How big is infinity? - Dennis Wildfogel
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- čas přidán 9. 07. 2024
- View full lesson: ed.ted.com/lessons/how-big-is-...
Using the fundamentals of set theory, explore the mind-bending concept of the "infinity of infinities" -- and how it led mathematicians to conclude that math itself contains unanswerable questions.
Lesson by Dennis Wildfogel, animation by Augenblick Studios.
"No matter how big a number is, it's always close to zero than to infinity".
but negatives :( -1 -10 -100 -1000
@@Tevin-MK Also true for negatives though because -1 is "bigger" than -2...
I said this about space. If the universe is infinite but only 13.77billion years old. Holy smokes are we young! We might actually be the first species! Fermi paradox solved. Goodnight.
@@masonfarnsworth6730 lmao
Nah what about the number infinity divided by 2 plus 1. That's close to infin6 Lmfao
You know what makes me really sad for some people who made great discoveries?
When people reject the person's idea and insult that person, leaving that person to spend the last years of his/her life in misery, and then people finally accept it until AFTER he die.
Then his dead, depressed body gets a Nobel prize.
Then it's already too late.
I know, right? it's terrible
except nobel prizes aren't awarded post mortem of after death. For examppe Ghandi died the year he would've gotten a Nobel Peace Prize so that year no prize was given out at all.
Alex Chuoy Sorry, I don't understand what you mean by "post mortem of after death".
As for your example, it's kind of similar to what I said, because in the end, Gandhi never knew about the honor he received.
Anyar oops its post mortem OR after death. Ghandi didnt get the Nobel Peace Prize because he was dead. One of the rules is that you have to be alive to be awarded the prize.
Alex Chuoy Oh, okay. My bad.
For some reason, I seem to remember hearing about Nobel prizes being awarded to people long after they've died.
Weird. My memory has failed me.
TEDed: "How big is infinty?"
*Me as an intellectual: "Ask the night manager."*
Yes
Does understanding this reference make me a nerd?
Men: hmm yes IS the floor here made out of floor ?
I remember it too
Yep
You can take infinity out of infinity infinite times and still left with infinity.
We even have a shloka in Hinduism like that
"Purnasya purnamaadaaya purnaavashishyate "🙏🙏
True
This works for every number.
Well yes but actually no but also yes
It only works with "infinity"
Infinity - infinity • Infinity = 0
X - X • X = X
How big is infinity? Hint: Bigger than 5.
+Lugmillord No if i list the infinity of negative numbers
+Guilherme Medeiros Just because the set is of negative numbers, the cardinality isn't going to be negative... fail XP
+Lugmillord Hint: Smaller than infinity+1
Oh wait...
Hint: Bigger than 245355354243134143243654655746547658758756756544243143654765765764675764764664654754....
I think you get the point
YOU'RE GONNA HAVE TO DO BETTER THAN FIVE
This video is making sense and it's blowing my mind.
Your mind is having a good time
It makes sense
My mind is struggling 🤦🏾♀️
Infinity is piling up in your brain
Ok
Educational content like this is slowly making the world a better place. I really wish videos like this existed when I was in grade school. Thank you 🙏
I am a school student and I'm glad that I got the opportunity to learn these thing at a young age.
@@MarkWatney You learned nothing, except that some people intentionally corrupt mathematics
O hristiyan işareti bu müslüman dua işareti 🤲🏻
@@abdulkadiryukselking so wht
How big is infinity?
Me: it's infinitely big
Limitless !
ah you small joke cokkie
I broke the rules,look!
Omega,omega+1...
It is as well infinitely small
I guess some infinites are bigger than other infinites.
I guess Some infinities are faster than others and Not bigger.
+Cinichecuk I gues some infinities are just more handsome than others
+Cinichecuk I guess you 're watching too much The Fault of Ours Stars
+Cinichecuk looking for this
They'd have to be finite then.
1 is actually bigger than 9
Because of:
9 10
The 9 is to the 1 there is no number to "the zero"
5:47 god.... that's the most visually n aesthetically pleasing thing i have ever seen in my life
I have always struggled with the concept of how one infinity can be bigger than another infinity.
That's because it doesn't make sense. It's contradictory in it of itself.
