able to be parallel 😂 it confuses my brain and i love it
@DrPsychotic Wait until you see parallel lines curve into infinity and become straight. Black holes, time, and space becomes wild when you map it.
Spoiler ll
@DrPsychotic i thought the bit at 30:01 explained that one rather well. ;-)
do you fuking understand it intuitively?
I love the fact that every great mathematician has at least once in their life been labelled “corrupter of the youth”
Ramanujan Or Euler ?
tbf, pretty much everything new is labeled that way up until today, be it changes in how things are being viewed, new media (music genres, games and so on) or maths - as soon as something changes or something new is being made it's automatically bad all while people go on to ignore actual bad things going on.
Beefs between geniuses are way more vicious than those between dumb people. Newton spend considerable amount of energy on trying to destroy Leibnitz for example
The same charge Socrates was found guilty of.
Not even close
I learned about the diagonalization proof in one of my first college math classes. I said something like “this doesn’t seem like math to me, he kinda just found some creative logic to prove his point.” The prof whipped around, the most excited I’ve ever seen anyone be, and said, “my friend! That’s what mathematics is!!” ❤
Cool story bro
@Bluebloods7no no no, "cool story bro" is for when someone makes an obviously false or irrelevant story for manipulative purposes, not just when you don't care: did you not cover this in your internet classes?
@SimonBuchanNz who told you he didnt mean what he said?
@SnobiSnotexplain yourself
@SnobiSnotexplain what you mean
My mind broke at "now this is a bit of an oversimplification"
I applaud you for lasting that long 👏👏👏
Bro said his infinity is bigger than yours and people got mad
When you have infinite balls, you can do that kind of stuff.
@galahad692000😭 lmao!!
It's kind of the right metaphor.
Let's not have an infinity contest.
It's like the chicken or the egg of meth... Math.
My Infiniti is bigger than yours + 1
never felt dumber
I know how you feel, bro!
ikr those ancient people trated math like its a sport
unless talking about real gifted mathematical minds, it's all about exercising a certain language, the math language.
i can read and write in a few languages but understand nothing in others :)
Thanks for the validation
One has infinite sub sets and is the universe therefore infinity - and I've of many.
I can’t be the only one who watches his videos not understanding 90 percent of them
You're not alone
The beginning was easy but now I’m lost and I’m only halfway through 😮
Right on!
i swear theyre just making stuff up 😭
It's like some irresistible goo, I don't know what's it's made of but it's delicious🤣
I live only a stone-throw from Cantor's resting place and have workrelated ties to him. He is one of the unsung geniuses of our time and I'm really glad to see his work celebrated here. Thanks Veritassium.
My father was a mathematician and he would have loved this. He'd yap abt math history and I'd just nod and listen and not understand a word. I miss him so much.
he misses you too.
😢🫂
sorry for your loss mate
Same thing with my grandfather and the history of world affairs. I was too young and naive to understand or even take interest in the things he knew. Now not a week goes by where I don't at least once wish I could pick his brain.
@icedo1013same thing with my great grandfather
The moment Derek said (omega) the flash back hit me about the time Vsauce was counting past infinity
i really missed this kind of videos about pure math
omega to the omega to the omega .
i can still hear the "bwooong"
same! time to look up that classic
he also made a video on banach-tarski, its one of his most popular if im not mistaken
I like how this video contains facts from 3 or more vsauce video
Math proves two things to me. First, there are people a lot smarter than me. Second, there are people a lot more mentally disturbed than me.
same.
And these are usually the _successful_ ones. Survivorship bias and whatnot.
Math=disturbed nerds finally I agree with internet
@JCDenton2012Modder LOL!
@gastfaremis1136 why is this such a common theme in these comments? is this not beautiful to you? is math not beautiful? how is it mentally distrubing to do math?
Now I know that Buzz Lightyear wasn't overexaggerating when he said "to infinity and beyond!" ...and maybe "overexaggerate" isn't really redundant after all...
37 and 42 as random numbers.... not on this channel anymore you are killing it everytime
69 here
whats the thing with 37?
@noonehere6994 Watch his video on it.
