/sci/ - Science & Math

[Anonymous No.4866665]

how solve?

e^x-x=0

Btw, I've been thinking, could there be a set of numbers that when used allow false equations to be used? much like imaginary numbers, but maybe not exactly?

equation related but pic not

[Anonymous No.4866677]

not allow false equations to be used

*allow false equations to be true

[Anonymous No.4866678]

i found it funniest when people called and made legit religious questions and they couldn't answer them

[Anonymous No.4866688]

>>4866677
>allow false equations to be true
yes you idiot, they're called solutions to the equation.

[Anonymous No.4866712]

I swear this problem, or a similar one, pops up like once a month on /sci/. Use the Lambert Omega Function.

http://en.wikipedia.org/wiki/Lambert_W_function
/thread

[Anonymous No.4866753]

<div class="math"> e^x - x = 0 <div class="math"> x e^{-x} = 1 -x e^{-x} = -1 </div> <div class="math"> -x = W(-1) </div> <div class="math"> x = - W(-1) </div> Here W(x) is a product log or Lambert W function. Because it involves a transcendental function and an algebraic solution, the solution will involve a different transcendental function. The solution won't be simple and pretty is what I'm getting at. Also Wolfram Alpha.</div>

[Anonymous No.4866757]

<div class="math"> e^x - x = 0 </div> <div class="math"> x e^{-x} = 1 </div> -x e^{-x} = -1 <div class="math"> -x = W(-1) </div> <div class="math"> x = - W(-1) </div> Here W(x) is a product log or Lambert W function. Because it involves a transcendental function and an algebraic solution, the solution will involve a different transcendental function. The solution won't be simple and pretty is what I'm getting at. Also Wolfram Alpha.

[Anonymous No.4866766]

Could there be a set of numbers which allows false equations to be used. It sound silly, but the creation of complex numbers worked wonder for algebra and many other branches of mathematics. It would have to be considered on a case by case basis. Find what numbers you would need to have the properties you want and see what that gets you. It will usually get you nonsense or a contradiction, but it might give you something interesting.

[Anonymous No.4867083]

>Btw, I've been thinking, could there be a set of numbers that when used allow false equations to be used? much like imaginary numbers, but maybe not exactly?

Infinity

[lel i tral u !S0ooHAHDTU No.4867224]

<span class="math">e^x=x[/spoiler]
<span class="math">\frac{d}{dx}e^x= \frac{d}{dx}x[/spoiler]
<span class="math">e^x=1[/spoiler]
<span class="math">xlne=ln1[/spoiler]
<span class="math">x=0[/spoiler]

[Anonymous No.4867385]

>>4866766
but C is the algebraic closure of the reals. Every poly splits over it, so what other relations would you require solutions for that aren't already in the complex numbers?

[Anonymous No.4867412]

>>4867224
nice work. this is a cool problem