Are there any aspects of it you're still struggling with? Perhaps I can help address some of them.
@@MuffinsAPlenty Yes, please address how one infinity is bigger than another infinity. I understand the concept of cardinality, so no need to go there.
@@wade5941 Cardinality is what people mean when they talk about some infinities being bigger than others. Ultimately, it's a generalization of how one thinks of sizes for finite sets. Are you looking for an explanation of why "size" is a good descriptor for cardinality?
@@MuffinsAPlenty Infinity is unbounded space, time, and quantity. Again, I understand that one specified infinity can have more elements than another specified infinity. Even though the one infinity has more elements than the other, they are both still "unbounded" and infinite. I understand that one infinity can be a subset of another infinity, but both would still be infinite. I think my struggle is why does cardinality even matter when it comes to the concept of "infinity". I understand why it matters in the world of mathematics. I suspect I am making this harder than it needs to be, so will understand if you move on.
May we always remember and pay our respects to Georg Cantor. 🙏
how big is infinity, simple think the biggest number you can think of and add even the smallest value you can think of to it. keep doing until your mind exploades
Graham's number?
Actually infinity is a concept of how number dont stop
INDOMTM4X r/whooosh
not realy just imagine that 3 is the biggest number i can think of and -3 is the smallest i add them and it gives 0 so is 0=infinty?
armando valente r/whooosh buddy.
Mathematics is not the one who has limitations. We are
Cesar Escobedo But what if you think matematics as a human convention?
Human built mathematics, which had them confined to understanding. :P
Actually Godel literally proved that there can't be both consistency and completeness of axiomatic systems at the same time. Therefore all mathematical logical systems have some unprovable statements
Mathematics IS we
If we have limitations, math has them too
(I'm not an english speaker, my grammer can be bad)
problem: mathematics is bound to whatever container our reality is in. like, our reality follows maths, some other reality could too, but there must be other realities which don't. but, to be honest, such "reality" does not "exist" same way as ours, so it can never be discovered.
How do we interpret infinity?
TedEd: A pretzel.
That read more’s fake😂😂🤣
Ye but how ... is that even possible?
jr.akuchi Dre if the “read more” is fake, i wouldnt see the chinese text. (im using the chinese version of youtube)
Ok
B
This is one I'm going to need to watch a few times. I've been pausing this so much the first time to digest something then pow, the next reality check comes in. Great way of showing this mathematical conundrum.
I'm scared.
I'm sacred
I'm terrified :c lol
Flurry Heart I’m 4 months late but I like you.
I'm scared I won't finish detective Conan in my lifetime
Nothing to scare... -_-
When your just on 4th grade and you already have a existential crisis.
Here, let me simplify it.
Pretty damn big.
Remember me when your comment get popular
Ayasha no
Our earth itself is pretty damn big. Infinite has no limits.
Remember me too :( I am one of the intellectuals that understood this video before you simplified it
Ok
Title: How big is infinity?
Me: OMG!! *There’s a pretzel in my head?!*
MEME: becuase a prezel is infinity
♾ Is ♾ times bigger than: 84846473838383746467373837374637288373646373737373736736737373635363737373763637282837377363647473737373736378292918283783929101010101001928374746287373638393983837373737383838292929387312 to the power of 84846473838383746467373837374637288373646373737373736736737373635363737373763637282837377363647473737373736378292918283783929101010101001928374746287373638393983837373737383838292929387312 to the power of 928383836636372727377383837384859595959949448474288229827364728929282837373746474747838292910018273635436637373738839393939939393! (! Means factorial, for example A factorial means all positive numbers smaller and A itself multiplied with eachother for example 4! Is 24
🥨 :)?
Its pink. Looks a bit moldy
@@paulneamtu1373 wrong lol
so... basically "some infinities are bigger than other infinities"
+
Indeed, infinitely many infinities are bigger than infinitely many other infinities, e.g., the infinity of all real numbers is bigger than the infinity of all whole numbers and the infinity of all the subset of real numbers is bigger than the infinity of all real numbers and so on and so on.
