Zundamon is a vocaloid, not anime ^_^ A comparison might be calling Taylor Swift or Lebron James famous American actors. Just because they appear in similar forms doesn't mean they're the same
@@UnemptyVoidIn general, Vocaloid especially means singing voice synthesizer, not speech synthesizer. However, the word is referrd to singing voice synthesizer, Vocaloid, developed by Yamaha at first.
@@UnemptyVoid well calling something 'anime' really doesn't mean it has to be from an anime. Just anything generally in that popular Japanese art style can be considered pretty anime.
In Japan, these characters (or their voices) are used in all kinds of situations Some cafeterias use them for broadcast purposes, and they are also used in racist videos by the wicked. Of course, math lecture videos are no exception. My favorite Zundamon are those explaining general topology and abstract algebra.
I would say that it is indeed easier: 1. Have your mind open 2. It's only an introduction to a new domain and not some problem to solve. (for example 458674*58712 will require a lot more attention to solve even if the process is basic) 3. You don't have another 15 subjects, and 4 other homework for tomorrow
@@KarolOfGutovo It's in the style of teaching. Plato wrote a lot of books where he pictures Socrates asking simple question to another person. By simply asking the questions the other person manages to learn a lot of things, and then Socrates claim he didn't teach him anything : he just asked questions. The video presented it in a very similar fashion, where the teacher says very little and the student learns mainly by answering questions asked by the teacher. It plays in the philosophy of Plato where he believed that the soul is immortal and accumulates knowledge throughout its lives. And to explain why we don't recall this knowledge he posited that it is dormant and we just need a little nudge to awaken it, hence Socrates didn't teach the man but awoken the knowledge he already had. Edit : Correcting small grammar mistakes
Zundamon is a vocaloid, not anime ^_^ A comparison might be calling Taylor Swift or Lebron James famous American actors. Just because they appear in similar forms doesn't mean they're the same
wow, i cant believe i actually learned something new from this. im failing my calc 2 class in college and i desperately need Zundamon to explain to me everything about convergent series before my test in 2 days. subscribed
I'm surprised I haven't seen many UA-cam videos in this format! Plato's dialogs are some of the oldest and most respected writings in European history (and didn't Mencius or Meng Zi use dialog too?) we should have more dialogs. It's a great way to introduce surprising or confusing topics. And the English voices are understandable and well-written!
I didn't see that anywhere in the comments so I'll help around just in case some wonder ... At 6:42, what she is explainingis the following operation : ae=be ae-be=0 (a-b)e=0 a-b=0 or e=0 (impossible since it is defined to be non zero) a=b That's the comparison between the two coefficients being talked about.
You are assuming the properties of an Integral Domain. If ab = 0 we cannot conclude that either a or b is 0 unless we know to be working in an integral domain.
@@charlesleninja and in this case we even know we are NOT in an integral domain as (aε)(bε)=0 for all a,b∈ℝ but neither factor is zero if a and b are nonzero
@@nobody-sq3nq Exactly, even just with Epsilon Squared we know not to be working in an integral domain. But there could be an argument where the Dual Numbers are "semi-integral" in the sense that if you multiply Epsilon by a non-zero real number, it is non-zero. In which case the argument of the original comment would work.
1. If a is real, and aε = 0, a = 0. Proof: Case a ≠ 0 0 = 0×1/a = aε×1/a = ε. But ε≠0. Then a=0. 2. If a, b is real and aε = bε, a = b. Proof: (a-b)ε = aε-bε = 0. For 1, a-b = 0 → a = b. 3. z = a+bε, w = c+dε. a, b, c and d real. If zε = wε → a=b Proof: zε = aε+bε² = aε wε = cε+dε² = cε → aε = zε = wε = cε → (by 2) a = c.
@@aloi4 If a is a zero divisor, a doesn't have multiplicative inverse. In your proof, you assume that a isn't a zero divisor to prove that a isn't a zero divisor.
The only reason I prefer the japanese version, and this may go for a lot of others too, is because the english voices sound way more robotic, I wouldn't have a problem with it otherwise
I watch both japaneese and english and I kind of get your point, but I dont really mind. Maybe my standards are low but I still like both of them. Both dub and sub are amazing.