@noonehere6994 I had the same question but I found something, look up "veritasium 37", he's made a video on this number , that it is very often chosen randomly
@noonehere6994 i'M NOT OLD
My wife is a math and chemistry major and watching stuff like this makes me glad I stuck to chemistry. It's interesting but also makes my head hurt and makes me appreciate my wife even more. Celebrating 25 years today and looking forward to many many more.
infinitely more?
May God bless your twins, wife, and you.
I don't have the answers, life is too short to know everything,
But I believe there's a creator to everything, and everything in the infinite it has conscious understanding of
Even if you created a time machine, and studied everything, I do believe you'd only find God at the center of everything.
I do believe God came as a human named Jesus, to reach us 1 on 1.
I don't have an understanding to everything, but I believe there is power in the name Jesus.
Through Jesus everything was created, and everything is for Jesus.
When you start looking at every dot on your body, every color, every sound, every thought, dream, everything
It goes on infinitely...
I believe Jesus was there before the big bang
Before the beginning of everything
And I hope in the end of our lives we get to see God.
I trust God loves us, and there's no knowing if anything is real, so I want to believe God loves you, and I pray he watches over you.
In Jesus name amen
you could say she used her axiom of choice to find you out of infinite possibilities. Technically, kids are the duplication factor; if you want to look at it in a more biological frame.
I'm a 3D artist and I had no idea what I was getting into, since the strong foundation needed is both creative and mathematical (at least logically;) but out of those two I found a happy joy in quantum physics studies. My husband is a news producer; almost my complete opposite. Where Im stoic he's incredibly emotional. He's tall, I'm short. We also seem to follow patterns of change that flip certain traits between the both of us. After 17 years I'm convinced people are just as able to be considered physical representations of inverse kinematics.
I'm happy to hear about your marriage. May it stay strong an your life be graced by love as long as exitance is true.
Aww that is awesome, wishing you guys many more years of happiness
It seems like you two have an amazing chemistry in a relationship that could last infinity + x ehh?
One of the favourite microblogging posts I've made was:
"My favourite anagram of Banach-Tarski is Banach-Tarski Banach-Tarski."
No engagement, but at least it made me laugh.
😂😂😂😂😂
that's insanely clever ong
I am sure you have heard the following one: what is yellow, curved and complete? A Bananach space.
@borovitinshund Well even in Medieval times certain knights on a certain quest knew the Earth's is not in fact flat or spherical but is in fact Banana shaped so that makes perfect sense to me!!
Love it
Bro published a paper saying that you can divide out 1 infinitely, and then immediately started getting death threats. "The Georg Cantor situation is CRAZY"
Victorian mathematicians are ridiculously over-dramatic.
Cantor: "I have this esoteric mathematical theory that I haven't been able to prove yet and that almost nobody outside of higher mathematics understands. It also has almost no application in the real world, and almost no one will ever hear about it because it is so advanced."
Kronecker: "THINK OF THE CHILDREN!!!!!!"
Victorian? Cantor, Zermelo, Tarski, Banach, Kronecker, non of them english and non of them vassals of the british empire. Nineteenth-century mathematicians is the appropriate term, even Belle Époque mathematicians is more appropriate since they were continentals.
Other esoteric mathematical theories of the time include the theory of algebraic curves, which can now be seen in computer graphics, robotics, and guided missiles. All math is theoretical until it isn't
@topobabotas Dude it was a joke
@ahuramazdag923 cop out
@aaronboone5387 That's why I watch. For the curves. 😂
The resolution to the Axiom of Choice paradoxes is the most mathematician thing imaginable: "the validity of the axiom has been left as an excercise for the reader"
Andrew Tate Hears About the Guy Who “Broke Math and Himself”
It started as a casual conversation-Tate sitting in a podcast studio, legs wide, mic too close, ranting about how men “need to reject weakness” and “wake up at 3 a.m. to bench their fear.”
He was mid-rant about how algebra is useless for millionaires,
when one of the interns casually mentioned:
“Yeah, but what about that one guy who broke math and himself? You know, the one who solved some equation that didn’t exist and then just… collapsed emotionally?”