Abhipsha Sahu
Infinite is infinite not a number just unlimited no limits
@Michael OchoaRomero wrong
Multifinity is bigger and smaller than Omnifinity
If you'd be my Maths teacher I'd probably have better grades.
My grades varied hugely depending on who was teaching. This does in fact make a huge difference and I have to say that when I learned our main maths teacher died in his 50s I did not exactly shed many tears...
If you worked harder you'd have better grades. People always blaming others for their own failures.
@@petergianakopoulos4926 that's true, it's also true that if I taught myself all the maths at home from books and the internet I would have better grades, but the point is the teacher is there for a reason
@@petergianakopoulos4926 the work you put in and the quality of teachers both make a difference. You can't substitute one for another. A good teacher alone wouldn't get you good grades, neither would just hard work.
Yeah you would do better in philosophy math, this video isn't about the academic one.
I love every bit of this... my mind revels in the infinities of infinity, running the still-growing yet essential finiteness of my intellect around the curves of the flexible boundaries of that which I can always learn more of without exhausting it!
I like put myself to suffer like recently i watch video about how to imagine higher dimension and now how to understand infinity.
The pain.
Yeah I understand the joy behind that pain. I, most of the time do not completely understand such videos but I feel good after watching them.
Apeirophobia?
Well now I just feel really bad for Georg Cantor. That faint sad expression at 5:39 just broke me.
yeah, ya lost me
Nataly RAW lol
Nataly RAW youre blonde right? lol
islezeus nope, and it's you're*
islezeus come on then
Nataly RAW what a jenny ass
3:46 this concept is further explained in vertasium's "infinate hotel "video
1:51 "Does THIS convince you?"
Go home math, you're drunk.
??????????????????????????????????????????.
No!
And you are drugs METH!
magicstix0r nope math is not drunk
@@weirdgaming996 r/whooosh
wow john green was right. some infinities ARE bigger than other infinities.
Oddly enough, his explanation of the fact was wrong.
that bc john green sux
Vi Hart gives a nice explanation
***** Take a moment to watch the video. It suggests a very natural measure by which you can compare two infinities.
well said! i
I learned more from educational channels like Ted Ed than from my entire career in school.
You should've paid more attention in school then
@@mohadams3754 I actually do pay attention, I'm a good student with good grades, they just don't teach useful stuff at all and just stress me out.
Video: “How big is infinity ♾”
Me: Infinite
I have a fear of infinte anything. Why did I click this video?
To face the fear and render it to dust spilling from the palm of your hand?
So that is to say... you are afraid of infinte things?
To infinity and beyond!
M_ Vanvid yeahh!! Buzz Lightyear
Infinity😂
Buzz lightyear
me: *watches first 20 seconds of video*
also me: uhh, my head hurts now
The sheer simplicity in this explanation is mind blowing.
y'a nkown 3.14=1NFYN1TY
If math has limits, is it possible to know all of mathematics? Or is it an infinity simply.smaller than another infinity?
It is not possible to know everything there is about mathematics, because it is said in the video that there are questions that can't be answered, so you don't know if something is this or that, thus you don't know everything about mathematics
That's where weed comes in, my man. As it does for me, it'll show you some really interesting concepts such as hyperinfinity that's pretty much like this video. Mind you, not every strain can get you to do this.
Kurt Godel proved that in any logical system capable of modeling basic arithmetic, you can create statements that cannot be proven or disproven. (He actually used Cantor's diagonal argument presented in the video!)
This is an exceptional video, and by far the best aid I have found to understanding the basics of this remarkable area of maths to a degree that a non-mathematician can understand things. How amazing to see not only that there are different levels of infinity, but an infinite number of these levels. And inspiring to be told (even if this is not explained) that there are questions in maths that cannot be answered, such as the continuum hypothesis. How to react to these mathematical discoveries? Wonder and also humility.
There are many mathematical conjectures that can't be solved.
remembert mathematics is only the structure of all possible things in world and if mathematics have a limit then it might be a world break and all things of science will break down
Math has limits, science is still OK
@@agimasoschandir true, this world isn't made from math. It's created with the law of physics, math is there only to help in describing it.