Thank you for the helpful comments! I'm glad that some people like the English voices. At the same time, honest feedback is highly valuable. I will work on improving the quality of the voices. In particular, I've heard that Metan sounds more robotic compared to Zundamon, and I agree. I will prioritize fixing that.
@@zunda-theorem-enWe appreciate the fact that you're even creating an English dub of your high quality videos. AND you're taking constructive criticism where it counts and following viewer feedback. This shows you respect your audience. And that in turn in ABSOLUTELY awesome. Keep up the amazing work boss. Have a good one 🫂. Im aiming to be a mathematician in the future too! So these videos push me into constantly wanting to learn. Thanks!
I've just found this English Dub channel, thank you! I was directed from a link in your English Sub channel. I love your videos, but I'd also like to have seen the dual numbers defined via the polynomial ring. R [ X ] / < X^2 > (the real numbers adjoined X, quotient by the ideal generated by X^2) This is how my professor introduced them and I think it makes them a lot more concrete and easier to grasp from first introduction, and easier to accept the notion that something can square to zero without being zero.
i mean that's true, but its probably easier to just say "what if this thing was true? What would be the consequences?" (which is what happened with the complex numbers, which definitely were not original defined as a quotient ring!) than having to explain rings and their quotients.
Thanks for pointing that out, it definitely helped me appreciate the concept more especially when compared with the similar quotient ring definition of the complex numbers. I think that approach would be too tough to explain to anyone who doesn't have a basic grasp of ring theory though, so I get why the video skipped it.
6:48 you can't divide by epsilon but you can prove this in a different way: b1*eps=b2*eps => (b1-b2)*eps=0, eps is not zero so that (b1-b2) must be zero, so b1=b2
@@maindimpro2618it's not a division, it's conclusion: if product of multiple terms is 0, one of terms is equal to 0. We know that eps!=0, so b1-b2 has to be.
@@wumi2419that property doesn't hold over the dual numbers since eps*eps=0. The real argument is that we define dual numbers to be equal iff both their components are equal.
@@wumi2419 That's not true. You can only use the argument "if product of multiple terms is 0, one of terms is equal to 0" when you are operating in what it's called an Integral Domain, which isn't the case. For example eps*eps=0, but both are different from zero.
what have i stumbled upon this time??? jokes aside your content is very fascinating. the problems are interesting, the way the audience is led through each part of the lecture is amazing as it makes everything way easier to understand. as for the english, i don't see anything wrong with it either. please keep this up!
I did not expect to be drawn in this much by cute anime characters explaining math, but I really enjoyed this. The explanations are very good, too! You do a very good job of introducing concepts and building on them.
Since dual numbers are among those concepts I've never heard of (even though it's actually hiding in FTC all the time), I can feel even clearer that this video is at a pace just as suitable as my "real" professors. This video might be slow for people with the smallest bit of prior knowledge, but it helps start from scratch. Also, Plato's dialog form leads us to "discuss" in the absence of an in-person lecture. btw I didn't know Zundamon can speak English so well
I really like the style of the video, I'm glad you're taking in the feedback to improve the voices, that will make it even better though I already quite like it. But I've seen few people comment on how good the pedagogy is here. It's really well explained and made intuitive, we're discovering a topic by doing, not being handed down some info about it. Overall great teaching and very engaging !!
It stresses me out that I enjoyed this. It also stresses me out that I've spent so much time listening to the soundtrack of a certain game that I immediately recognized it here.
in the sense that it uses the epsilon symbol, and that it is an extension to the reals, yes. Actually, now that i think about it, if you mean infinitesimals as in differential forms (e.g. dt or dx), kind of, yeah! they arent 0 but powers make them go to zero! If you mean infinitesimals as in the surreals, thats a bit more of a stretch.
@@catmacopter8545epsilon and dx are infinitisimals with special conditions. The condition or epsilon is that epsilon²=0 and the condition for dx is that dx approaches 0.
