@@inutamer3658 просто эти голосовые банки поддерживают эмоциональные параметры. Тебя так легко впечатлить.😏Кстати, существует зеркало этого канала на японском, там эти двое говорят по-японски, и подача несколько отличается.
@@math1183 No, not even close. { 1 | 0 } is not a valid surreal number, because it breaks a law of construction where all elements of the left set must be strictly less than all elements of the right set (this may be inaccurate, see Wikipedia’s page on Surreal Numbers for more information). Flip them around to get { 0 | 1 }, and you get 1/2, which we can hopefully agree is not infinity.
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.
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 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.
@MsGinko Unfortunately the video is very misleading and it’s a shame cause this is such a delicate yet beautiful topic in mathematics. An indeterminate form is the “form” of a limit that can’t be determined, in other words, it is a limit value that is indeterminable. The example most well known is 0/0 because on the one hand, the limit as x approaches 0 of f(x)=x/x equals 1, but on the other hand, the limit as x approaches 0 of g(x)=2x/x equals 2. The limit forms of both are 0/0 hence 0/0 is an indeterminate form. Positive infinity minus positive infinity is indeterminate because of the limits as x approaches positive infinity of the following two functions: f(x)=x-x and g(x)=2x-x. The limit of the first is zero but the second is positive infinity. Hence it’s an indeterminate form. Positive infinity plus positive infinity is a determined form that being positive infinity which is undefined. One can rigorously prove this using sequences, but to simplify it, it’s essentially because adding anything positive to an already upward unbounded sequence will remain upward unbounded. Your proof is wrong in a couple fundamental ways. First of all you can’t just define 1/0 to be infinity, you have to use limits of sequences. Therefore while you can use arithmetic of limits, you can’t do arithmetic using 1/0 and especially not dividing by zero.
@@ccbgaming6994 The problem here is that you confuse the +∞ (positive infinity) with the ∞ (infinity). They are not the same. Everything you mention is perfectly valid on the "extended real number line". The intention of the video is to show that the "extended real number line" can be represented by an another metric space called "projectively extended real line", which introduces the concept of a "point at infinity".
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. 💚💜
Zundamon not always understanding, but also sometimes understanding and figuring it out intuitively helps me feel like i'm doing my best to learn ^^ thank you!!
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.
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.
I had an epiphany on this topic a number of years back, based on one of the teaching methods I was shown as a child. Division is taking the numerator and breaking it into Denominator groups. By attempting to divide by zero, you are breaking the numerator into no groups. It cannot be calculated because it is erasing the numerator. Mathmaticians should really treat it identically to multiplying by zero, because the result is identical- the absence of a value.
@@aroventalmav888 Interesting. Do you know the name of the method? It doesn't make much sense to me since zero is not the same as "no valid answer", so I'd love to know more.
If you're interested in this topic and including the 0/0, try the transreals introduced by anderson. It's a but like NaN in computation, but you can construct it and prove that 0/0 = 0^0 in transreals.
There's also the "wheel algebra" where you also define "0/0" as another point outside the circle called the "error element", and you define every other undefined result to be equal to that term.
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.
(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
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
Mathematicians used to ignore roots of negative numbers. Because it did not make sense, it was undefined, but now we use it everywhere. Maybe it's the same case with 1/0
very projective geometry approach, I remember my favourite sentence of that class back when I took it was "parabolas are also just ellipses". However, of course there are many different approaches. For example one can try to functional analysis on it, so 0\in\sigma(0_X), assuming that X is for example a banach or hilbert space. In fact, if the entire space is {0}, the 0 operator is gonna be every possible operator, because all that an operator that maps from 0 to 0 can do, is mapping to 0. So in that case, 0/0=0^(-1)(0)=0, because the operator is both surjective and injective obviously, so it has an inverse. In \doubleR, you can't find an inverse because 0 is in the residual spectrum of the 0 operator, with the 0 operators range not even close to being dense in \doubleR. You could however look at the preimage and see that 0^(-1)({0})=\doubleR, which is also why I feel uncomfortable that 1/0=\infty is the result of this video, because obviously {1} otinRan(0), and the 0 operator would have to map \infty to 1, so that the preimage 0^(-1)({1})={\infty}, which is a problem due to alot of reasons. you know, a long time ago I also studied electrical engineering, and they really don't mind at all about dividing by 0, they just do it, so maybe sometimes it's a good idea (damn, my former math faculties will hate me for bringing this up). I thank you for your efforts on this projective geometry approach.
