Forbidden Division: Point At Infinity

[@floofynooplz4268]

wake up babe new zundamon’s theorem en drop

[@kakarooottttt4298]

"No, even anime girls can't get me interested in advanced math". This is what I used to believe in

[@blarblablarblar]

The world has been shaken

[@inutamer3658]

I'm a math major and I love how thorough they are with the concepts. They really show passion on the topic

[@guilerso7796]

Math is cool actually and i hope more people discover it Recently it was my best discovery

[@zawatsky]

Метан и Тето - самые очаровательные кудрявые воки Японии.🥰Ещё Цуина Кисараги, возможно.☝😉

[@philkaw]

They did surgery on projective space

[@catmacopter8545]

dehn surgery...

[@math1183]

And I'm pretty sure the ratio definition is the construction of surreals?

[@osbourn5772]

Lots of advanced math here. Here's what I think I found, but correct me if I'm wrong: 1:57 - This is a homeomorphism between the circle (also called the 1-dimensional sphere) and the projective line. A homeomorphism is (informally) an invertible function that maps close points to close points. You may have heard of homemorphisms in the joke "a mug is the same as a doughnut", and this is just another example. This particular function that converts from points on a circle to real numbers is somewhat similar to the tan function from trigonometry. 3:24 - The concept of a point at infinity is called the one-point compactification of a topological space, although here it is being equipped with algebraic operations. The one-point compactification of the real line is called the real projective line. There's also a real projective plane, which (I think, I might be wrong) is nice for working with conic sections because things like circles, parabolas, hyperbolas, and ellipses are all actually the same thing in real projective space. 6:04 - Defining two objects to be equal to each other is done using something called equivalence classes, and brackets [] are standard notation when dealing with equivalence classes. Here, equivalence classes are being used to define homogeneous/projective coordinates. 12:42 - "Well-definedness" is a technical term used when defining functions on equivalence classes. When you define what equality means for a set X using equivalence classes, and you want to construct a function whose domain is X, you have to prove that the function "respects" the defined equality. 13:43 - Adding both a positive and negative infinity gets you something called the extended real numbers, which are also useful but very much a different concept than the projective line.

[@APaleDot]

"I don't really get it... but ok" is basically her catchphrase at this point.

[@Wou_]

You are a brilliant teacher. The whole demonstration on this video, as well as in your other ones, is incredibly easy to follow and understand even for someone like me who's always struggled with even school level math. You do a fantastic job at setting the building blocks of what concepts need to be introduced first in order to later introduce more complex concepts, and the dialogues between Zundamon and Metan have a reasonable pace and are excellently supported by the whiteboard images. Thank you for such an impressive content. Love it. 💚💜

[@marcelmajewski5373]

Thanks for the explanation on why some indeterminate forms are actually indeterminate. My math teacher never showed proof why 0*∞, ∞ - ∞, or ∞ + ∞ are indeterminate. He just told us that they could be different sizes or just can't be treated like numbers. Your simple proof using ratios really showed me why they're indeterminate. These lessons are really simple and fun to watch, keep it up!

[@fsponj]

Wait.. how is ∞ + ∞ indeterminate?

[@MsGinko]

@@fsponj because ∞ is not equal to +∞. Similar case (∞-∞) with the same proof: Let 1/0 = ∞ ∞ + ∞ = ? 1/0 + 1/0 = (1*0+1*0)/(0*0) = (2*1*0)/(0) = 2*1*(0/0) Indeterminate.

[@itsbishop2285]

I highly enjoy the little part at the end where it gives you a new skill unlock

[@cdkw2]

13:23 me when I see higher level maths

[@Waterwolf221]

I love zundamon

[@lucas0_03]

Zundamon is better at math with each video

[@zacharymiller3591]

Can't believe I made it to a video 2 mins after it dropped

[@Cr_nch]

8:06 Yes Zundamon speak your truth 🗣

[@mole2100]

Zundamon so adorable

[@darkknight1105]

It has always bugged me how it was impossible to divide by 0. So at one point I decided to define infinity as 1/0 just out of curiosity and ended up with the exact same results found in this video! (even if my method wasn't rigorous at all). It was nice seeing that I was not the only one thinking about this. This video made me happy today.