@@catmacopter8545 woa, i didn't relate the condition e^2=0 to that of differential forms d^2 = 0. Except e is thought of as a number, and d as a "nilpotent" operator.
It's basically how Newton did derivation when they were called fluxions and fluents, later we adapted Liebniz's notation of derivation and Newton's flux theory became just a neat historical fact.
Interesting concept. Also, interesting subject! I had never heard of dual numbers, but they seem they could be very useful in automatic differentiation, or even just differentiation done by hand. As for the format, I think the mechanical voices are a bit harsh and not very expressive. Can you try either voice acting the characters yourself, with a voice changer, or using some more expressive AI voices?
Also, if you start from the regular unit circle in the complex plane and take a thin slice around the real axis, in fact an infinitesimally thin slice, and then stretch it vertically back to infinity to fill the plane, you get the two lines shown in the dual number plane. Could this be a useful mental image to understand how dual numbers works?
Dual numbers aren't that useful computationally, however they are super useful for theoretical mathematics. A surprising fact is that directional derivatives correspond to ring maps from smooth functions to the dual numbers. You can use this to generalize notions of the tangent space to much funkier objects like the Zariski tangent space.
This opens so many possibilities. So basically you can introduce any "unit" and work with it in the mathematical field, simplify and calculate things, and then see if you have to still assume it down the line, or if it is not even needed. That's so genius! My gut feeling still tells me that I should be careful with that, but it sounds like a great way to address this. Maybe I could use this together with full inductions to calculate things 😁
@@dogedagog0-ol6pd ig i truly it is more methodical the normal way... But it is pretty beautifull how making new numbers forms derivatives and limits and infinitessimals out of nowhere (sorry for the bad english) have a good weekend :D
What if we imagine a three-dimensional space where there will be real numbers on one axis, imaginary numbers on the second, and dual numbers on the third?
I _knew_ my math teachers should've been anime sprites.
Zundamon is a vocaloid, not anime ^_^
A comparison might be calling Taylor Swift or Lebron James famous American actors. Just because they appear in similar forms doesn't mean they're the same
@@UnemptyVoid erm, she was never a character for the vocaloid software
@@UnemptyVoidIn general, Vocaloid especially means singing voice synthesizer, not speech synthesizer.
However, the word is referrd to singing voice synthesizer, Vocaloid, developed by Yamaha at first.
@@UnemptyVoid well calling something 'anime' really doesn't mean it has to be from an anime. Just anything generally in that popular Japanese art style can be considered pretty anime.
@@UnemptyVoid
Zundamon is for NEUTRINO, not VOCALOID.
It's strangely engaging to hear anime characters talking about high-level maths.
its my favorite genre
exactly
In Japan, these characters (or their voices) are used in all kinds of situations
Some cafeterias use them for broadcast purposes, and they are also used in racist videos by the wicked.
Of course, math lecture videos are no exception.
My favorite Zundamon are those explaining general topology and abstract algebra.
High-Level???
This is more of a basic level understanding for another topic lol
The cute cartoonish robotic voices makes my brain think this is elementary math for kids and my brain actually processed it easier!
I would say that it is indeed easier:
1. Have your mind open
2. It's only an introduction to a new domain and not some problem to solve. (for example 458674*58712 will require a lot more attention to solve even if the process is basic)
3. You don't have another 15 subjects, and 4 other homework for tomorrow
Socrates teaches Plato dual numbers, animated, colorized, 2024
Dual numbers are a very modern concept, nineteenth century.
@@KarolOfGutovo
It's in the style of teaching. Plato wrote a lot of books where he pictures Socrates asking simple question to another person.
By simply asking the questions the other person manages to learn a lot of things, and then Socrates claim he didn't teach him anything : he just asked questions.
The video presented it in a very similar fashion, where the teacher says very little and the student learns mainly by answering questions asked by the teacher.
It plays in the philosophy of Plato where he believed that the soul is immortal and accumulates knowledge throughout its lives. And to explain why we don't recall this knowledge he posited that it is dormant and we just need a little nudge to awaken it, hence Socrates didn't teach the man but awoken the knowledge he already had.
Edit : Correcting small grammar mistakes
@@charlesleninja ah how i missed when philosophy class was this simple.
