quallenjäger

@AkivaWeinberger that was a nice intuitive way, Thanks alot

thanks akiva

got cha

@AkivaWeinberger 1/2 then

I mean it can't be coincidence right

Why does this long division $(x^2 - 4x + 3) / (x-1)$ leads to the other root

that means I have a root at 3 as well right?

I know how to do it but I am not sure why this give me the other root.

yes

how does it give me the other root?

@AkivaWeinberger is there any proof to that formula? I googled it but I always found some high school maths stuff

what is the standard procedure to write a general polynomial $f(x) = ax^2 + bx +c$ in root form?

the form $f(x) = (x-y_1)(x-y_2)$ applies only if a = 1 right?

because it is +1

I have to normalize it right?

Suppose I am given a polynomial $f(x) = ax^2 + bx + 1$, how do I factorize it? can i still write it in $f(x) = (x - y_1)(x - y_2)$ where $y_1, y_2$ are the roots to the $f(x)$

just swa it

ops got it

how can I let the browser dissplay the latex here?

Has been a while

@Ted

Hey Ted

or whats like again?

.\bash_after?

what is the name of the file with alias

anyone familiar with linux?

it is just a bad notation isnt it? is it equivalent to $x*\int f(y)dy$?

what does terms like $x*\int f(x)dx$ mean? Can I pull the x inside the integral?

Anyone is familiar with integral against local martingales?

I go back to work

Thank you Ted!

Oh I see

I see, so it is basically in the direction of from $v$ to $w$?

But I can have two arcs, which arc are we considering for the unit circle?

I don't understand, would the intermediate theorem mean, that for any two tangent vectors $f(a)=v,f(b)=w$, which can be thought as a function on the unit circle, there must be a point $\psi$ on the arc enclosed by $v,w $, such that $f'(s)=\psi$ for some $s\in[a,b]$

Darboux theorem works only for $\Bbb R$?

I see your point. The problem that $(t^3,t^2)$ worked is because we can guarantee the continuity of the derivative by shrinking its tangent vector length. But if we keep the length as constant, then the only way to guarantee the continuity of the derivative is that the direction is closed to each other right?

But if the derviative is nowhere zero but not continuous, it could be some cusp right?

In other words, there cannot be such sudden change of the direction of the tangent vector?

@TedShifrin Would it mean, that if the path is at natural parametrization and is $C^1$, there cannot be such cusp?

better than pointed out by some expert to embarrass my self.

@TedShifrin At least i noticed it earlier

I just noticed that I have totally written up some rubbish in my thesis because of that.

I might have to come back again :D

@TedShifrin I see, thank you. I will work out these

I didn't quite get your second argument, what the problem if the tangent vector of the arclength-parametrized curve has to switch direction?

But yeah, in string theory, landscape and swampland are actually classifications of physical theories, whether it is compatible with string theory.

Well people get bored at work. I used to give stuff very weird names to make these dry written papers bit interesting.

Are they simply landscape and swampland?

Can someone explain what anti-de sitter space and de sitter space are?