This Shouldn't Exist

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#math #brithemathguy

This video was sponsored by Brilliant.

Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. Viewers should always verify the information provided in this video by consulting other reliable sources.

[Hadar]

I think that at this point BriTheMathGuy is just rage baiting for comments. xD

[scottleung]

Interesting concept, but I don't think any math teacher would be down for it.

[Anu_bff]

2:52 You say that the integral of 0 is 0, but since the derivative of a constant C is 0, the anti derivative of 0 is just some constant C.

[ssaamil]

We could take this so SO far and I'm all in for it.

[SIXSHAMAN]

I have a question about treating dy/dx as a fraction. There are times when we can treat it as a fraction, that's fine. But when CAN'T we treat it as a fraction? I can't think of an example.

[unflexian]

man I was looking for this exact thing yesterday, weirdly defined integrals. try making more of these, pushing the limits of the notation is facinating

[YouTube_username_not_found]

The result in the end is unjustified.

First, you cannot antidifferentiate functions at a point like that. Antidifferentiation is done over intervals because it takes into account not only the value of the function at a point but also the values of the function around each point of the domain, so the answer at x=e is definitely wrong.

Second, According to Darboux theorem, Derivatives have the intermediate value property and since the function in the video doesn't have this property between e and any real a > e, then it can't have a primitive... unless we eliminate e from the domain in which case the primitive is simply a constant function over the interval ]e, +inf[

[gunhasirac]

This looks like a form of product integral

[pillegraknel]

Man I'm lying in my bed, covered in cozy darkness watching a nice video with a nice dark background and then suddenly a F*ING WHITE LASER BEAM burned thru my retina leaving me hurt and blind. Thanks brilliant for not having a dark mode option or a logo for guys with dark background.

[thebeardman]

Physicist be like well looks about right just expand it and integrate it no problem

[createvideo]

Marathon man, just started the video now and my answer is x+c

[StephenOpara-vg]

This guy just insulted thousands of years of extreme rigor in mathematics. You used a graphing calculator to solve a limit. What laziness, what if graphing calculators didn't exist yet.

[WIDSTIGETHEVLOGGER]

Are you insane? (Respectfully) if the integrand approaches infinity so does the integral (so why put it as undefined), and the anti derivative of 0 isn’t necessarily 0, it’s a constant🤘

[annxu]

ok can you do ∫ψ^dx(x)
where psi is polygamma function

[XzErxZeS]

help me find the rational approximation of the inverse sum of cubes.

[divisix]

What if we interpret ln(dx)=ln(1-(1-dx)) by the logarithm series (treating dx as a differential 1-form) 1+(1-dx)+(1-dx)^2/2+… and then x^ln(dx) as )^2 ln(x)^2/2+…

If we truncate the logarithmic series at (1-dx)^n/n for some given positive integer n, we have (under the above interpretation) ln(dx)≈1+H_n-n dx and H_n dx)+…, where H_n denotes the nth harmonic number, then the part without dx becomes the sum for k=0 to infinity of ln(x)^k (1+H_n)^k, and the part with dx is the sum for k=0 to infinity of -kn(1+H_n)^(k-1) ln(x)^k dx. 

To get back to the infinite case, it seems we cannot take n to infinity first since the harmonic series diverges. If we sum over k first, we get 1/(1-ln(x)-H_n ln(x)) for the part without dx, and this goes to 0 as n goes to infinity. The part with dx would be -nln(x)/(1-ln(x)-H_n ln(x))^2 dx, now since the asymptotic limit as n goes to infinity for the harmonic series is H_n~ ln(n)+γ where γ is the Euler-Mascheroni constant, this part becomes Looks like this diverges…

[Vsevolodbochkov]

I miss times when bri was just a cheese

[magma]

I have constructed a definition for an integral of the form \int_{x=a}^{b}f(x, dg(x)) where g is a function of x. It can be defined as \sum_{k=1}^{N}f(a+(b-a)*(k/N), g’((b-a)k/N)*(b-a)/N) and if we have the special case of g(x)=x and f(x, dx)=h(x)dx, we end up with the standard integral

[JEKaviator]

Cool video, but it's antidifferentiate, not antiderive