Lol, I was reminded of the dialogue between Socrates and meno
@@charlesleninja Ah, ok. I was not acquainted with that.
bro got anime fans to learn math
Tons of mathematicians already are weebs 💀
@@AlgebraicAnalysis you can make a philosophical essay out of this!
Zundamon is a vocaloid, not anime ^_^
A comparison might be calling Taylor Swift or Lebron James famous American actors. Just because they appear in similar forms doesn't mean they're the same
bro got math fans to learn anime
@@UnemptyVoidno one cares
"So small, it's square is zero!" remains the best way to describe epsilon to me.
everything about this feels so hyper targeted oh my god
Ooh ho! Hello azali. Didn't know u were a math enthusiast
this changed my life
Bro i never thougth that i se your coment here
Of course
You obtain epsilon?
I GOT JUMPSCARED BY THE ENGLISH DUB THINKING IT WAS THE JP CHANNEL
this is very cool
so 1, i, and epsilon is a Pythagorean Triple?
Bro thats crazy
Wait a minute
that's kinda crazy to think about
😨
Can someone explain this?
A deep discussion between two of the wisest philosophers of our time. Truly touoching.
I don't think philosopher is better than mathematician.
lol
It's so weird hearing Zundamon without all the のだ's
At 0:30 I was expecting VSauce to come out and say “or is it?”
wow, i cant believe i actually learned something new from this. im failing my calc 2 class in college and i desperately need Zundamon to explain to me everything about convergent series before my test in 2 days. subscribed
Did you pass
@noletaw6013 nope. im gonna fail the class
ϵ : You
ε : The guy she tells you not to worry about
You are "in" and he's "small" so honestly you have nothing to worry about.
13:39 my friends when I offer to help
VOICEROIDに多言語話せられるの初めて知ったわ(笑)(笑)
This channel fills the hole in my heart that was left after I finished all 6 math girls books.
Oh finally the contents I was looking for the ages, Numberphile plus Zundamon.
I'm surprised I haven't seen many UA-cam videos in this format! Plato's dialogs are some of the oldest and most respected writings in European history (and didn't Mencius or Meng Zi use dialog too?) we should have more dialogs. It's a great way to introduce surprising or confusing topics.
And the English voices are understandable and well-written!
Dual Numbers are cool, but why is an anime character teaching me dual numbers lol
Времена такие
It's the only way I can actually pay attention, so I'm not complaining
Why not?
@@obz1357 if the only way to get your attention to smth is to slap anime girls this is honestly sad 😿😭
@@Ne-vc5pm I know 😭😭
I didn't see that anywhere in the comments so I'll help around just in case some wonder ...
At 6:42, what she is explainingis the following operation :
ae=be
ae-be=0
(a-b)e=0
a-b=0 or e=0 (impossible since it is defined to be non zero)
a=b
That's the comparison between the two coefficients being talked about.
You are assuming the properties of an Integral Domain. If ab = 0 we cannot conclude that either a or b is 0 unless we know to be working in an integral domain.
@@charlesleninja and in this case we even know we are NOT in an integral domain as (aε)(bε)=0 for all a,b∈ℝ but neither factor is zero if a and b are nonzero
@@nobody-sq3nq Exactly, even just with Epsilon Squared we know not to be working in an integral domain.
But there could be an argument where the Dual Numbers are "semi-integral" in the sense that if you multiply Epsilon by a non-zero real number, it is non-zero.
In which case the argument of the original comment would work.
1. If a is real, and aε = 0, a = 0.
Proof: Case a ≠ 0
0 = 0×1/a = aε×1/a = ε.
But ε≠0. Then a=0.
2. If a, b is real and aε = bε, a = b.
Proof: (a-b)ε = aε-bε = 0. For 1, a-b = 0 → a = b.
3. z = a+bε, w = c+dε. a, b, c and d real.
If zε = wε → a=b
Proof:
zε = aε+bε² = aε
wε = cε+dε² = cε
→
aε = zε = wε = cε
→ (by 2)
a = c.