@@That_One_Guy... agreedddd
Am I the only one who misses the intro to the Ted Ed Videos? Ah, the music, the combination of clips of their videos, all being combined to make the shape the a brain of a person, which had closed eyes. This person opens those close eyes at the end of the intro. This signifies that it's putting knowledge into us. It's so nostalgic! Sad that it's gone, Happy that it was created in the first place.
One, Two, Three, Infinity, anybody?
*infinity+1...*
Something like "infinity+1" does actually exist within the ordinals.
infinity +infinity
Infinity*Infinity
tochoXK3 yeah omega+1
Infinity is one more than 8
NEIN!
No. Infinity is between twelve and thirteen.
Water Spray 12.5 = infinity confirmed
Ryan S. Don’t you mean... infinnati
thats nine
Thank you so much for uploading this video. It is helping me get through the pandemic!
Great! Salute to your efforts in making learning fun!
This is an absolutely fantastic video. Good narration, amicable voice, and fascinating content. Thank you for uploading, and give my thanks to the creator of the video.
So... each number is a tiny infinity. Inspirational.
dam, i learn so many things from ted ed, the intro is so cool, the explanation is good and this channel is good if you want to learn things.
I agree
I really love the way this is explained
For some reason, this makes me remember my big goal in chemistry: to find out something that no human has ever found out or proved before, no matter how crazy or stupid it may seem. Lol.
+SamThe RandomG1rl and boy does it! ;)
Sammy Dreemurr you can try to be the first person that can harness nuclear fusion energy.
in case you do it remember i believed in you before anyone else sammy dreemurr
I want a video about impossible numbers, I don't know why but I find them so interesting.
Omega
This video is very interesting! I knew a lot from it! Thank you!
me at the start of the video: *his teacher is getting rekt*
me halfway through: *so he is not getting rekt then*
me at the end: *??????????*
I just suffered a stroke.
How big is infinity?
Me: *Minecraft*
damn bro that was actually hilarious
Nope, that's 30 million blocks
Not really bro. Minecraft will either stop on its limits (roughly around 30 million blocks), eventually render an already existing chunk, or if you remove its limitation, stop when it completely fries your computer.
Minecraft is 8x bigger than Earth which is not infinite
What y'all say is true, but that was my first thought, because Minecraft is practically infinite and that's awesome -3-
love the sound at the end of the video when ted've blown my mind.
Infinities based on greater infinities that are always growing and get larger. Truly amazing!
If I'm not mistaken, the last bit in this video is false/incomplete: the results that Godel and Cohen reached about the Continuum Hypothesis are dependent on the ZFC (or at least ZF) set of axioms - the fact that "truths" depend on axioms should actually be the more important aspect to focus on.
palmomki
Damienation Animations
Yes, but try explain ZF(C) to "common people". It may seem "easy", but Skolem's paradox shatters everything.
So you need some intuition, and the easiest way is to "accept" ZF(C)
I do believe you're right
IF YOU GUYS FEEL SMART ENOUGH TO SOLVE CONTINUUM HYPOTHESIS
POST YOUR PAPER HERE, THERE ARE FAMOUS MATHEMATICIANS like Terence Tao, John Conway, etc
michaelnielsen.org/polymath1/index.php?title=Main_Page
Infinity is 8 letters long. Answer: 8
Wait. 8 flipped to right = infinity
But how can a person become more comfortable with these concepts? I want to understand the world in mathematical terms but stuff like this turns my brain to soup 😫
there's nothing to understand here buddy
Spoken like someone who's good with numbers... Check your privilege@@applecider9630 😜
Check out the video by Vsauce called how to count past infinity. After that try reading Naive Set Theory by Paul Halmos. After that try learning some ZFC set theory. Most importantly, take good notes, and remember to have fun.