[@mjay_arts4]

Cool! :D I tried defining it in such a number and found many difficulties lol

[@Mulakulu]

Keep in mind, dividing by 0 and defining it to be ∞ loses some predictability and consistency in normal math. 1/0=2/0, so just multiply both sides by 0, and get 1=2. Also, for the limit as x approaches 0 from the negative side of 1/x, it approaches -∞, so getting ∞ there from the assumption that 1/0=∞ is inconsistent. That is why 1/0 is not defined by default, since it can equal anything. Tread carefully friend.

[@mjay_arts4]

@@Mulakulu learnt it in the hard way haha

[@ferlywahyu342]

(1/0) is solution for this equation 1+x=x This is like water in a tank that is already full. When you pour 1 liter of water into a tank that is already full with a volume of x liters, the volume of water in the tank remains x liters. I think (1/0) has its own algebraic rules

[@carterwegler9205]

This is only true if you let 1/0 =♾️ and are very careful or you let 0/0 exist (which is still indeterminate even if 1/0 exists) 1 +1/0 would become (1*0)/0 + 1/0 = 1/0 This could become (0+1)/0=1/0 Or: 1 + 1/0 - 1/0 = 1/0 - 1/0 1=0 Oops... Perspective geometry is good at avoiding some of these problems but algebra quickly falls apart when indeterminate forms start creeping in

[@ferlywahyu342]

@carterwegler9205 add rules x-x=0 not aplicable for 1/0 😁

[@livek1238]

I need two things: 1. Division by 0 being acceptable 2. Zundanon and Shikoku kissing

[@Unofficial2048tiles]

I don't know who the second character you mentioned is, but anyway, WHA-

[@livek1238]

@Unofficial2048tiles Shikoku is the pink-haired girl

[@msolec2000]

@@livek1238 Her name is Metan

[@cdkw2]

1:55 omg animations!!!!!!!

[@thepro4805]

i was waiting for this!! i knew it was coming

[@empty5013]

first they draw you in with cute voice droids then they force you to learn math

[@zawatsky]

При том, что глубокомысленных песен я в их исполнении не припомню. У первой "Встречайте Зунду!" наиболее знаменита, у второй - декадансы... Впрочем, ИИ-Зундамон неплохо справляется с алгебраическими задачами, а вот геометрические ей даются труднее (как всем нейросетям).

[@Minty_Meeo]

YOU FOOL! YOU DIVIDED BY ZERO! YOU HAVE... uh... not doomed us after all?

[@Amonimus]

The last year of school and first year of university mentioned something similar when introducing limits and infinity. If 1/x can be interpreted as slicing up something into small pieces and placing them into cups, then if x=inf, you'd be be to be grinding the object to such fine dust you'd be breaking elemental particles while the cups would fill the universe, and you can't have that, so x needs to be a real number. Inversely, if x=0 you're just not slicing up anything and can't continue.

[@mandarinbot3616]

loving this way of teaching maths

[@misti_kumro]

For anyone who wants to learn more, study Wheel Theory. It's basically an extension of the set of real numbers.

[@IsaacDickinson-tf8sf]

