Відео

25:32 i don't understand the bottom statement as true what im reading it as goes as thus: the left side has two parts, the first part is inside the parenthesis and basically says "a set that is both prime and less than 100" and the second part is the C which basically says "everything except that set". that's cool, makes sense the right side basically says that it is a set that contains two general sets, the first set is all numbers that are not prime (the prime with a C). the second set is that is also contains all numbers greater than 100. With those definitions, it's clear that the right side contains both numbers like 4, 6, and 9; and also, numbers like 110, 220, etc. this is because it has a UNION and not an intersection. HOWEVER the left side says that the numbers are everything EXCEPT "numbers that are prime and less than 100". This means that the left side contains numbers like 110, 220, etc, but NOT numbers like 4, 6 and 9. Now, i'm not stupid, i know that i'm not disproving this guys theorems. the question i have is where am i making a mistake? i don't understand the logic behind the sentence and equation? can anyone help?

The droning noise makes this completely unwatchable. Why do that?

Great video! It would have been really nice to see the actual approximation as a 3D function (the values over the x-y plane), not only the section at x=0.

I love Will Wood's music, but he's an even better mathematician :) <3

Вся разница вот в чем: Тэйлор предложил полиномиальное разложение в ряд, а Падэ - рациональное приближение.

@DrWillWood 10:34 Should be 0.073, instead of 0.73.

Night before exam! Yess 4am

Math exam tomorrow. I love you

Love those multilevel narketing campaigns

Nice…✨ Nice choice of background sound btw…

Dear Dr Will Wood. Can you explain the relationship between equation at 4:27 and Newton's cooling law? At first glance it seems to make sense, but in Newton Law of Cooling there is no spacial variable? Also the unit of 2 equations is not the same. For Newton's law of cooling, the unit of dQ/dt is Watt, but for the second equation, the unit is W/m. Can you help explain this?

Wait doesn't he sound like the guy who explained different dimensions xkcdhstguy???

thank you DR.

Such a great video! I'm cramming for exams in my uni right now, and this was super useful and pleasant to listen to! Way more understandable than our professor's notes lol

The last point really drives home what a monstrosity this function is

What would be the integral of this function ? (between 0 and 1 for example) Undefined ? 1/2 ? some other ratio ?

I didn't know that there's a rational number between any two irrationals. Because there's also an irrational between any two rationals, does that mean you can't go from one irrational to another without going through a rational, so the number line alternates in some sense between rationals and irrationals?

won't the l2 norm be a circle instead of a square at each point. i.e. similar to a making a 3D shape by rotating each point of g(x) about f(x) as center and then taking the volume of that shape. Of course we are then applying a square root after this.

Involved in the Reign of Terror.......imprisoned and survived prison? So, he wasn't "involved" in the Reign of Terror but he WAS imprisoned during the Reign of Terror. Why was this?

What is cardinality of set A= { 1, 2, 3, 3, 3 }

The point about the set being 'limited' to what supposed to be in it, as opposed to the content of some wider set (e.g. thinking 'all even numbers' is the set of natural number) is a mistaken perception. Part of that problem is that there is a confusion between 'counting' and the labels of the objects of the set (such as 'numbers'). The label '1', and the count of 'first element' are (can be) conceptually distinct things. This matters when explaining that the size of the 'even numbers' and the size of the whole numbers are both the same because you can count (bijectionaly) both of them. Another example is software engineers who like to start at 'zero' (also labelled '0') as their first element of their set that's an ordered list/array. Their 'forever' is 0 to (aleph.null-1) ;-)

Okay, but what's the Fourier transform of this function?

There is a definition of phi as the most irrational number, where it’s written as a continuous fraction of ones all the way down. If two takes the place of the last digit in this continuous fraction construction for phi, then those two numbers are not separated by a rational number. I think this runs into some methodological issues. However, you can do this digit substitution with finite values of phi, for which it is possible to find a rational number. It is only problematic to find it when the digits occur at the end. Still, any continuous fraction can be flipped inside out, though you may run into problems with infinity, though an equality sign by definition makes an equation finite if one side has finite value.

Thank you so much for your videos!.

Where Fourier?

Lovely as always. 💜

Amazing quote for Fourier in the beginning ! Thank you!