@@anishia i just think we will never have a theory that explains everything, there will always be something we won't understand
4:40 is where the video finally starts
4:15 the decimal you can't produce! It takes infinitely many steps:)
Good video. One gripe: the impossibility to prove the continuum hypothesis one way or the other does not show a limitation of mathematics. Mathematics is a system in which we draw implications from things known to be true to prove further things to be true - but this chain has to start somewhere, and it's at axioms, which are simply our starting points that we do assume as true without proof. Zermelo-Fraenkel set theory axioms are what "math" as people generally understand it is most commonly based on nowadays, and from those axioms you can draw an implication neither to the continuum hypothesis nor its negation. There is no reason why those have to be the axioms though, and starting from another set of axioms you could very well answer the continuum hypothesis - it'd just be a different kind of math, but logically just as valid. This isn't a case of "well technically" with no real implications to mathematical work, either - different sets of starting axioms do get used at times, with the most obvious example being plain ZF vs ZFC, which is Zermelo-Fraenkel but with the axiom of choice added in, which seems natural yet is controversial because it creates some weird things like the Banach-Tarski paradox where you can cut up a sphere in a finite number of pieces and yet reassemble those pieces into two identical spheres. And so, problems are considered in ZF and ZFC separately.
Underestimated comment
One basic axiom would be 1+1 = 2?
@@kevinsantillans7415 It could be, but in ZF based math there's no need: 1+1=2 is actually already something you construct out of other things rather than a basic axiom. The ZF axioms are things like "if two sets contain the same elements, they're actually the same set", "if you have two sets x and y, there also exists a set z made up of the elements of both x and y" and so on. To get to 1+1=2 from there, you go "let's call {[set of sets constructed in a specific manner]} a set of Integers: {0, 1, 2, 3, ...}, and let + stand for a specific set operation". You can then show that when you define numbers and addition as such ("numbers actually stand for specific sets" and "addition stands for a special operation on those sets"), it works exactly as expected. So, 1+1 = 2, but also 2+2 = 4, 5+9 = 14 and the rest.
You re very easy to understand. Great didatic!
thanks for all your vids
Judge: anything else?
6ix9ine: I know how big infinity is
Here is how big infinity Is: imagine a hotel with infinite rooms. This hotel can both be full, and still have vacant rooms, at the same time. This is because in order to equal an infinity(of hotel rooms) you need another infinity(of people) and since it is still an infinity, you can still have vacant rooms since an infinity can never be filled.
+Fez Master And what goes beyond infinity?
***** Nothing. Infinity is a fake concept that goes on forever. But, since it does go on forever, you can never equal it.
Well what goes beyond infinity isn't nothing. Instead it is again infinity. Meaning if you had infinity plus infinity times infinity you get infinity.
However if you have infinity divided by infinity^2 you get 0 because the rate that infinity reaches infinity is much faster on the denominator. #calculus
+Jason Hong but, they had said that there are many infinities. Maybe infinitely many infinites hshsh
+Fez Master If you want to know how big infinity is, just think of an unimaginatively incomprehensibly huge number to represent infinity, and realize that that number is precisely as far from infinity on the number line as is the number 1.
I've heard everything this video has said before having completed 10 years of University studying engineering. However that made sense, looks like the next interesting conversation with my son and daughter
This reminded me of The Fault in Our Stars- "Some infinities are greater than other infinities."
Favourite and valid quote
I want to curl into a ball and die
🅱
Math: has limits
Minecraft: So we meat again...
Omg. This video published back when I was living in my homeland in a small village. Just a very simple life
holy moly 8 years ago the old ted Ed intro what world are we in
I want to thank you Steve Busceme for this math lesson. I'm going to go watch Fargo now.
Wonderfully concise explanation of cardinality ("size" of a set) and Cantor's proof. But I think the more common version is where the new decimal number is defined as nth digit= nth digit of nth decimal number plus 1 (mod 10, so 9 becomes 0)
Funny how i had a question about the ccountability of rational numbers on my Math exam and i get this in my recommended videos two days later
Cantors diagonal arguement was first taught to me by my algorithms professor , it wasn’t tested on or anything, but was just interesting and helped with understanding some concepts
P
@@SEBithehiper945 NP
6:13 There is a glitch in the matrix. [Did anyone else get that glitch in his voice?]
How big is infinity?
Gerog Cantor: which one?
These animations were sooooo good
"Not because it's crazy, or anything"
Ted-Ed, I spilled my coffee because of you
Still confused. How can an infinity be greater than another infinity? infinity is endless!
Exactly! As soon as we say an infinity is bigger than another we are measuring infinities. If we can measure an infinity then it is not an infinity at all!
