/sci/ - Science & Math

>>5397281

http://en.wikipedia.org/wiki/Full_employment_theorem

Well, well, well, show that the series

<span class="math">sum_{n=0} x^n / n![/spoiler]

takes the same values as e^x for all x.
(directly, not over Picard Lindelöf or some shit.)
reals to the power of reals are bitches if you can't use the series expansion imho

Usually fairly small things.

Like when I saw that the deRham cohomology group (where you take the closed and drop the exact forms) is really just a factor group in the sense you'd read in an algebra book on page 5. Before I never saw the appeal of commutative groups.

Also, factoring out prime ideals to get fields. Pretty kewl idea.

Any generally, many concepts which you work on in your head for ages and, at long last, you find a picture in which everything can be interpreted for the first time.
To me, it doesn't even matter if that's not the right way of thinking of things, it's pretty important to me to be able to find a working concept to get on.

And interestingly, thinks I'm happy to understand are almost always the things I'm learning about privately.

>>4497055
>algebraic quantum number theory
The only thing I associate with all these expressions together is primon gas. So what is it about?

>>4365270
oh, I'm refering to
http://phdchallenge.org/

>>4365162
you copypasted that, can that be?
that must have been months ago :)

>>4354135
video related
http://www.youtube.com/watch?v=y6ZMscMp8UM

university?
I actually know busted gals who do AdS/CFT in 2+1 dims.
shit is cash.

>>4090036
>FullSimplify
btw. wanna hear a cool story?
Last month I found a bug in Mathematica.

I tried to gave a basic answer in the original thread
>>>/g/21229051

>>4017448
- given Ax = 0 has just the trivial solution
assume (QA)x = 0 has a non-trivial solution, i.e.
(QA)v = 0 with v=/=0
multiply by Q^-1 ==> Av = 0
that a contradiction, so (QA)x = 0 only has the trivial solution
- given (QA)x = 0 has just the trivial solution
if Av=0 with v=/=0, then (QA)v is zero too, which is is a contradiction, so A only has the trivial solution too.

>>4006176
Have you mastered String Theory yet?

>>3997866
>What is string theory all about?
About (quantized) strings as fundamental objects in spacetime. This is too vague.

I don't really know why Josef is saying you don't need reals. Eighter he's taling about the fact that Calabi-Yau manifold are complex, in a generalized sense, or he's talking about some post apocalyptic (post-quantized) scenario where you only use spectra to describe spacetime and you don't have real neighborhoods.

>>3997867
I'm not denying sets of reals being sets. I wanted to seperate R from any real manifold. (any manifold with R^n as tangent space.)

>>3997875
Where do you disagree?