Tate froze.
“What?”
“Yeah, he like… disproved something? Invented a new number or dimension? I dunno. But he cried for 8 hours and now he teaches part-time in Vermont.”
Tate’s eye twitched.
His lips parted.
His sunglasses slid down slightly-the alpha’s version of cardiac arrest.
“You’re telling me… a man… broke math… and wasn’t celebrated?”
“Nah, he kind of broke himself too. Shaved half his head and gave his cat power of attorney. Total collapse.”
Tate stood up.
“That’s not masculine. That’s not logic. That’s chaos in socks.”
He paced.
“Real men conquer math. They don’t let numbers defeat them.
Math is for discipline. For bank accounts. Not… emotional collapse.”
The intern shrugged.
“He rewrote three laws of physics, though.”
Tate turned toward the camera.
Face flushed.
Voice shaking with rage.
“Any man who breaks math is a man who was never strong enough to multiply. Real men divide pain and subtract weakness
I don't think the axiom of choice is necessary. That's my solution.
I don't understand who are you talking about? @Owen-o4q
@CliffSedge-nu5fv Okay, NF user.
@Owen-o4qabsolute masterpiece of a comment
i just absolutely love the narrative of a man who went insane because he knew he was right, he just couldn't explain why he was right until someone came later to explain why he was right
to then he be shown that it was up to you to decide if he was right or not
I don't know... It's been suggested that people working in logic didn't go mad but were drawn to logic because of their tendencies
I'm autistic - I have this problem some times. I explain a really simple thing to a person and they totally don't get it. Then they will get another person and I will explain the super simple thing and they will not get it. I can only assume the words coming out of my mouth do not match the thoughts in my head.
Like the Chinese proverb.
If you stick by your guns for long enough, fire powder will be provided, dude.
@piccalillipit9211 I think it is the opposite. The words coming out of your mouth do not match the thoughts in the other person's head. Do not assume that your explanation is wrong. It could be as simple as a matter of two persons talking two different languages. The difficulty relies on discovering a common language, which is something rather difficult to do, no matter if you are autistic or not. Just try not to get frustrated by the lack of common ground, if it happens.
With natural numbers and square numbers, what happens when you do it the other way? Every square is a natural number, so match every square number to it's natural number. Now you have matched an infinitely many square numbers, but have not matched every single natural number. That seems to lead to the idea that infinity does have differences in size.
27:51 "Infinite Balls" -Veritasium 2025
😂
Lol
ligma
Me when I see a abysmal chance of winning the lottery : F*ck it, we have infinite balls
Don’t forget 96 million black balls
Love how he deadpanned 37 and 42 being random numbers he just picked out of his head.
What is 37?
37 and 42 are so-so random! :D
Nice Lil tip of the cap to the long time listeners
@MrKevo1237yess my brain went to that video instantly lol
should have picked 2. 2 for his little 2 inches
"it also creates ridiculous paradoxes"
110% scientifically accurate description of maths
🤣😂 Scientific accuracy wraps around at 100%, so it ist only 10% accurate.
@rickrock2525 No, everyone knows that scientific accuracy wraps at 5 sigma. /j
Every time I see something about infinity I'm always like "please stop trying to do definable operations using indefinable concepts" it frustrates me to no end.
Someone out there is sane too!!@StaticR
@Ethan-uf4jp I made a much larger set of comments but essentially, infinity is undefined, if you were to define it it would no longer be infinite and you can't do any math using undefined values where the result isn't also undefined.
The guy who proposed this definitely had infinite balls.
Cantor's diagonalisation proof has always been my favorite. It has so many implications, but yet everyone can easily understand it.
Agreed.
yes, it's very elegant!
@jmironULH26 this is the definition of elegance 😁
Agreed, it is a deep insight that occurred to no one for thousands of years, yet can be explained to basically everyone.
I can’t understand it. Here is what I don’t get: you can indeed make a new number by serialization that is different from every other by one. But why can’t we do that with natural numbers?
Why does “0.” matter? I can’t agree with this proof just based on my likely naive logic that by removing that ‘0.’ prefix from the new real number we will create a new natural number
“and before you know it, you've got infinite balls.”
