/sci/ - Science & Math

I would guess in this direction

http://en.wikipedia.org/wiki/Measure_%28mathematics%29#Properties

>>4589249
every polynomial p(x) of degree n really is p(x)=(x-a)(x-b)...
(fundamental lemma of algebra)

I read "Q[x] <x-3>" as the set of polynomials "q(x)(x-3)^m", where q is any polynomial with coefficients in Q and m is any positive integer. That works out with {f(x)|f(3)=0} since the polynomial "q(x)(x-3)^m" (like for example "(x-4/9)(x+6)(x-3)) has 3 as zero.

x^2-1=(x+1)(x-1), so +1 and -1 are the zeros of Q[x]<x^2-1>

>>4336342
>>4336348
the point is that Mathematica should compute the exact result. Clearly, the function has complex values before 0, but the integral should never see them.

Have you tried not typing 0.5, but 1/2 OP?

>>4184934
It's Christmas morning after all. I for one just don't like these "number problems". However, as I said in the thread 2 days ago I think the idea is very good to post a question or theme on the fron page!
Anyway, I'll make a start and draw a picture

>>3343974
you could just solve it...

http://www.wolframalpha.com/input/?i=DSolve[%281-y[x]%29%2Bx+y%27[x]%3D%3D0%2Cy[x]%2Cx]

but that was of course not the point of the thread.

I'm studying physics and I love me some artsy chicks.

>>3312359
lol
I mean "why" not +varepsilon, instead of -varepsilon

help in what sense?
find your purpose in life?
I can't tell you what job you'll do...
Stay Calm and do the things you like. My best/worst advice.

furthermore:
hypotetically, can there exist a (black hole like) singularity without particles in it?
Like a moving black hole wave?

As you can see in this plot
http://www.wolframalpha.com/input/?i=%28x%2B1%29^2%2B%28y-3%29^2%3D%3D10
the centre is at M=(-1,3) (above and left from (2,2)).
so the tangent y=kx+d has to have positive k, not -3.
It turns out to be +3:

http://www.wolframalpha.com/input/?i=Solve[%28x%2B1%29^2%2B%28y-3%29^2%3D%3D10%2Cy]

http://www.wolframalpha.com/input/?i=D[3+-+Sqrt[9+-+2+x+-+x^2]%2Cx]%2F.{x-%3E2}


(there might be a less explicit calculation than what I did)