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.
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.
There's nothing to devide with. Like a stick in the river.. the stick is deviding by two.. so when you remove the stick.. the river is now one.. nothing left to do.
Zero is solved by t. Anything larger than zero is part of the t series.. t0 is not because its the point "where you have not yet started" 1/0 is a "non starter" equasion.
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
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).
I still dont understand why the forbidden division is not used in school or is not acceptable by some people and also does infinity times infinity is equal to zero also means that adding infinity with another infinity in infinity times right?
Ох, недавно как раз изучал эту тему, и она тоже меня взбудоражила - такое вроде бы не слишком сложное действие с нанесением на окружность всех чисел - и вот мы уже смогли добавить бесконечность
Cool video! Love breaking maths :) That's why I also aim to define division by zero. But at 10:26, there is a small and crucial inconsistency. You have mentioned previously that 0/0 is prohibited, at least for this episode, but in fact, by performing regular fraction addition operation, you assume that 0/0 = 1. The output result most probably is correct. Just the proof does not necessarily confirm it.
Thank you for your comment👍 I realize my explanation was insufficient, but please consider [a₁/a₂] + [b₁/b₂] := [(a₁b₂+a₂b₁)/a₂b₂] as the "definition" of addition.
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???
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?
I do have a theory 1/0 = E Where, E = the Last number in N, N = {entire number set from 0 to +∞). Basically E is the final number in the infinitely long number line if we assume Infinity is a length not number.
Well fundamentall flawed it seems The definition of E inherently contains inf, therefore there’s nothing happening considering you seem to be trying to alter definition of inf
@@TheSeiris I kinda wasn’t. People say that infinity is a length not a number. So I defined E as the very last number in the infinitely long number line.
@@TheSeiris btw, have ye heard of the smolest possible number? The number that comes right after 0? It's defined as S =1/E . (E is explained before) (I might be wrong tho. I saw a video on it long ago. And that's kinda how they defined it)
@@CristiYTRomania For example: 5 + 2 = 7 (?) 5/1+ 2/1 = 7/1 Is right (same denominador), but: 5/1 + 2/1 = (5*1+2*1)/(1*1) (5+2)* (1/1) = 7*(1/1) =7 I have assumed that (1/1) = 1 is true, according to math rules. Now: 1/0 + 1/0 is equal to 2/0 ? If that is true then (0/0) = 1 is also true... Can you see the contradiction?
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.
![Lp. Сердце Вселенной #60 РОЖДЕНИЕ ЛОЛОЛОШКИ [Финал] • Майнкрафт](http://i.ytimg.com/vi/YoR0pAV9FVQ/mqdefault.jpg)
wake up babe new zundamon’s theorem en drop
"I don't really get it... but ok" is basically her catchphrase at this point.
"No, even anime girls can't get me interested in advanced math". This is what I used to believe in
The world has been shaken
I'm a math major and I love how thorough they are with the concepts. They really show passion on the topic
Math is cool actually and i hope more people discover it
Recently it was my best discovery
Метан и Тето - самые очаровательные кудрявые воки Японии.🥰Ещё Цуина Кисараги, возможно.☝😉
@@inutamer3658 просто эти голосовые банки поддерживают эмоциональные параметры. Тебя так легко впечатлить.😏Кстати, существует зеркало этого канала на японском, там эти двое говорят по-японски, и подача несколько отличается.
the whole Zundamon format
is basically animated Socratic dialogues
In yukkuri form
They did surgery on projective space
dehn surgery...
And I'm pretty sure the ratio definition is the construction of surreals?
@@math1183 No, not even close. { 1 | 0 } is not a valid surreal number, because it breaks a law of construction where all elements of the left set must be strictly less than all elements of the right set (this may be inaccurate, see Wikipedia’s page on Surreal Numbers for more information). Flip them around to get { 0 | 1 }, and you get 1/2, which we can hopefully agree is not infinity.
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.
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!