@@aloi4
If a is a zero divisor, a doesn't have multiplicative inverse.
In your proof, you assume that a isn't a zero divisor to prove that a isn't a zero divisor.
The only reason I prefer the japanese version, and this may go for a lot of others too, is because the english voices sound way more robotic, I wouldn't have a problem with it otherwise
I watch both japaneese and english and I kind of get your point, but I dont really mind. Maybe my standards are low but I still like both of them. Both dub and sub are amazing.
@@cdkw2 I also like both, but the japanese voices are charming, which makes me prefer it
Thank you for the helpful comments!
I'm glad that some people like the English voices. At the same time, honest feedback is highly valuable.
I will work on improving the quality of the voices. In particular, I've heard that Metan sounds more robotic compared to Zundamon, and I agree. I will prioritize fixing that.
@@zunda-theorem-enWe appreciate the fact that you're even creating an English dub of your high quality videos. AND you're taking constructive criticism where it counts and following viewer feedback. This shows you respect your audience. And that in turn in ABSOLUTELY awesome. Keep up the amazing work boss. Have a good one 🫂. Im aiming to be a mathematician in the future too! So these videos push me into constantly wanting to learn. Thanks!
@@zunda-theorem-en now that I think about it I see it too, Metan does sound more Ai'ish
I've just found this English Dub channel, thank you! I was directed from a link in your English Sub channel. I love your videos, but I'd also like to have seen the dual numbers defined via the polynomial ring. R [ X ] / < X^2 > (the real numbers adjoined X, quotient by the ideal generated by X^2) This is how my professor introduced them and I think it makes them a lot more concrete and easier to grasp from first introduction, and easier to accept the notion that something can square to zero without being zero.
i mean that's true, but its probably easier to just say "what if this thing was true? What would be the consequences?" (which is what happened with the complex numbers, which definitely were not original defined as a quotient ring!) than having to explain rings and their quotients.
Thanks for pointing that out, it definitely helped me appreciate the concept more especially when compared with the similar quotient ring definition of the complex numbers. I think that approach would be too tough to explain to anyone who doesn't have a basic grasp of ring theory though, so I get why the video skipped it.
Zundamon's questions followed my thought process EXACTLY like it was crazy, and then Metan always gave a really good answer. This is awesome
6:48 you can't divide by epsilon but you can prove this in a different way: b1*eps=b2*eps => (b1-b2)*eps=0, eps is not zero so that (b1-b2) must be zero, so b1=b2
On last step you already divided both sites by epsilon ( |ε|=0
@@maindimpro2618it's not a division, it's conclusion: if product of multiple terms is 0, one of terms is equal to 0. We know that eps!=0, so b1-b2 has to be.
@@wumi2419that property doesn't hold over the dual numbers since eps*eps=0.
The real argument is that we define dual numbers to be equal iff both their components are equal.
But wouldn't (b1-b2)*eps = 0 mean that b1-b2 = eps also?
@@wumi2419 That's not true. You can only use the argument "if product of multiple terms is 0, one of terms is equal to 0" when you are operating in what it's called an Integral Domain, which isn't the case. For example eps*eps=0, but both are different from zero.
Ah dual numbers, the answer to the question "What if we _intentionally_ added a zero divisor to a field"
You lose your livestock because you have no field :(
never thought i would an maths vtubers!
dual numbers are such a cool topic, the reason i start caring about group theory. great video!
This is hands-down the best way to teach math. Thanks for your content
This feels like a children's educational show for adults. I kinda like it
why is my math anime?
To help you remember
To get satisfaction while studying
Zundamon is a vocaloid, not anime
Always has been.
I love how you always talk about the most interesting subjects! I hope to see hyperbolic numbers soon!
I am Korean
I love your videos
Please continue your upload activities
The collaboration of Zundamon and math is just insane!!
Now you are making them in english! I watched your previous content with subtitles, but this is way better! Thank you so much!
This is really enjoyable to watch and kept my attention the whole way through. Would really appreciate if you did more!
damn, this was actually great and easy to follow. very cool!