I wonder if they wrote literally this in their research paper
That's what she said.
Thats what liquid courage gets you
we've got infinite balls before GTA6 (yes, I searched through the comment sections just to write that comment)
@Ibasirov Allat just to write it as a reply.
I have no idea why I'm watching this at midnight when I had a big problem counting my classmates in elementary school…
Oh wow you go into elementary school and watched this video? That is really really impressive
@guitaek "had"
@noahniederklein8038even only being in elementary school 13 days ago makes it not less impressive
Asking myself the same question brother
@noahniederklein8038 oh true, thanks for clarification
This reminds me when I was a child and I used to play imagination battles with my brothers and friends saying things like: "My shield has infinite protection", and they would go: "Oh yeah?, my sword has infinite + 1 strenght" and so on
Even more remarkable is, that Chuck Norris counted to both the end of countable infinity as well as the uncountable one. Both TWICE!
He would break all your infinity shields and swords!
😂 yeah, I also compete my friend on elementary school about something infinity, I thougt I win when I claim something infinity, but he revenge with 2 times infinity 😂 until I start think about infinity time infinity, but he answer with 2 time infinity of 2 time infinity which is became more absurd and nonsense
yeah, concept of infinity + something else looks very suspicious in term what "infinity" defines here.
Childhood logic battles hit different 😂
It’s all fun and games until your sword powers reach infinity plus omega1.
I freaking love how meta this is.
"for the axiom of choice to be true you must choose a universe in which it is true"
Absolutely beautiful.
Is its truth “entangled” with a reality which its untrue?😱
Vsauce be like hold my beer
This is like the most nerdy/elaborate april fools joke I've ever seen.
no wonder! looks like i live in the wrong universe
Fr
29:10 "Nobody is interested in the equivalence of two obviously false statements" is definitely something I will find a way to use in an argument 😂😂😂
:p
I've thought exactly about almost everything stated in this video. Literally. I believe I shall come up with the Infinite Energy Equation one day. It's always been something that has constantly bothered me and very very little things bother me for such a long time. I've had dreams about uncovering it. If I do, hopefully, I will come back to this post. I will try and publish the equation to the whole world, though it will be really hard for everyone to know about it before I'm killed. You all should just know that if this equation is used to create weapons because of the way you crazy beings like to kill each other, it will be the end of everything.
@UnlockYourMind-c8s what do you mean by infinite energy equation?
Buahahhaha infinited E don't existing or you treat whole E changes as once and conservation of E as constant and termination and death not existing but not in a Buddist way, some worms eat you, than birds eat worms, than maybe plants benefit from a pop and create some rocks which will be flushed by water or create oil and deliver E to planet than maybe you became part od volcan ground for some plants....
I just don't see a way to became a human again.... Sorry Buddists
@UnlockYourMind-c8s yeah i am also working on a n infinite energy equation, maybe we coudl work together somehow
One of the few Veritasium videos where my brain just shut down.
Thank you so much for actually illustrating your videos by hand and not with Ai, i just realized how much I appreciate this over ugly Ai slop
Give it a few years and AI will be more impressive 😩
@steveg8533 If you love abysmal dogshit maybe
@steveg8533 impressive ≠ (does not mean) human
Yeah, "science" RUclips has become saturated with AI slop creators. A lot of whom peddle absolute nonsense as science. I love misinformation.
@steveg8533maybe, but it’s taking away from humans who put their heart and soul into their craft…
Ah yes, the Banach-Tarski Paradox, still left me puzzled even when Vsauce and Veritasium explain it to me.
That's what I thought this video was going to be about.
Yep. There it is 2/3 through.
@sonofbrIt kinda is
How did you do dat
Honestly Vsauce did it so much better
divide nonmeasureable in some smart way -> loose ability to measure results in classic way.
