Okay so I was bored and thinking about some equations stuff,

>>7952237
infinite power tower

lambert W function

>>7952253
okay thanks man

>using limits that 0.9... = 1
Depends on the topology

>>7952268
This might be the stupidest post of the day.

You can use Newton's method to approximate the answer. If you don't know Newton's method, you take a guess,x, say .5, and you plug it into the expression x-f(x)/f'(x), where f'x is the derivative. The derivative of the function is e^x +1, so basically you plug in .5 into x - (e^x + x)/(e^x+1), and plug that value back into x, and again etc until you get reasonably close. Pretty sure this number is transcendental, so no way of representing it algebraically

>>7952332
any hints to work out the Newton's method ?
like, where do I start to study stuff that will lead to the proof of this method ?
I particularly like proving this kind of stuff y'see

File: Bildschirmfoto 2016-03-23 um 22.30.04.png (34KB, 789x197px) Image search: [Google]

34KB, 789x197px

That's [math]-\Omega[/math].

https://en.wikipedia.org/wiki/Omega_constant

>>7952344
>any hints to work out the Newton's method ?
>like, where do I start to study stuff that will lead to the proof of this method ?
Calculus 1? Just draw a triangle with sides the vertical line from x to f(x), the tangent line at x, and the (appropriate portion of the) x-axis. Newton's method should be immediate from that picture.

You can use Newton's method to approximate the answer. If you do not know Newton's method, you take a guess,x, say .5, and you plug it into the expression x-f(x)/f'(x), where f'x is the derivative. The derivative of the function is e^x +1, so basically you plug in .5 into x - (e^x + x)/(e^x+1), and plug that value back into x, and again etc until you get reasonably close. Pretty sure this number is transcendental, so no way of representing it algebraically.

>>7952383
I don't get what the fuck you are trying to say.
Sorry for that but can you explain what I am even supposed to do with that triangle ?
Like, for starters, what even is the point of Newton's method.

>>7952506
Newton's method allows you to find points where f(x)=0 if you start close enough to x.
Let x0 be a point close to x, let x1 be the intersection of the tangent of f(x) at (x0,f(x0)).
Generally
[math]x_{n+1}=x_n-\frac{f (x_n)}{f' (x_n)}[/math]