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LOL. The sum(D^n)=D/(1-D) operator expression is so cool. It won't surprise me, if the manipulations you did can make perfect sense in some formal way.

Thanks well explained

John Gabriel on MVT: ruclips.net/video/_bvJKe8OgWg/видео.htmlsi=jFl3T3MF0CE182eg

k*-i≠-k*i or do I misunderstand quaternions

Now do calculus on Z

Hi sir I have a question, can you show that the recursive property for the gamma function also works for negative arguments?, thanks.

I'm Norman Wildeberger and I approve this message

I needed this video 2 years ago, while taking real analysis course. Thank you sir! brilliant follow of thoughts

Are you aware that the living French genius mathematician, Alain Connes, Fields Medal, has built since 40 years The Synthetic Theory of Calculus, on CONTINUOUS AND DISCRETE Fields, based on Von Newman Non Commutative Algebras, from which he even digged out an INTRINSIC SELF EMERGING MATHEMATICAL TIME, as a instrincic spontaneous cyclic regularity. The point is thus no longer to question about Calculus on discrete Fields, but to build an entire coherent universal theory that can as well deal with DISCRETE OR CONTINUOUS Fields, or even FINITE ones, as particular cases of the Global Theory necessarily based on NON COMMUTATIVE ALGEBRA of Clifford and Von Newman. What you are playing with is l^2, vs L^2. What’s up is the Master Mind Algebra that holds both as particular wings, and fly much much beyond. But for that you need absolutely NON COMMUTATIVITY. And that’s not a surprise since Commutativity is such a narrow particular case of the wild ocean. It’s the exception that confirms the Rule : NON COMMUTATIVITY !

Why do we only need n to tend to positive infinity? Wouldn’t this correspond to only one sided limit (h tends to 0 from the positive direction) in the real number version?

I forget what Wildeberger said about this, but he has done amazing things without the real numbers.

(pi^3)-sqrt10.8=666^.5109989

This is an interesting challenge. Is there a use case for this question or just a puzzle for its own right?

How the arithmetic operations addition, subtraction, multiplication and division are performed within that group?

| sin n | is a giveaway that the serries will track the harmonic series and hence diverges. If the series had sin n, instead of | sin n |, the resulting series would still diverge.

-Changing the subject, what's with the short back and sides.- Oops ... I mean changing the subject allows you to calculate the short side.

That is a very bad definition for "the derivative". For example it makes the derivative at x=0 exist for f(x)=sin(pi/x) for x not 0 and f(0)=0. Just use one of the standard definitions instead.

"magenta_hoodie / long hair = green_t-shirt / short hair." The Pennian Theorem

Unnecessarily complicated.

I remember there was a solutiion like this, but I forgot how it worked. Can someone tell me how to prove it? a^2=c^2-b^2 a^2=(c+b)(c-b)

Why does one need the smaller triangle (only in order to send it towards the original triangle at the end and look at the limit) at all? One can just use the original triangle all along and make the exact same argument.

Great video ❤

That's why this is not possible to change order or infinite amount of operands in a series

Your thumbnail looks like sum of product of vectors (a,b,c) and their transposes (a',b',c'). And this misinterpretation of your thumbnail is also correct 😂

"I'll indicate this angle with the smell of dead otters in a drainpipe, and this other angle with the smell of strawberries."

sedEnions

Can't you just solve for y(x) using the quadratic formula, then just plug-in a,b,c, r, s and t to get the graph?

Thhhhhank youuuu

It's just one of the Euclid's theorems in another form

Why do you need the a' b' c' triangle? You can do the same without it, pushing the ' edges to the large ones

Cool 😎 🆒️

I will be writting down this amazing identity!

The Exactly solution is Y(x) = -2log(x) + C when A = 0

This will follow even for a general triangle

Why do you need a' and b'? You can simply use x and y to reach the same conclusion: x/b=b/c, y/a=a/c, and x+y=c, which is Einstein's proof.

8:33 Clothing change 9:17 Good place to stop

just treat a, b and c as functions of some variable (say t) and take d/dt of both sides in the Pythagorean theorem.

I don't think you've done the spherical Pythagorean theorem yet. I think you should, it's very elegant yet relatively simple while not being fully intuitive at first.

Hi, 8:34 : the fastest hairdresser in the world!

So how can we even be certain that the alternating harmonic converges to ln(2) then?

the way I finished the proof was to note that a/a’ = b/b’ = c/c’, so you can multiply aa’*a/a’ = a^2, and same for the other two

Now do it again on the hyperbolic plane. 🙂

In fact it doesn't matter if you use radians or degrees - so long as everything is kept in terms of sin(x), cos(x) or tan(x). When the angle itself starts to appear in the equations as a variable in its own right, that's when you need to start switching.

Question: why go to the trouble of making the a'-b'-c' triangle? Just draw the perpendicular from the right angle to the hypotenuse and do the same math. If the perpendicular has length d, then you have a triangle with sides a b c, one with sides d y b, and one with sides x d a, all similar, so a/c = x/a, b/c = y/b, then cross multiply to get a^2 = cx and b^2 = cy, then add them together to get a^2 + b^2 = c(x + y) = c^2, which is the exact same logic that you did. No need for the a' b' c' thing. I believe this proof was known in antiquity (I've heard that it was the proof used by the Pythagoreans themselves, but I don't know if that's actually true).

I did not see it coming, feeling so stupid

Very beautiful proof.

Well to be precise we need to prove that x+y=c’. In other words that the end of perpendicular is exactly on the edge of the triangle

boy what the hell is on your shirt

I like those color contrast. Interesting video though!