9:00 so in simple words he used source “trust me bro”
just vibes
More like “trust me bro” on steroids but y’all don’t know bout that these days
he has god and anime on his side
Lol
☠️☠️☠️☠️☠️☠️☠️
Fun Fact: an anagram of "Banach-Tarski" is "Banach-Tarski Banach-Tarski"
Underrated joke
This video gave me flashbacks to old Vsauce videos on Banach-Tarski and counting past infinity. I’m so glad you’re still posting videos, please continue
exactly what crossed my mind too when i saw the video upload
That was the most mind blowing video to me back then
Right after his intro where he described what we were about to learn about I thought this would be about Banach-Tarski and thought about that Vsauce video
I hope veratasium knows about that Vsauce video...
@ of cause he knows
What is remarkable to me, is there are folk out there who figure this stuff out before anyone has even thought to figure it out.
Brilliance.
Engineers do that all of the time. None of these people were engineering in this video.
Indian mathematician Ramanujan said that the formulas came to him in his dreams.
@armend_hammer just shut up
I understood absolutely nothing of what you were talking about, but I still watched the video.
Same.. And english is not my native language so i understood nothing x2
Or is it x2?
You now have a little more detail about what you don't know, and you are now familiar with the name Cantor and the fact that he showed infinity is a lot more complicated than we once thought. Small gains maybe, but gains nevertheless.
This was not one of his better, clear, or interesting videos.
@Zer0Blizzard agreed.
0%understanding 100%vibing
“you can’t just well-order real numbers”
“what if we said we can?”
“oh ok then”
Underrated comment
The normal ending
I’m lost at 20:07…
Same brother
Same here
skill issue
I am honestly pretty decent at math and even I was just like "hmm yes..root 2 root 2 root 2"
They just lost me at infinite number of balls. I swear, nerds will do anything to overcompensate. 😂
I was 13 when Michael from Vsauce released his video about the Banach-Tarski Paradox… now seeing this almost 10 years later has brought back so many memories… but the fact that I remember so much goes to show how important this kind of educational content is. Amazing job 👏
That was ten years ago? I remember that video so clearly, it feels like yesterday. Time flies huh?
And also how effective Michael was a conveying a concept. The man had elite teaching talent
"I was 13 when Michael from Vsauce released his video about the Banach-Tarski Paradox…"
_Or _*_did_*_ he??!_
I grew up on Vsauce and Veritasium videos xD. Now I'm studying physics with an aim for astrophysics research.
The second Derek mentioned the 2 spheres I recalled Michael. Not that I understood that video back then but I at least recalled it :D
Me looking at the title: It's the axiom of choice isn't it
Video: yup, it's the axiom of choice
30:01 "You can think of geometry like a game" well I've got just the news for you
GEOMETRY DASH 💨
this is proof robtop was ahead of his time when he made geometry dash
“GEOMETRY DASH” *🔥🔥🔥🔥🔥🔥*
GEOMETRY DASH
Polygon Run
1:51 He says "1.00000001 but subtitles and the graphic show 1.00000000001" - I must object in the strongest possible terms :P
Oh come now, you can't reasonably hold someone to their subtitles when 99.0000001% of subtitles on RUclips are inaccurate. But yeah, roast them on the graphic. Get em! 😂
@Ayelis Not to harp on this point, but auto-generated RUclips subtitles are different. In this case, I believe Derek himself uploaded the subtitles and simply didn't count the zeroes. :P
Of course, my objection is tongue-in-cheek, but it's something I noticed!
AmmoGus1 Regard ahh comment
@Ayelishe put those subtitles himself, so yeah it’s entirely his fault.
That’s like saying 6 but the captions say 14
Minor error at 3:11 - 269 written as square of 16, all the next squares are shifted by 1, fixed in the next picture
Thats actually kinda strange. still, one error is still impressive for such a complicated topic
@LiterallyJaceBeleren some youtubers make these mistakes intentionally to create traffic in their comment section as we now do..
Man, I thought i was the first to notice this
@usebrain514kind of conspiratorial take
@usebrain514 wow, these conspiracies are everywhere. I mean, I believe you, but it's still very weird.
I cannot be a mathematician.
"If you choose not to decide, you still have made a choice." - Rush
W reference
I was mind blown when I realized that was also a choice, I was also 8
Excellent.
I will choose a path that's clear : I will choose free will.
The genius of Neil Peart to boil down philosophy into a single line.