I figured out another way to define using division by 0. We still say 1/0 is a point at infinity, just use the different perspective to define it. Just by using n/0 *0 =n and then we have to use n(1/0)(0) and get n(0/0)=n so 0/0 is one in this case. To resolve the issue with 0/0 being indeterminate, I developed congruence, where two numbers are congruent if they are a*0 and b*0 and a is equal to and congruent to b. we now set a rule that you can only multiply or divide by 0 if the two sides of the equation are congruent, i.e. will be equal after dividing or multiplying by 0. To have the congruence identities for 0, 0 is congruent to 0*1,1-1,0^1. That’s it. For Example, 1-1 is not congruent to 2-2 because it is 1(1-1) vs 2(1-1) so 1(0) vs 2(0) and 1 cannot equal 2, so you can’t divide by zero here. To learn more about this point at infinity, we can look at the negative integer factorials. (-1)!=(0!)/0=1/0, and (-2)!=((-1)!)/(-1)=(1/0)/(-1)=(1/0)(-1)=-1/0. We have to make sure now that 1/0 is not -1/0 or 1=-1 after *0. So 1/(0*(-1)) is not 1/0 so 1(0) is not-1(0). Resolved with the same thing. But we learned that-1/0 is not 1/0. Or at least they are not congruent. They still both equal the point at infinity, but won’t be the same because they are not congruent, meaning you can’t multiply by 0 here to reach a contradiction. A while back I proved to myself that there are no values in the negative integer factorials that are 1, by defining that a factorial would stop once a factorials value was one, showing that 1/0 could be rewritten as the product of every negative variable integer. I’ve also shown myself that if 1=2 then every number is the same number, so I know that issue. 1/0 is commonly referred to as “infinitely many” when referring to the number of Dimension D unit objects to fill a unit Dimension D+1 object because the number of points of length 0 on a line of length 1 has to be 1/0 if 0*(1/0)=1, induction does the rest. Vertical slope is undefined, but vertical slope of 1 unit is 1/0 slope, like on the step function. 1/0=0^(-1) Also in this 0^0=1 and is congruent to 1 because otherwise 0^-1 doesn’t work. That also means that 0^n is not congruent to 0^m unless n=m and n is congruent to m. Just so you know, n=m if n is congruent to m is true. All this does is say 1/0 is not the same as 2/0 but they are the same level of infinity, so that 1 can never equal 2, and it resolves 0^0 and 0/0 and (1/0)/(1/0) indeterminate forms by saying the true value is 1, but you need to factor back what went in to keep both sides the same. Yes I know that this all means n/0 - n/0 is n because n(1/0)(1-1)=n(1/0)(0)=n(0/0)=n(1)=n. Also this makes sure that the formula 1/n=(1/(n+1)) +(1/(n)(n+1)) should hold true, even for when values are 1/0, giving congruences. The only issue is x^(1/0) and we can kind of resolve this by using some diabolical notation: NAN(x)=x^(1/0) so NAN(x) ^0 is x. NAN(NAN(x))=NAN^2(x), and that to the 0 is NAN(x). That’s everything this should have to offer.

[@IoT_]

Hmm, it is somehow similar to the concept of Wheel Algebra, as both aim to resolve certain issues with division by zero. In Wheel Algebra, a structure is introduced where division by zero is defined without leading to contradictions like in standard arithmetic. Your approach, involving congruences and the redefinition of operations with zero, parallels this attempt to give meaning to expressions that traditionally involve undefined behavior. However, there are differences as well. Wheel Algebra provides a complete algebraic structure that includes a special element for handling division by zero, called "bottom" or ⊥. It avoids the indeterminate forms by treating them as a distinct entity, while your method introduces congruence rules that try to distinguish between certain forms of division by zero, specifically using factors of zero to differentiate expressions like 1/0 and -1/0. Additionally, your exploration of factorials and congruence to address negative integer factorials also strays into territory that Wheel Algebra doesn't directly address, focusing more on the properties of numbers as they relate to infinity, factorial behavior, and congruences. Both approaches aim to extend arithmetic beyond its usual boundaries, but your system uses more tailored rules around congruence to attempt to resolve paradoxes, whereas Wheel Algebra sticks to algebraic properties within a predefined structure.

[@IsaacDickinson-tf8sf]

Thanks!