Wait.. how is ∞ + ∞ indeterminate?
@@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.
@MsGinko Unfortunately the video is very misleading and it’s a shame cause this is such a delicate yet beautiful topic in mathematics. An indeterminate form is the “form” of a limit that can’t be determined, in other words, it is a limit value that is indeterminable.
The example most well known is 0/0 because on the one hand, the limit as x approaches 0 of f(x)=x/x equals 1, but on the other hand, the limit as x approaches 0 of g(x)=2x/x equals 2. The limit forms of both are 0/0 hence 0/0 is an indeterminate form.
Positive infinity minus positive infinity is indeterminate because of the limits as x approaches positive infinity of the following two functions: f(x)=x-x and g(x)=2x-x. The limit of the first is zero but the second is positive infinity. Hence it’s an indeterminate form.
Positive infinity plus positive infinity is a determined form that being positive infinity which is undefined. One can rigorously prove this using sequences, but to simplify it, it’s essentially because adding anything positive to an already upward unbounded sequence will remain upward unbounded. Your proof is wrong in a couple fundamental ways. First of all you can’t just define 1/0 to be infinity, you have to use limits of sequences. Therefore while you can use arithmetic of limits, you can’t do arithmetic using 1/0 and especially not dividing by zero.
@@ccbgaming6994
The problem here is that you confuse the +∞ (positive infinity) with the ∞ (infinity). They are not the same.
Everything you mention is perfectly valid on the "extended real number line".
The intention of the video is to show that the "extended real number line" can be represented by an another metric space called "projectively extended real line", which introduces the concept of a "point at infinity".
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. 💚💜
I highly enjoy the little part at the end where it gives you a new skill unlock
Life can be romanticized as if it were an RPG, :D, where you can unlock abilities or spells with experiences or studying hard
Can't believe I made it to a video 2 mins after it dropped
Zundamon not always understanding, but also sometimes understanding and figuring it out intuitively helps me feel like i'm doing my best to learn ^^
thank you!!
13:23 me when I see higher level maths
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.
Cool! :D I tried defining it in such a number and found many difficulties lol
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.
@@Mulakulu learnt it in the hard way haha
I had an epiphany on this topic a number of years back, based on one of the teaching methods I was shown as a child. Division is taking the numerator and breaking it into Denominator groups. By attempting to divide by zero, you are breaking the numerator into no groups. It cannot be calculated because it is erasing the numerator. Mathmaticians should really treat it identically to multiplying by zero, because the result is identical- the absence of a value.
@@aroventalmav888 Interesting. Do you know the name of the method? It doesn't make much sense to me since zero is not the same as "no valid answer", so I'd love to know more.
If you're interested in this topic and including the 0/0, try the transreals introduced by anderson. It's a but like NaN in computation, but you can construct it and prove that 0/0 = 0^0 in transreals.
Zundamon is better at math with each video
inspirational
There's also the "wheel algebra" where you also define "0/0" as another point outside the circle called the "error element", and you define every other undefined result to be equal to that term.
I love Zundamon and math, so this channel is great!
これ見ると数学と英語勉強できていいな
How tf did I get here?
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.
YOU FOOL! YOU DIVIDED BY ZERO! YOU HAVE... uh... not doomed us after all?
(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
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
@carterwegler9205 add rules x-x=0 not aplicable for 1/0 😁
I need two things:
1. Division by 0 being acceptable
2. Zundanon and Shikoku kissing
I don't know who the second character you mentioned is, but anyway,
WHA-
@Unofficial2048tiles Shikoku is the pink-haired girl
@@livek1238 Her name is Metan
Timestamp?
@enzogamerukbr just hoping it'll happen
8:06 Yes Zundamon speak your truth 🗣
Mathematicians used to ignore roots of negative numbers. Because it did not make sense, it was undefined, but now we use it everywhere.