I love this format so, so much! I did not think I would be into this, but oh how wrong was I. Amazing work.
what have i stumbled upon this time??? jokes aside your content is very fascinating. the problems are interesting, the way the audience is led through each part of the lecture is amazing as it makes everything way easier to understand. as for the english, i don't see anything wrong with it either. please keep this up!
I did not expect to be drawn in this much by cute anime characters explaining math, but I really enjoyed this. The explanations are very good, too! You do a very good job of introducing concepts and building on them.
Great content on all fronts. Genuinely enjoyed it and the explanations were really nice. Thanks for English version, looking forward to next videos
우와... 애니메이션 캐릭터들로 이런 좋은 영상 만들어주셔서 고마워요! 이제 영어를 열심히 공부해야 할 이유가 생겼군요.
best video i accidentally clicked on
This quickly became my favorite math yt channel, great work!!!
I’m so happy to have found the channel!
日本ではもはや御馴染みになっているボイスロイドの解説動画だけど、コメ欄から察するに英語圏の人達にはまだまだ目新しく、そして奇妙なものとして映ってるようですね。
それぞれの反応が面白い。英語をしゃべるずんだもんもなんだか可愛くて素敵。
I saw the original japanese channel back then and i can somehow understand it,but the fact you made a new english channel is really awesome!
Well this was an unexpected gem.
the ending was very satisfying, seeing a concept that i felt was very abstract being a core of something so important
This was my first video of this channel! I think it was a very interesting way to teach, their interactions are very cute, keep up the good work
Since dual numbers are among those concepts I've never heard of (even though it's actually hiding in FTC all the time), I can feel even clearer that this video is at a pace just as suitable as my "real" professors. This video might be slow for people with the smallest bit of prior knowledge, but it helps start from scratch. Also, Plato's dialog form leads us to "discuss" in the absence of an in-person lecture.
btw I didn't know Zundamon can speak English so well
Wow. That was actually educational. I'm surprised. I didn't know anything about epsilon. Good job!
This is like a revelation for me, never thought that you can assume epsilon backward like this lol
Bro this unironically helped me at school
What a great idea for a channel! It sure would encourage people to learn maths!
I wish you the best of luck!
Zundamon sounds pretty cute "i dont weally get it" but like other people have noted Metan is a little robotic, awesome that you're working on it!
This video showing up in my recommendations turned out to be an interesting result!
I really like the style of the video, I'm glad you're taking in the feedback to improve the voices, that will make it even better though I already quite like it. But I've seen few people comment on how good the pedagogy is here. It's really well explained and made intuitive, we're discovering a topic by doing, not being handed down some info about it. Overall great teaching and very engaging !!
It stresses me out that I enjoyed this. It also stresses me out that I've spent so much time listening to the soundtrack of a certain game that I immediately recognized it here.
We got anime characters teaching modern algebra before GTA VI.
Great content. Hope this channel skyrockets quickly.
this is absolutely amazing; please keep it up!
I'm confused that I understood this more easily than I understood it in my native language!
Wow this is the best video I’ve watched
Me imagining gaining real knowledge aside of chess vids from UA-cam before clicking this video
Technically epsilon could be thought of as a small number where it’s square can be ignored like Taylor series
9:27 basically
Essentially an infinitesimal
This feels like a way to show limits with epsilon
It was the best thing that youtube recommend me in a long time.
I went in curious, got out with my mind firing on all cylinders at the implications of this "simple" idea
Thank you for doing an english version please continue !
I dont expect ずんだもん speaking English and teaching Math lesson.
But I watch whole video anyway, good job.
Thank you so much, now derivatives for me are gonna be 10000000%x easier
Is this related to infinitesimals in any way?
Yes
No
in the sense that it uses the epsilon symbol, and that it is an extension to the reals, yes. Actually, now that i think about it, if you mean infinitesimals as in differential forms (e.g. dt or dx), kind of, yeah! they arent 0 but powers make them go to zero! If you mean infinitesimals as in the surreals, thats a bit more of a stretch.
@@catmacopter8545epsilon and dx are infinitisimals with special conditions. The condition or epsilon is that epsilon²=0 and the condition for dx is that dx approaches 0.