3:11 Your mapping from natural numbers to square numbers is incorrect from 16.
Talk about attention to detail. I also noticed 😂
Yeah but what you noticed first is that 19 squared is not 400
@fortheloveofmathematics You're absolutely right! 😂
Was about to comment on this. At a glance I thought "Wait, 16x16 doesn't end with 9..."
And square of 17 is 289 not 269😅
5:00 flashbacks from the hotel video
Same 😂
SAMEE
YES EXACTLY LOL
ah yes the grand hotel paradox
Let's not have an infinity contest.
Mid-clip, I was half expecting a drive-by shooting from a horse carriage.
When I watch a Veritasium video that is more focused on science, I follow along quite well. When it's maths-heavy, my brain in minute one is "yes!", then "yes." then "...yes" until about halfway through when my brain politely asks me to rewatch the first half again. This is just bonkers.
@PhilipBarkley It's not just you. Cantor's math was so mind fuckery (endearing), that his teacher called him a corruptor of the youth. I really hope that sentence doesn't get misunderstood.
😂😂😂😂😂😂😂😂real
You have a polite brain? Mine seems so rude sometimes...😊
@AutisticGramma You have a brain? To me it's just a tiny kitty inside the head
37 or 42 is NOT random at all, true veritasium viewers will get it
I wonder what happens after a thought that becomes two
There is no thing as a truly random number or occurence, we live in a deterministic system, it only appears chaotic because we aren't aware of all the variables
@neosmagusTell me you don't know anything about quantum theory without telling me you don't know anything about quantum theory.
@neosmagus You have little faith :)
En cuanto vi los número me di cuenta!!
As a german mathematician myself (focussing on differential topology) this story makes me proud. All these men contributed to my passion so much and seeing this story presented sparks my hope, that more people learn that math can be so fascinating and is even material for a captivating plot.
Hello I am class 11 student from India interested in maths can I get ur contacts
Die Antwort lautet acht
😂
Hi, I am interested in learning advanced mathematics. Are there any books you recommend for self study, or would you say doing a bachelor at a university is the better choice?
@Leandery9i Well, I would say if you have the opportunity for a BA at a university, I would go for it any day. Math is so broad and this way you will gain insight into everything on a high level. Find out what exactly it is that fascinates you and cherish it! :)
"BEFORE YOU KNOW IT , YOU HAVE INFINTE BALLS "
Love how the existence of "axiom of choice" depends on your "choice"
I was just thinking that 😂. You have to choose to choose
Kind of implies free will.
Choice is just an illusion.
Implies ultrafinitism - likely nothing is infinite in the actual universe, and human invented infinites-involving math might simply be contradictory in the end
@ReverseDominion How so? If the axiom itself is indeterminate until used or observed, does that mean choice doesn't exist until it's used or observed? The axiom is only an illusion if you decide it is an illusion, meaning choice / free will or lack thereof is itself a choice... this again implies choice must exist, but can be ignored.
"Saying that infinity drove Cantor mad is sort of like mourning St. George's loss to the dragon: It's not only wrong, but insulting"
-- David Foster Wallace, _Everything and More_
Great read.
I've read this book like 3 times
But it makes a good title. Draws in huge viewership numbers; without seeming too click-baity.
Interesting
you can not pick 37 anymore.
73 likes as of writing this
Isn't that the worst hand or second worst in Texas Holdem Poker
No. 3-4-5-6-7 - you can make a straight. I believe unsuited 3-8 is the next worst hand, but then I’d have have to check the chance of a runt coming to high card vs a straight.
But given that 2-7 is worst, I would assume so, otherwise 2-6 would be worse than 2-7.
Haha 😂
In the UK there is a computer called Ernie. It’s used to draw lottery numbers. It based its random seed on background radiation produced by stars.
Why not just measure quarks for true randomness
Horror is probably the most accurate description of anything that involves quantifying infinities
Did Cantor know the phrase, "I am rubber, you are glue. All bad things rub off me and stick to you!" arrow archer 8:47
"If there is no problem, create one"
- Mathematicules
Sally went to the market with 10
Watermelons…
Mathematicians: what if she gave 1.00000026 of them to Greg????? How many melons would she have left?!?
