What's the video where you talk about this??

Can you share a video that you explain the log of 0

“x amount of clocks” 😭

e^x amount* ;}

I would say pi amount

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@@EEEEEEEE bro I’ve seen ur account a year ago, I even commented on ur vid look

Astrophysics student: all 3d shapes approximate a sphere and all small numbers approximate 10.

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Lol, this made me laugh

π^2 = g

sin(x) = x

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@@EEEEEEEE 😂

Education is always better when you're actually interested

@@EEEEEEEE e^x

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ENgineers: seeing e rounded to 2 decimal places feels so wrong. It should be e=3

@@hareecionelson5875 Who told you that?

@@carultch apologies, I meant e=pi

@@hareecionelson5875Still, who told you that engineers round pi and e so they equal each other?

Talk about greek elementary kids and π, γ, the ζ function, sum and product

isnt e like a coeficcent or sum

@@antifearless_No, not necessarily… it’s a number. Eulers number = e which equals 2.72. Basically, e = 2.72. :)

@@tWiGgAyyy oh ok thx

Don't forget he invented a whole branch of mathematics just to solve a problem the area's king came up while thinking random shit

I recommend 3blue1brown's video 'what if your bank gave you an imaginary interest rate' It really boosted my understanding of what e means, and what it means to take e to the power of something

No...

What do you mean you “didn’t realize that”? That’s the basic definition of what a derivative is…

It's the y-coordinate, not the x-coordinate. If you want a function whose graph's slope at every point is equal to the x-coordinate, you must solve the differential equation y' = x, which gives you y = x^2/2+C.

@@MrZorx751) If you're referring to the slope of the tangent line, I wouldn't call that the "basic definition" of what a derivative is. I think that title goes to the following: f'(x) = lim h -> 0 (f(x+h)-f(x))/h 2) Just because they knew that the derivative represents the slope of the tangent line and that d/dx(e^x) = e^x, that doesn't mean they had considered how those two facts interact. It's possible to know two facts without knowing a third fact that logically follows from the first two, as you may have just never thought about it before.

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how is it obvious?

@@Joffrerap he’s an economics student who I assume learned about e in the past

The trick is with the complex numbers

Uh... yep. That is indeed what that number is named.

The number e is Euler's number. It is a coincidence that Euler's number is named e, as that is the name he chose. It really stands for exponential. The exponential function of a constant base equal to e, is the function whose derivative is itself. In other words, draw a line tangent at any point on y=e^x. The slope at the point (x, y) will equal the value of y. In essence, it is the form of the exponential function that makes its calculus the most elegant. For any other function in the exponential family, such as 2^x, you end up accumulating a coefficient out in front every time you take derivatives. d/dx of 2^x for instance, is ln(2)*2^x.

Definition D(e^x)/DX = e^x He used a great way tô understand that

Look up the exponential spiral.

Yeah, but e doesn't really get a lot of screen time until the calculus arc. (Best part of the series, in my opinion.)

Calculus would be even more of a pain, if you didn't have e for exponentials, or radians for sine and cosine. You'd have chain rules showing up everywhere, and wonder why you keep accumulating pi/180 factors when you take derivatives of trig functions.

No, Pi x e ≠ Pi + e

-1, assuming this is to be parsed as e^(iπ).

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It's called a pronumeral. A symbol (usually a letter) used in place of a number. It is a coincidence that Euler's name starts with E, and the number he's known for, is also called E. It stands for exponential.

You see, it all began when mathematicians realized they needed some kind of symbols to represent some of their numbers. One day, one of them was rooting around in a box and found a sheet of paper. "Hey, what's this?" they said. "The... the 'alphabet'? Huh." And it was good.

Because you compound the interest continuously, instead of just once at the end of the year. The problem is, no one defines interest rates that way, so this premise for defining e makes no sense to most of us.

Numbers are not invented, they are discovered