Maybe it's the same case with 1/0
My new all time fav maths channel❤❤
Zundamon so adorable
I love zundamon
Thank you Zundamon and Shikoku, I'm feeling smarter already!
please never stop posting 😭🙏
11:46 Isn't using the equality to prove the equality "circular reasoning"?
the equality beforehand was a well defined equivalence class
very projective geometry approach, I remember my favourite sentence of that class back when I took it was "parabolas are also just ellipses". However, of course there are many different approaches. For example one can try to functional analysis on it, so 0\in\sigma(0_X), assuming that X is for example a banach or hilbert space. In fact, if the entire space is {0}, the 0 operator is gonna be every possible operator, because all that an operator that maps from 0 to 0 can do, is mapping to 0. So in that case, 0/0=0^(-1)(0)=0, because the operator is both surjective and injective obviously, so it has an inverse. In \doubleR, you can't find an inverse because 0 is in the residual spectrum of the 0 operator, with the 0 operators range not even close to being dense in \doubleR. You could however look at the preimage and see that 0^(-1)({0})=\doubleR, which is also why I feel uncomfortable that 1/0=\infty is the result of this video, because obviously {1}
otinRan(0), and the 0 operator would have to map \infty to 1, so that the preimage 0^(-1)({1})={\infty}, which is a problem due to alot of reasons.
you know, a long time ago I also studied electrical engineering, and they really don't mind at all about dividing by 0, they just do it, so maybe sometimes it's a good idea (damn, my former math faculties will hate me for bringing this up).
I thank you for your efforts on this projective geometry approach.
i was waiting for this!! i knew it was coming
I wouldnt be suprised if terence tao was behind this
I only can hope to be a good enough Mathematician so that Zundamon can teach my work to others
I'm early to the best UA-cam channel of all time 🗣️🗣️🔥🔥🔥
1:55 omg animations!!!!!!!
thank you for letting me break the seal
Can I just say I love your content.
Unlike similar setup, zundamon is not a stupid apprentice but has actual good points
Proof far left and far right on political compass are same
peak education system, right here!
Hot take but Zundamon hotter ngl
best channel
The real projective line!
you can get an intuitive idea of why infty+infty doesnt work by remembering that this infinity is unsigned
1/0 + 1/0 =
(1*0+1*0) /(0*0) =
2*(0/0) =
Indeterminate.
1/x + 2/x = 3/x ?
(1*x + 2*x)/(x*x) =
(1+2)/(x)*(x/x) =
(3/x)*(x/x) =
If (x/x) = 1
Then
1/x + 2/x = 3/x
Same denominador sum is true only for x≠0 because (0/0) = 1 is false.
For anyone who wants to learn more, study Wheel Theory. It's basically an extension of the set of real numbers.
Zundamon getting HEATED over 1/0 = infinity 🔥 This is UNACCEPTABLE 💢👊
Exactly my reaction when the screen shows my answer is wrong and i still didn't realize what my mistake was
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.
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.
Thanks!
Ah, I just noticed that there is a bit of an Elmer Fudd softening of R's to W's in these anime girls.
The limit explanation for why zero is undefined is enough
As a middle school student in not best korea this exploded my mental i'll come back here approximately 1972 years later bye bye
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).
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
There's nothing to devide with. Like a stick in the river.. the stick is deviding by two.. so when you remove the stick.. the river is now one.. nothing left to do.
Zero is solved by t. Anything larger than zero is part of the t series.. t0 is not because its the point "where you have not yet started" 1/0 is a "non starter" equasion.
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
I love it but it felt a bit tense when cute anime girls needed to find a common denominator between two frac... ratios with the same denominator.
loving this way of teaching maths
there!s no way, the creator behind this is so smart to lure me with these anime girls so he can teach me math
first they draw you in with cute voice droids
then they force you to learn math
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).
this is actually really interesting
Great video 👍 you did a good explanation!
thanks zundamon
I still dont understand why the forbidden division is not used in school or is not acceptable by some people and also does infinity times infinity is equal to zero also means that adding infinity with another infinity in infinity times right?
finally, i can nourish my brain again
Ох, недавно как раз изучал эту тему, и она тоже меня взбудоражила - такое вроде бы не слишком сложное действие с нанесением на окружность всех чисел - и вот мы уже смогли добавить бесконечность
"you have broken the seal of division by 0".
huh.
Wasn't the Riemann's sphere a sphere placed on (0;0) and not centered there?
ずんだもん！
おー遂にずんだもんも英圏進出か
やっぱ英語圏の人間ずんだもん知らない人多いみたいだね
instead of sleeping early for my lectures, i am once again here watching anime girls teach math 🙂
Don't let homies know I fw this 💀
1/0 = undefined, but some people say 1/0 = +-infinity.
