Honestly, the looks/animations of the videos are just a bonus - I stick around because your explanations are the most clear and elucidating I've ever seen, often exceeding 3b1b
Your channel has been incredible! ❤ I am a math/physics undergrad in America. Most of your videos have left me with new perspectives and appreciation for the intense beauty of mathematics. Your animation quality and the clarity of your explanations rival that of 3blue1brown. Keep up the good work! I am excited to see what you make next! I believe that this channel will eventually become very popular
I agree: youtube makes it possible to really *show* things and animate them, which was never possible in textbooks. That's what all the symbols and formulas are for: to refer to parts of the bigger picture. Now you can just point directly at those parts and move them around. It makes things much more intuitive.
@ The other factor is that RUclips makes it possible for somebody like you, with superior teaching skills, to be available to everybody. We’re no longer stuck with our local teachers and professors. It’s similar to how the invention of sound recording made the best performers available to everybody, everywhere. I really hope that local teachers and professors will become obsolete in the same way that the local village accordion player did.
The preview resembles a thing I did with pixel shaders, while exploring various fractals(Mandelbrot, Julia sets, Ducky fractal etc) I repeatedly applied projection matrix, using homogenous coordinates (x,y,z,1), somehow assigning z value(probably with a parabolic function z=const*(x^2+y^2)) so it was something like: take a picture, project it on parabola, take a picture again, project on parabola and so on(about a hundred times in total). If the projection plane was tilted(or shifted) a bit, it looked very similar
Division by zero breaks everything because 0 doesn't have an inverse in all rings except the {0} ring. You can prove that if you have a ring where 0^-1 exists then that ring is {0}. Also, in a ring one of the first things you prove is that 0*a = 0 for all a in the ring.. but by definition of inverse, you would have 0 * 0^-1 = 1. So you conclude that 0 = 1 , so for all a in the ring, a = 1*a = 0*a = 0, and that leads you to the ring being just {0}.
NOTE: had to reverse image search(may be inaccurate) half of them, but they match the icon and general content. List of channels displayed from 2:00-3:00 TOP ROW - 3blue1brown - Mathologer - khanacademy - MathTheBeautiful - rationalityrules - ron-math - eigensteve BOTTOM ROW - (Eigen Chris) UCN8wTUlSAroLslWyf87E2pw - mathemaniac - Aleph0 - PhysicswithElliot - RichBehiel - SanderKonijnenberg - sudgylacmoe
I'm also a software dev, undergraduate in computer science and ending a Physics one. Your teaching amazing and passing is just as good to have us thinking the subject until the next one comes up. I think division by zero is a zone of trasition, it's a degenerate state, where either you lose dimensionality information as in linear algebra projection transformations or have an ambiguity as in geometry with unknown polar/azimuthal angles at the origin/poles, also in algebra they're related of to a curious pythagorean triple involving dual numbers, imaginaries and reals, the division by zero is not possible in scalar or row vector algebra, by an incompletude, but you can work around it using dual numbers matrix representation or poles and residue theorems from complex calculus, with some clever tricks. Spoilers: you arrive at differentiation operations. Borrowing again from LA, zero is the kernel of any morphism in math, so itself acts as a pivot, that makes any sum, product or exponential with it meaningless since you get the original operand, zero or one. The unique place where it changes anything is when divided by itself since 0 = k0, so k = 0/0, where k is literally anything you can put in an equation involving inverses, be it number, vectors, matrices, tensors, shapes, sets, etc.
One fairly obvious (but not deep) reason for division by 0 being problematic is that multiplication by 0 is many-to-one, whereas multiplication by k for k != 0 is one-to-one. So if we define the function mul_k(x) = kx then the inverse function div_k(x) = x/k exists for all k except zero k since mul_0(x) = 0 for all x Because of this, an implication like: a*(x-y)=b*(x-y) => a = b is false if x=y (since the multiply is non-invertible), and if you can hide such a step in a proof then you can apparently prove nonsense like 2=1
> why div by 0 allows this obisously, because it's uncertain and following the definition of division you can grab any result from it making reasonable equations into useless math. Wonder if category theorist have category for those.
Honestly, the looks/animations of the videos are just a bonus - I stick around because your explanations are the most clear and elucidating I've ever seen, often exceeding 3b1b
Wow, that's a major compliment. Thank you so much!
Your channel has been incredible! ❤
I am a math/physics undergrad in America. Most of your videos have left me with new perspectives and appreciation for the intense beauty of mathematics. Your animation quality and the clarity of your explanations rival that of 3blue1brown.
Keep up the good work!