@@catmacopter8545 woa, i didn't relate the condition e^2=0 to that of differential forms d^2 = 0. Except e is thought of as a number, and d as a "nilpotent" operator.
英語版あったんだこのチャンネル…
昨日見た動画だから(訳が)見える見える…
I'm having trouble figuring out whether I stayed up too late and am now hallucinating this video.
I am utterly confused about what I have stumbled into but I love it
Awesome!! I legit had zero idea this exists! Now Dual Numbers are stuck in my head with anime characters lmao.
Jesus Christ what fresh hell have I fallen into
First I'm learning math from the AI Taylor Swift and now I'm learning math from two anime figures. Isn't UA-cam amazing?
Wow this video is excellent! I'm going to share it with my students right now!!
This has to be the most adorable thing I've seen this year
It's basically how Newton did derivation when they were called fluxions and fluents, later we adapted Liebniz's notation of derivation and Newton's flux theory became just a neat historical fact.
Wow new music in the video.
Very cool and thank you!
The differentiation thing blew my mind, that's crazy.
I just saw this and I BEG YOU PLS CONTINUE THE ENGLISH VERSION ❤❤❤
I am 3 minutes in and i am quitting if she says "dual numbers are like complex numbers" one more time
What I really truly need is a lecture about Hilbert space given by Beavis. I have had that concept in the back of my mind for years.
I didn't know Zundamon and Metan teaching me Math was something I needed😂
I somehow couldn't get my eyes off this...I didn't expect it to seriously teach about Maths but it did and I understood!!
That is so cool!!! I just learned complex coords and calculus so this is extra cool. Thank you for teaching me! :D
ずんだもんが英語しゃべってる？！
Wow, I thought it was just a fun exercise but the way it suddenly relate to derivative it amazing!
Interesting concept. Also, interesting subject! I had never heard of dual numbers, but they seem they could be very useful in automatic differentiation, or even just differentiation done by hand. As for the format, I think the mechanical voices are a bit harsh and not very expressive. Can you try either voice acting the characters yourself, with a voice changer, or using some more expressive AI voices?
Also, if you start from the regular unit circle in the complex plane and take a thin slice around the real axis, in fact an infinitesimally thin slice, and then stretch it vertically back to infinity to fill the plane, you get the two lines shown in the dual number plane. Could this be a useful mental image to understand how dual numbers works?
Oh wait, there's a JP channel with subs? Well, I already understand 90% of what they say, so I'll rather watch that ^_^; よろしくお願いします。
Dual numbers aren't that useful computationally, however they are super useful for theoretical mathematics. A surprising fact is that directional derivatives correspond to ring maps from smooth functions to the dual numbers. You can use this to generalize notions of the tangent space to much funkier objects like the Zariski tangent space.
This opens so many possibilities.
So basically you can introduce any "unit" and work with it in the mathematical field, simplify and calculate things, and then see if you have to still assume it down the line, or if it is not even needed.
That's so genius!
My gut feeling still tells me that I should be careful with that, but it sounds like a great way to address this.
Maybe I could use this together with full inductions to calculate things 😁
This is such an underrated channed ❤❤❤❤❤❤❤❤❤. I love it
limits should be taught this way
I think the normal way would make more sense instead of just making new numbers again
@@dogedagog0-ol6pd ig i truly it is more methodical the normal way... But it is pretty beautifull how making new numbers forms derivatives and limits and infinitessimals out of nowhere (sorry for the bad english) have a good weekend :D
You mean using dual numbers or using lolis?
@@dogedagog0-ol6pdNeh
@@nestorv7627 lolis ofc
Great video!! i don't even study math at the time, but this was interesting to watch anyway :3
I spot the use of the best math font ever, STIX 2. your good taste is noted
1:21 but what if there was an x such that x(0)=y | y≠0, pum all n/0 problems solved
What if we imagine a three-dimensional space where there will be real numbers on one axis, imaginary numbers on the second, and dual numbers on the third?
Dual numbers look like the generalization of the Maclaurin expansion, used extensively in Physics and Engineering
13:00 Well That Derivative Part Was Really A Shock🗣️🔥