8:48 😂😂😂😂😂 “because I said so” is crazy 😂😂😂
31:10 so the solution is to choose whether you can choose or not, brilliant! 😅😅😅
Bruh, i was thinking the same thing
To think they went through all the fuss to reach this conclusion. It's about as ironic as it's unnecessary
Important to note is that this doesn't mean the Integers are well ordered, only that they can be well ordered.
"What do you want to eat?" "I don't know..." "Just pick something!! And I swear to god if you start with this Cantor guy again I am going to lose it!"
When my wife says “what would you like for your birthday present?”, the problem isn’t even that I don’t have an axiom of choice - within a set or sub-sets, it’s rather that what I want doesn’t fit into any pre-existing ser or sub-set.
lol.
I’m fired up after watching this, so good!
Wow, what a video. Making the connection between the "axiom of choice", and the "axiom of parallel lines" in geometry, absolutely blew my mind in the best possible way. Beautiful.
and then there's the axiom of muffin
@muffin.muffin.muffin.muffin You appear to be the chosen messenger of this new glorious muffin message.
WOW
it's simple called - magnetism...I know the secret.
I agree. People started by arguing whether these axioms were true or not, or tried to prove them. Then models were found in which they are true, and models in which they are false. For the parallel postulate, the debate is long over, but for AOC, it is still controversial, but we are heading towards a more mature view.
3 things that fast-tracked my financial growth:
1. Taking action NOW instead of waiting
2. Reading Encoded Abundance
3. Focusing on consistency over motivation
Such a great tips, thanks mate! I read that book yesterday and I was shocked
Is the book really that good, I keep reading about it everywhere..
IS the book only in English pls?
Thanks for the advices! Can you tell me where I can get the book you mentioned?
Who is the author guys?
A small piece of advice in animations:
use mild (doesn't even have to be noticeable) hue shift in large gradients across the screen.
This will avoid banding in low data frequency areas, especially at lower resolutions.
That's interesting. Why does this work?
@lonestarr1490 Banding happens because there are as many as 2160 pixels of width, but only 256 possible values for each color, meaning each color happens for bands between 8 and 9 pixels wide. Adding a hue shift improves this banding (though it doesn't fully eliminate it) by adding an additional color that can break up the banding by blending in its own banding pattern.
@bobogus7559 Ah, different hues "band" at different times, thus you overlap the bands, which results in a smoother gradient, right? Neat.
@lonestarr1490 Just to add, that 2160 divided by 256 values math works out only in perfect uncompressed conditions. In practice, with typical video compression, it can be even worse, due to quantization and color space conversions, chances are you'd get even fewer than 256 bands (or even some unwanted colors around transitions), thus increasing the need for doing hue shifts, or steeper gradients, or dithering, or something else, to mask the issue.
I don't see a way to add this unless you have custom texture for each gradient and not using any built in ones from the editor. But I don't know his workflow.
Wow the hilbert hotel is everywhere huh
How fitting that the axiom of CHOICE is true if you make a CHOICE for for it to be true but it's also untrue if you make a CHOICE for it to be untrue.
I’m actually working on Axiom of Choice² about choosing whether or not to include the Axiom of Choice in your system. Well, I’m not actually working on it. I should. But it’s lunchtime. And I’m hungry.
@app-o-matix Isn't applying this Choice², even if you chose not to, automatically including the Choice?
Both are linked in quantum realm
Choice is all but an illusion
That’s true of all axioms.
0:38 that's either a reference to one of his previous videos or it's proving his previous video correct
When I heard him pick 37 I knew he did it on purpose.
to the video/ short why is this number everywhere
Likely not random numbers.
37 is a reference to one of his previous videos, and 42 is the number of his channel logo. You can spot it on his channel banner,for example.
he did that at 0:37
@Void6445 42 is a reference to "The Hitchhiker's Guide to the Galaxy" form -Isaac Asimov- Douglas Adams.
28:41 "no one knew what was going on"
Glad I'm not alone, from beginning to end. 😅
This was not one of his better videos.