Top 16 greatest mathematicians of all time 👇 Carl Friedrich Gauss Euler Newton Euclid Archimedes Leibniz Pierre Laplace Joseph Fourier Bernhard Riemann George Cantor Rene Descartes Alan Turing David Hilbert Kurt Gödel Fermat George Boole

I expected this to lead somewhere.

Dear Will, thank you. You have answered a question, I have been pondering for the past 42 years. As I watched your video, I was teleported back, "through space and time" to the summer of 1982. I was studying Fourier analysis and I had an epiphany, the first time my "wave function collapsed". I simply realized,"If you give me any function, any function f(x), I can express it in terms of a simple combination of sines and cosines." - Pure mathematics at its best, QED. Or as Sidney Coleman said it, "The career of a young Theoretical Physicist consists of treating the harmonic oscillator in ever increasing levels of abstraction."

Wait, how is one part or the other, contiuous, at the end of video?

......so what was the fourier transform of the dirichlet function? You said he invented it to prove a point but never said how it proves that point

There are unknown way to visualize subspace, or vector spaces. You can stretching the width of the x axis, for example, in the right line of a 3d stereo image, and also get depth, as shown below. L R |____| |______| TIP: To get the 3d depth, close one eye and focus on either left or right line, and then open it. This because the z axis uses x to get depth. Which means that you can get double depth to the image.... 4d depth??? :O p.s You're good teacher!

thank you so much, this is what the future of education looks like

My mind 🧠 🤯

This will only work as long as the PDE is linear, right?

Nope

Cant see any bound between Fourier's lifestory and his maths solution. I dont mean that autor was wrong when added history to this video, but it need better connection of scenario parts.

wish i could listen to this but your decision to add unneeded background music interferes with understanding.

Epic video as usual; never fails to disappoint. You upload too little and too late 😔

That which is like to itself in differentiation and exponentiation must be directly related to the exponential function, and Gamma(z) is equal to it for certain values, and seems to oscillate between cosine and sine at multiples of 1/2. In fact, it seems to act like a generalization of exp(z), and Gamma does after all show up in the partial sum of exp(z) itself which would also seem to imply a way to possibly generalize factorial given a means to compute the nth digit of e in some base? So far, my guess is there's probably a sum of four independent terms involving the exponential which I hypothesize from the likeness and alternative representation of the simple sum of complexes z + w as z+w=\left(\sqrt{z}+i\sqrt{w} ight)\left(\sqrt{z}-i\sqrt{w} ight)=\frac{1}{2}\left(e^{-i\arccos\sqrt{z}}+e^{i\arccos\sqrt{z}}+i\left(e^{-i\arccos\sqrt{w}}+e^{i\arccos\sqrt{w}} ight) ight)\cdot\frac{1}{2}\left(e^{-i\arccos\sqrt{z}}+e^{i\arccos\sqrt{z}}-i\left(e^{-i\arccos\sqrt{w}}+e^{i\arccos\sqrt{w}} ight) ight). Consider also product_(n=0)^(k) (x + i n) and the particular products with which this product converges as k goes to infinity. All of this leads me to believe that perhaps there's some simple sort of representation by generalizing the imaginary unit if not the complexes in a particular way such that something simple along the lines of f(z)^n = Gamma(f(z) + n)/Gamma(f(z)). With that, and with being able to represent any Gamma(z) for z in the rectangular region [0, 1 + i] (or really any such region [n+ik, n+1 + ij] for integers n, k and j), both representing Gamma sufficiently with which to create some sort of symbolic arithmetic (provided certain comparative operations can be performed symbolically), as well as computing arbitrarily good approximations of Gamma(z), would be trivialized-and that's just what I'm looking for. Am still sad I didn't get addicted to complex arithmetic sooner 😔

what a genius

Ok

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Can you tell about decomposition over Bernstein polynomials? Is it even possible?

Very bad 👎👎explaion

So, can you Fourier transform the Dirichlet function?

Hey, man! Amazing video! Loved the background story!!! I would like to know if you can do the same for the Laplace Transform. I did a lot of digging through the years and I actually figured that it just came to be what it is from trial and error. However, I am aware that there is a way to derive it from Fourier Transform. Anyway, would be awesome to see you covering these topics as well!

Can you transfer heat through a photon? Or how about a frequency like gamma or infrared. Or is heat strictly bound to physical matter?