[@worstl]

I'm early to the best KZbin channel of all time 🗣️🗣️🔥🔥🔥

[@asterain4828]

best channel

[@arceliph]

I only can hope to be a good enough Mathematician so that Zundamon can teach my work to others

[@evandrofilipe1526]

Edit: I guess I should explain a bit more. We still get all that cool stuff without division by 0 as long as we use basis vectors squaring to 1 and a basis vector squaring to 0. Why not use geometric algebra to avoid all this confusing division by 0 and division by infinity stuff honestly. I've done limits in a calculus class and it seems this isn't enough of a justification to define limits of 0/0

[@aireyroblox]

this is actually really interesting

[@MathewSan_]

Great video 👍 you did a good explanation!

[@MakeChildrenLearn]

thank you for letting me break the seal

[@WaddlerTheDuck]

Zundamon getting HEATED over 1/0 = infinity 🔥 This is UNACCEPTABLE 💢👊

[@guilerso7796]

Exactly my reaction when the screen shows my answer is wrong and i still didn't realize what my mistake was

[@thebeardman7533]

In physics we use infinity as a number all the time so I used to writingx/inf = 0 that one is very common since all the the integrals must convergence

[@GVS2001]

Zundamon reaction is just my reaction

[@conrad5342]

The approach ♾️ does not have a sign sounds amazingly convincing. I am just wonder how this concept does not contradict with the two limits of exp(x).

[@Mr.MaccaMan]

thanks zundamon

[@jackmehoff9957]

I love listening to these.

[@SarinQ_Q]

Спасибо за работу!❤

[@quantumspark343]

Beautiful channel

[@irfanmuzaki6698]

ずんだもん！

[@compositeur8455]

The limit explanation for why zero is undefined is enough

[@BucketCapacity]

The real projective line!

[@pizza8725]

∞+∞ tehnically equaling to 1 seems so cursed

[@basictutorialsforeveryone4247]

finally, i can nourish my brain again

[@kawaiisopiky]

there!s no way, the creator behind this is so smart to lure me with these anime girls so he can teach me math

[@npc2164]

Ah yes. 2 anime girls saving me from failing collage. What time to live on.

[@conrad5342]

Wasn't the Riemann's sphere a sphere placed on (0;0) and not centered there?

[@andreiinthedesktopworld1178]

"you have broken the seal of division by 0". huh.

[@boium.]

Wow, it's so weird hearing this in English. I was used to the Japanese voices.

[@GVS2001]

Waiting for Zundamon sphere

[@Skarnercrystaline]

Why does Zundamon have such thick thighs like holy shit those are cakedn

[@bigboyrenki]

0 and infinity have cool symmetry between each other. Neither one can be positive or negative; just like there is no positive or negative zero, there is no positive or negative infinity.

[@Jae77]

instead of sleeping early for my lectures, i am once again here watching anime girls teach math 🙂

[@joemama-fk7qn]

1/0 = undefined, but some people say 1/0 = +-infinity.

[@redpacific359]

ah yes, the bubble thought when i was 6 🤔

[@Flower_The_Floral_Queen_BFB]

Im no mathematician but the 1/0=∞ and 1/∞=0 feels weird, If we solve it (in an algebraic way) we get 1/0=∞ ⟹1=0•∞ Which is 1=0??? And the same answer to 1/∞=0 ⟹1=0•∞ Which is 1=0???

[@evandrofilipe1526]

I feel the same way

[@MsGinko]

1/0=∞ ⟹ 1=0•∞ is false, because it is necessary to multiply by the factor (0/0) on the left side, which is forbidden.

[@matitello4167]

Bro you just said 0/0=1, you did the process wrong

[@APaleDot]

They say in the video that 0•∞ is an indeterminant form, meaning it could be either 0 or 1 or any other number, there's no way to tell.

[@Happy_Abe]

So would 1/x be continuous on the whole real number line if we say 1/0= infinity and that positive and negative infinity are the same?

[@mateo301]

I love this chanel

[@aIbertI2798]

ずんだもん調子はどうだ

[@Muhammad_Essameldeen]

Does anyone have any idea about how to make videos like that?

[@zawatsky]

Тебе нужны Voicepeak или Voicevox с соответствующими голосовыми банками, несколько кадров анимации персонажей, плагин LipSync 2D и любой видеоредактор, поддерживающий простую анимацию. Например, Adobe After Effects.