I love listening to these.
∞+∞ tehnically equaling to 1 seems so cursed
Cool video! Love breaking maths :) That's why I also aim to define division by zero.
But at 10:26, there is a small and crucial inconsistency. You have mentioned previously that 0/0 is prohibited, at least for this episode, but in fact, by performing regular fraction addition operation, you assume that 0/0 = 1. The output result most probably is correct. Just the proof does not necessarily confirm it.
Again, 11:14 is inconsistent with 9:19
Thank you for your comment👍
I realize my explanation was insufficient, but please consider
[a₁/a₂] + [b₁/b₂] := [(a₁b₂+a₂b₁)/a₂b₂]
as the "definition" of addition.
@@zunda-theorem-en I'm looking forward to seeing other videos from you, they are interesting!
Ah yes. 2 anime girls saving me from failing collage. What time to live on.
I DON'T REALLY GET IT BUT OKAY 🗣️🗣️🗣️🗣️🗣️ 🔥🔥🔥🔥🔥
Zundamon reaction is just my reaction
Beautiful channel
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???
I feel the same way
1/0=∞ ⟹ 1=0•∞ is false, because it is necessary to multiply by the factor (0/0) on the left side, which is forbidden.
Bro you just said 0/0=1, you did the process wrong
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.
Спасибо за работу!❤
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?
I do have a theory
1/0 = E
Where, E = the Last number in N,
N = {entire number set from 0 to +∞).
Basically E is the final number in the infinitely long number line if we assume Infinity is a length not number.
Well fundamentall flawed it seems
The definition of E inherently contains inf, therefore there’s nothing happening considering you seem to be trying to alter definition of inf
@@TheSeiris I kinda wasn’t. People say that infinity is a length not a number. So I defined E as the very last number in the infinitely long number line.
@@TheSeiris btw, have ye heard of the smolest possible number? The number that comes right after 0?
It's defined as S =1/E . (E is explained before)
(I might be wrong tho. I saw a video on it long ago. And that's kinda how they defined it)
this is division by 0 propoganda and im here for
love you
break the taboo
Tldr lim 1/x when x approaches 0 is infinity but 1/0 itself is undefined
ah yes, the bubble thought when i was 6 🤔
Proof 1/0 = Infinify:
1 / 0.5 = 2
1 / 0.2 = 5
1 / 0.1 = 10
1 / 0.01 = 100
1 / 0.00001 = 100000
1 / 10^-x = 10^x
Therefore:
1 / 0 = Infinity
This is beautiful as a calculus student
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?
Wow, it's so weird hearing this in English. I was used to the Japanese voices.
No solution bc if 1/0=a then a*0=1 number holds true for that.
This channel is subarashi!
Why does Zundamon have such thick thighs like holy shit those are cakedn
11:00 Wait, 1/0 + 1/0 is not simply 2/0 that is 1/0 ?
No, because the following definition must be used:
[ a/b ]+[ c/d ]= [(ad + bc)/(bd) ] = [ (1*0+1*0)/(0*0) ]= 2*[0/0] indeterminate.
@@MsGinko Ok, thank you! Thought I could write 1/0 + 1/0 = (1+1)/0 = 2/0
@@CristiYTRomania
For example:
5 + 2 = 7 (?)
5/1+ 2/1 = 7/1
Is right (same denominador), but:
5/1 + 2/1 = (5*1+2*1)/(1*1)
(5+2)* (1/1) = 7*(1/1) =7
I have assumed that (1/1) = 1 is true,
according to math rules.
Now:
1/0 + 1/0 is equal to 2/0 ? If that is true then (0/0) = 1 is also true... Can you see the contradiction?
Calculus 1 flashbacks intensify 😂
Are ee going to double back on sone of that philosophy? Can Zundamon tell me if abstract objects are real?
Could you do something on Pollard's rho algorithm? It’s more in the realm of programming but I still find it interesting
10:57
Doesn't ∞+∞ equal 2*∞. So you could say that ∞+∞ = ∞, because 2*∞ = ∞ (according to 9:13)
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.