@Zer0Blizzard it's a fantastic video, it's just that the topic is very difficult, esp to people unfamiliar with it
I have till now been utterly utterly puzzled by the axiom of choice. Now I am just utterly puzzled by it.
As a biology student, my mind can't fathom a single word this dude just spoke 😭
haha
This is where we biology majors hide in the comfort of the Krebs Cycle 😂
I took biology for 1 semester then I switched into chemistry then I switched into physics then finally I switched into math. Looking back, biology is like for kindergartners
@reptileandad Can I show u my theory on astrophysics, I sent a message to Neil Tyson. Can I send it??
@reptileandad The need for people in a science field to insist that their particular science field requires one to be much smarter than people in other, unrelated science fields is usual the best proof to have that the person you're talking to is, in fact a childish buffoon.
I need a brain surgery to comprehend this one.
no we need new DNA
You only need to solve the goose in the bottle koan.
I have a tractor. It has a throttle and a hydrostatic drive which increases and decreases speed, depending on the RPM. It is listed as having infinity speeds. Someone asked me how many speeds it has (since some tractors have numbered speeds, and only have, say 5 speeds). I say it has infinite speeds. He says "yea, right. So you can go 100 miles an hour?" I say no, I can't go ALL of the speeds, I can just go infinite speeds. There is still a minimum and a maximum. He stares at me and rolls his eyes. He walks away.
Lucky he just walked away without punching you in the stomach first :D
Ratio of infinity vs infinite ratios
I remember the moment I went from “that’s so dumb” to “ohhhhh I get it!” when my 7th grade math teacher explained this to me
@NostraFnDamus lol
It doesn't have infinite speed
It has infinite number of possible speeds
Although due to quantum mechanics its probably a very small number like 10 to the 35 or something
Very happy that Cantor was able to see his work taken to the axiom so after his mental breakdown his hard work and thoughts were asserted and respected.
First mention @0:20 🎉
Thats funny
I need to ask, is the origin of your name the same meaning as the word quoted on the video or is there another story and you just happen to be here watching a random video which quotes a word ridiculously close to your name by coincidence? This stuff intrigues me
@danielmacdonald3130his or her name might be axel and he or her just got confused and wrote ummm lol
Funny man here
@danielmacdonald3130 Same meaning. It's not my name, I'm just a nerd...was kind of surprised this name was still available (made in 2024)
0:13 I immediately blurted out Banach Tarski xD
same xD
Same xd watched vsauses video
One of my all time favorite things to meditate on!!!!🤗😀
It’s been like a decade and I still don’t understand that vsauce video😭
@chromezinc - Keep trying. It will click eventually.
-Before you know it , you got infinite balls.
+ Sounds interesting
this is the only reason i checked the comment section
I’ve always had the outlook that the mathematical axioms we create to describe things that happen in the universe aren’t actually the rules that the universe follows, but frameworks that characterize our observations of how things happen. It’s like finding an expression that properly matches an experimental data curve. As such, I think this extends to logic itself. Our deductions about what should make sense are based on the patterns we observe, but the universe isn’t actually bound by those patterns, it just tends to follow them.
still waiting for a proof
Hey, thats kinda cool
THIS, YES
Wrong.
@TheAgainstermind elaborating why?
It’s amazing how math is substance outside of ourselves. The formulas already have to work before anyone ever discovers them.
It's because mathematics is a description of the universe and it's laws, and since it predates us, it's all there already.
@Rundvelt Nope. Mathematics is entirely a construct of the human mind. Some of it can be used to describe the physical world and the rest can't.
One means nothing, one what?.. How much does that thing weigh? 17.. 17 what thats useless without context 17kg now it means something.
@hb1338 If our universe's core properties were different, our math would also be different.
@hb1338 If civilization was wiped out and a new species evolved, would they discover the same mathematical laws?
23:30 "Hi Vsauce, Michael here!"
i am cooked
😂😂😂
Real😭😭🙏
Same 😂
why
Whyy
This video reminds me of Vsauce's video "How to count past infinity" except that is Veritasium's version. Both of them, amazing! Nice work!