I am excited to see what you make next! I believe that this channel will eventually become very popular
Thank you so much! That comment made my day.
RUclips as a learning resource is *hugely* under-appreciated. I’m glad you’ve jumped into this as a content creator.
I agree: youtube makes it possible to really *show* things and animate them, which was never possible in textbooks. That's what all the symbols and formulas are for: to refer to parts of the bigger picture. Now you can just point directly at those parts and move them around. It makes things much more intuitive.
@ The other factor is that RUclips makes it possible for somebody like you, with superior teaching skills, to be available to everybody. We’re no longer stuck with our local teachers and professors. It’s similar to how the invention of sound recording made the best performers available to everybody, everywhere. I really hope that local teachers and professors will become obsolete in the same way that the local village accordion player did.
The preview resembles a thing I did with pixel shaders, while exploring various fractals(Mandelbrot, Julia sets, Ducky fractal etc)
I repeatedly applied projection matrix, using homogenous coordinates (x,y,z,1), somehow assigning z value(probably with a parabolic function z=const*(x^2+y^2))
so it was something like: take a picture, project it on parabola, take a picture again, project on parabola and so on(about a hundred times in total).
If the projection plane was tilted(or shifted) a bit, it looked very similar
Division by zero breaks everything because 0 doesn't have an inverse in all rings except the {0} ring. You can prove that if you have a ring where 0^-1 exists then that ring is {0}. Also, in a ring one of the first things you prove is that 0*a = 0 for all a in the ring.. but by definition of inverse, you would have 0 * 0^-1 = 1. So you conclude that 0 = 1 , so for all a in the ring, a = 1*a = 0*a = 0, and that leads you to the ring being just {0}.
NOTE: had to reverse image search(may be inaccurate) half of them, but they match the icon and general content.
List of channels displayed from 2:00-3:00
TOP ROW
- 3blue1brown
- Mathologer
- khanacademy
- MathTheBeautiful
- rationalityrules
- ron-math
- eigensteve
BOTTOM ROW
- (Eigen Chris) UCN8wTUlSAroLslWyf87E2pw
- mathemaniac
- Aleph0
- PhysicswithElliot
- RichBehiel
- SanderKonijnenberg
- sudgylacmoe
Those are all correct.
I've also always loved math!
Too bad that this love isn't mutual.
🤣
a division by zero is a contradiction in most cases, and everything follows from a contradiction
I'm also a software dev, undergraduate in computer science and ending a Physics one.
Your teaching amazing and passing is just as good to have us thinking the subject until the next one comes up.
I think division by zero is a zone of trasition, it's a degenerate state, where either you lose dimensionality information as in linear algebra projection transformations or have an ambiguity as in geometry with unknown polar/azimuthal angles at the origin/poles, also in algebra they're related of to a curious pythagorean triple involving dual numbers, imaginaries and reals, the division by zero is not possible in scalar or row vector algebra, by an incompletude, but you can work around it using dual numbers matrix representation or poles and residue theorems from complex calculus, with some clever tricks. Spoilers: you arrive at differentiation operations.
Borrowing again from LA, zero is the kernel of any morphism in math, so itself acts as a pivot, that makes any sum, product or exponential with it meaningless since you get the original operand, zero or one. The unique place where it changes anything is when divided by itself since 0 = k0, so k = 0/0, where k is literally anything you can put in an equation involving inverses, be it number, vectors, matrices, tensors, shapes, sets, etc.
One fairly obvious (but not deep) reason for division by 0 being problematic is that multiplication by 0 is many-to-one, whereas multiplication by k for k != 0 is one-to-one.
So if we define the function mul_k(x) = kx then the inverse function div_k(x) = x/k exists for all k except zero k since mul_0(x) = 0 for all x
Because of this, an implication like:
a*(x-y)=b*(x-y) => a = b
is false if x=y (since the multiply is non-invertible), and if you can hide such a step in a proof then you can apparently prove nonsense like 2=1
I am Dutch, and I had absolutely no idea you speak Dutch. Also, "right" and "straight" are both correct translations from "recht" in Dutch.
"Rechtdoor" vs "naar rechts".
@AllAnglesMath If you study rights, you study "rechten". They even have the same proto-germanic origin.
Thought you used manim as well.
The way I do things these days is to ask AI what it would do in my situation:
"- Ask AI." It replies.
"- Thank you very much!"
Always love a good self-referential joke.
Fourier was great video
Thanks, glad you liked it!
> why div by 0 allows this
obisously, because it's uncertain and following the definition of division you can grab any result from it making reasonable equations into useless math. Wonder if category theorist have category for those.