[@Muhammad_Essameldeen]

​@zawatsky thanks for your help but last question, what about the maths in the middle of the screen? Is it LaTex somehow or what?

[@ozzi9816]

Could you do something on Pollard's rho algorithm? It’s more in the realm of programming but I still find it interesting

[@NihalPushkar]

nice representation of \infty as on circle, though for addition and subtraction I would have taken limits rather than using [] since I think \infty + \infty = n. d.

[@z0ru4_]

love it

[@tusharkaushalrajput]

Make a channel for kids too my little brother also love to learn form zundamon.😊

[@alexchan4226]

1/0 is undefined.

[@APaleDot]

Not if you define it.

[@Unofficial2048tiles]

did they even watch the video

[@catmacopter8545]

aw man i thought this was wheel theory lol

[@zawatsky]

Уважаемые Тохоку исходят из неверных посылок. Всё же →0 и 0 - это разные величины. Ноль подразумевает отсутствие аргумента, а по определению деления: сколько раз нужно сложить аргумент с самим собой, чтобы вернуть значение. Поскольку аргумент отсутствует, вопрос некорректен, как и пресловутое изречение Карлсона: вы перестали пить коньяк по утрам, да или нет?

[@mjay_arts4]

A dream come true! 10/0 stars ✨

[@K1zls0]

This is gonna save my college year thanks 😂

[@17duchuanle]

Nice video

[@brandonsaffell4100]

Are ee going to double back on sone of that philosophy? Can Zundamon tell me if abstract objects are real?

[@eWosMrV]

Did i enter the wrong Gensokyo?

[@sfglim5341]

In 2d space isnt there a line at infinity and multiple points at infinity? Idk i haven’t studied projective geometry

[@kodirovsshik]

Is it just me or something about their voices changed since the last video?

[@Effect_channel]

If 1/x=y, than 1/y=x If x=0 and y=∞ it's true

[@TheWin475]

Hot take but Zundamon hotter ngl

[@flummarington]

infinity + infinity doesn't work in the ratio system but x * infinity equals infinity where x is any number... wouldn't infinity + infinity = 2 * infinity in which case the answer would just be infinity? I feel like sum of infinity can be defined like this... right?

[@Pallid3]

10:57 Doesn't ∞+∞ equal 2*∞. So you could say that ∞+∞ = ∞, because 2*∞ = ∞ (according to 9:13)

[@MsGinko]

because ∞ is not equal to +∞. Similar case (∞-∞) with the same proof: Let 1/0 = ∞ ∞ + ∞ = ? 1/0 + 1/0 = (1*0+1*0)/(0*0) = (2*1*0)/(0) = 2*1*(0/0) Indeterminate.

[@fcolecumberri]

How do you make voicevox work in english?

[@zunda-theorem-en]

It needs to be combined with other tools. You can find videos attempting the same challenge on KZbin👍

[@fcolecumberri]

@@zunda-theorem-en which tools?

[@Vengemann]

Can you make a video on 0^0 There's always been a thing about this stuff Most consider that x^0=1 so 0^0 must equal to 1 But In different senses 0^x=0 so 0^0 =0 Again many argue about 0²=0^(3-1) =0^3/0 so many here consider 0/0=1 so they also conclude 0⁰=1 But yet it has to be considered that 0^m=0^n then m must not always be equal to n Again It is sometimes true that 0^(m-l)≠0^n even if (m-l)=n Can you please give a intuitive or rigorous answer about that thing?

[@tangyzhangy]

banger content

[@MsGinko]

Zundamon > Chuck Norris.

[@FsFs3mk-u9n]

I don't get how the proof (11:50) is rigorous, can you please explain it further to me :3

[@windybee2020]

there is no quantity of zeros that equal one and asymptotes never touch a line but approach it so real numbers shouldn’t really represent infinity… i can’t accept this either 😭😭😭😭

[@cid2087]

So 2 times infinity does not equal to infinity plus infinity. What? Why? Huh?

