Wait according to this you could divide by e^x at the start and get that integral of one equals one

Say you remove 5 dollars from both envelopes. Then your odds get better: one envelope has 0 dollars and the other one 5 dollars, and by the same computation with "expected returns", the expected return of switching is INFINITY.

This is like that one meme where you get to choose if you want to swallow the red pill or blue pill but both choices are balanced. It's a 50/50, what do you expect? Even if you think about changing or staying in the answer, we wouldn't know which is which. 50/50 will always be like that, and will *BE* like that. The law of 50/50 can't be broken.

I love it

wonder if ramanujan found the solution or the original nested radical first

Bro proved intergral = 1 and 1/0= 1+1+1²...

I like the part where you substitute f(x) for x+2n+a despite f(x) is x+n+a by definition.

I liked the part where you introduce "a" and then 4 steps later, you just put "a=0"

This is so funny. I busted out laughing more than once lol

I studied mathematics in college and graduate school and my god my analysis professors, especially functional analysis, would have lost their fucking minds lmao

There's probably a trivial amount of filtering on the resulting IDs too so they don't contain some specific substrings

Was this made with Manim?

I love @KZbin.

This is so cursed

Let's integrate the closed parenthesis

This channel should be called Rum & Math because there’s no way a sober person could come up with this

AAAAAAAAAH!! AAAAAAH! !!!!AAAAAAAAAAAAAAAAAAAHHH!!!!!!!!

What exactly do you mean by “operator” when referring to the integral sign? I know that you said to think in reverse, but what does an integral mean without a dx, if it means anything at all?

This was simultaneously an incredibly useful and informative lesson and incredibly confusing difficult to understand. Thank you for educating us!

For anyone confused about the plot at 12:20, it displays the component number on the x-axis and the corresponding value on the y-axis. For example, one of the eigenvalues for the Laplacian matrix is 2, which corresponds to the eigenvector (0.5, -0.5, -0.5, 0.5). With this in mind, the meaning of the plot should become self-explanatory.

You have a great teaching style.

New subscriber. Hate the video. Show me more physics pleb moves.

wat

You are probably correct in your analysis but this was a pretty bad explanation so if someone cam please hwlp me thar would be nice

What do you nean "you don't need that dx"... There are only very, very few cases where you can use the Integration sign without the dx and this isn't one of those cases (at least without furst defining what you mean)

This is my new favorite video on YT not gonna lie. I was laughing the whole way through out-loud. Yes, I am weird

Everything is an operator if you're lazy enough.

what did i just see???

Subbed for the title. :))

(1 - I)^(-1) = 1/(1 - I) = 1/(1 - 1/D) = D/(D - 1) f = D/(D-1)g ==> (D-1)f = Dg ==> f' - f = g' if g is a constant then f' - f = 0 ==> f' = f which one can define e^x to be the solution.