***** Actually it's really easy: infinity is not a measurment of size, it's an idea, and that's why regular laws of math don't affect it (you can read a little about it's usage in infinitesimal calculus and set theory - which are entirely different, but in their fundemental concepts are very similar).
Since infinity is not a measurement of size, quantity or length, when we say one infinity is "bigger" than the other, we do not mean it is bigger in size, but bigger in the way that WE grasp it. The claim that the real numbers' infinity is greater than the rationals' comes from the idea that you can find a method to count all the rationals in the world (even if not in practice, then in theory) - but you cannot find any method to count all the REAL numbers, not even in theory - and that's what Cantor has proven using the method shown in this video (called Cantor's diagonal argument).
Imaging there will be an endless race of 2 straight lines going with the same speed. 1 line goes first. That one will always stay longer the the other one. Though they are infinitely long.
did you watch the video?
James Jones Technically plunger is right. There is a difference between the size of an infinity ( which is nonsense ) and the size of an infinite set - otherwise known as a carnality. This video glosses over the distinction in the very first couple of minutes and the term has been used incorrectly again and again.
I hate when the person narrating the video makes noises with his tongue and cheeks, sort of like a chewing noise, i dont know why it disgusts me so much. Not hating though, i think this videos are really good, im subscribed and all.
I totally agree. In fact, I stopped watching because of it.
I found it terribly disgusting too.
oh my god i thought i was the only one! the lip smacking irritates me so much!!
He's probably using an electrostatic microphone or a ribbon microphone which capture these kind of soft sounds much better than more common mics (electrodynamic), coupled with the fact that he must have had moist lips and tongue while speaking this day (maybe he should have speak louder and drink more water..?)
By the way, it irritates me too haha
Misophonia
0:53 the same example is in George Gammow's book one two three...infinity
These things makes me question my whole life and universe but helpful
How big is infinity? Me: yes Him: *math sounds*
look i'm 7 years late
Me : bigger than 8
Mafs ...
Ted Ed infinitely taught me more then school did🅱️
How come I understand the later parts of the video but I don't get how you can make the list of fractions matching the numbers.....
infinity and the vastness of universe always amuzes me and blows my mind
One of the most beautiful subjects I've ever learnt, apart from Physics.
If the set of all infinities is infinite, which infinity is it?
Adam Crume The one that stole my brain's lunch money.
Adam Crume Good question, but you can actually prove that there is no "set" of all infinities
infinity.
actually there is no infinity. That's just a myth.
the only true thing is - ILLUMINITY
its a class not a set
The math Videos on this channel are always pure mindfuck
me: binging ted-ed vidoes instead of studying for my upcoming tests.
ted-ed: showing me a video that talks about the material i need to study...
guess you can never escape math.
you could also imagine this in a real life scenario where atoms make up particles. particles make up elements. elements make up materials and objeects which make up things like planets and the sun which could be miniature atoms to huge giants. Everything behaves differently in the quantum realm. whos to say theres no such thing as the opposite, such as a giants realm. maybe we are just tiny microbes in a speck of dust in a world many times bigger than ours, and the giants realm is the quantum realm to another world bigger than theirs. perhaps this is the true definition of infinity.
Big brain🤪
When you say "how big" is something, that means that thing is finitely big.
You can surely ask "how big" for infinite sets. For example: is it possible to map natural numbers one-to-one with rational numbers? Yes; so the two sets have the same size. Its it possible to map natural numbers one-to-one with real numbers? No; given any function from natural numbers to real numbers, there is some real number which the function does not cover. So real numbers are "bigger" (have a greater cardinality) than natural numbers. What about the set of all sizes of infinities? That's a trick question; such a set can be proven not to exist. (This is a proper class which is too big to be a set; so, in a sense, it is "bigger" than any set.)
Superb Ted😊
thank you so much
You can learn more math in several minutes of this video than you can in seven years of school.
Ludwig Wittgenstein because they waste fucking time
No you can't
Your comment is autistic.
Then you paid no attention in class
Good luck with calculus
Imagine, some guy spends his life scrolling down the pi day website, then four years in...
it stops
love to learn in this way. suggestion moving on just add a positive remark(sentence) at the end.
I am only 13 and I literally understood every single thing