[@rankoo965]

Cubic formula pliz😢

[@RyanYeo-j1m]

I DON'T REALLY GET IT BUT OKAY 🗣️🗣️🗣️🗣️🗣️ 🔥🔥🔥🔥🔥

[@typhoonnamikaze1567]

napa 1/0 ako don ahh.

[@leo-um3pj]

another video

[@user-qu2bp8zt6f]

:D

[@rankoo965]

🐈‍⬛🐈‍⬛

[@Tletna]

Metan, +infinity and -infinity being the same isn't 'intuitive' at all. You're just using a graph to say it's so. +infinity is 2 infinities away from -infinity. If you argue that 2 infinity = infinity, since infinity + C = infinity, then I'd argue then that 0 = infinity and numbers lose meaning at that point. We must say that + and - infinity are not the same unless we're in a special kind of system. Ah, then we see. Metan's a pro Reals mathematician. So, I guess we can ignore Leibniz and his pesky infinitesimals then, right? :P Metan allows 1/infinity, 1/0, and 0/1, but not 0/0? I got to say I prefer Zundamon over Metan so far in these videos. Also, any non infinity k could divide x here at 8:45 because when you multiple any k by 0, you get 0. So, if we're allowing such a calculation, no it definitely isn't like normal arithmetic math. Metan ignored the 0/0 that shows up when one adds k to infinity. So infinity + infinity isn't allowed but infinity^2 is? So, what system of math are we in during this video? It sounds familiar but I don't remember if you named it in the video. One doesn't always get the reciprocal simply by flipping the fraction. The Reiman sphere stuff was cool to bring up. Also, Metan: But people might look at you a bit strangely, you know. Zundamon: That's exactly what I want! Haha! I love you more and more by the moment, Zundamon.

[@windybee2020]

shouldn’t 0*infinity be 0 as you already stated anything multiplied by zero is zero edit: all my basic knowledge of math is getting wrecked rn 11:00

[@Vognar6]

Anything times 0 equals 0 is right, but anything times infinity equals infinity is right too. That's why 0 times infinity is undefined.

[@windybee2020]

@@Vognar6you can’t really multiply zero by anything though? if you multiply nothing by a supposedly indefinite value, it should still be nothing. nothing plus nothing makes nothing, and multiplication is just addition written differently (3+3 -> 3*2) so if your adding nothing on top of each other for an infinite amount, the sum should be nothing.

[@michaellin4230]

@@windybee2020 This stems from our definition of multiplication. If you define multiplication as repeated addition, how do you define something like pi*pi, or -2*-2? You're not really adding infinity 0 times in this definition of multiplication. Like in the video, if you define infinity to be the 1/0 and zero to be equal to 0/1, multiplying then together yields 0*1/1*0, which becomes 0/0(this is notation abuse but ignore it for now). 0/0 is undefined because it breaks a lot of rules of math, i.e. addition/multiplication are no longer consistent and you can prove that any number = any other number. So we define 0*inifinity as being undefined because if we did ascribe a definition/value to it, our system would be non-consistent and you can't do any math with it.

[@The_Commandblock]

I always imagine it like this: take a point that is infinitely close to 0. For example 0.00000...01. Technically this is the same number as zero. If we multiply this number by anything finite like 20 we still end up with 0.00000...20 which is just the same thing as zero again. If we multiply by 10 we can see the 1 moving one digit to the left. So if we multiply by 100000000... or move the one infinitely far to the left we would get something like 1. Note that this is an intuitive explanation and not like a 100% mathematically correct one

[@windybee2020]

@@michaellin4230 how would defining it make it broken? and if it you had to define it would it be 0 or infinity? multiplication in those situations can still be just representative of an addition of numbers like pi + pi + pi + (pi + -(3)) and 2 + 2 (-2 - (-2)) (multiplication of negative numbers would be subtraction not addition) so it is still repeated addition, just with more convenient notation.

[@aIbertI2798]

Day 1000 of tryna get pinned

[@kukproject]

🍘