@robjohn Nice and clean, thanks! You just gave me back my belief that math is a pleasant thing to do, after all :) I don't see how the Fourier transform helps at the moment, but I'd need to think a little bit more.
@Incognito I don't know if this fits the bill. Personally, I'm fond of Kaplansky's Set theory and Metric spaces. People seem to like Enderton's and Halmos's books a lot. See also the recommendations here
@AsafKaragila how about something like $\stackrel{\large\lt}{\sim}$ (I don't know if there's a proper command for that, I just used $\stackrel{\large\lt}{\sim}$)
@AsafKaragila Interesting, I have a similar proposal on meta, they may have some common ground, as mine is about letting room owners make plugins based on a trust model for almost exactly this sort of thing.
I shall return to my quest writing an exercise set in which I can slowly wade them into proving that the canonical ordering on $\mathbb N\times\mathbb N$ is isomorphic to $\mathbb N$ with the usual ordering - without explicitly finding the function.
@tb Area51 didn't generate enough interest in a Mathematica-specific Q&A site. Phira is upset that the users who were attached to the proposal were not notified it it being denied.
So, since the proposal failed and nobody is notified, only the persons who follow it closely will notice.
@robjohn I will just state it: If you plot the triplet (AM, GM, HM) of all possible positive $n$-tuples of numbers, then what region will you get? For $n=2$, the answer is simple (since $A \cdot H = G^2$). I am working on $n=3$. I have no clue about 4 and beyond.
@JM What can I say? It's definitely not the proper way to treat people who invested a lot of time for a company whose air to breathe rests on the fact that there are people willing to do this.
@robjohn Are you proposing asking a fresh question? Or are you proposing that you will write an answer to one of these two questions generalising the question?
I'm pretty sure he means a probability. I believe he's asking why some people want to do probability with finitely additive measures instead of using Kolmogorov's axioms.
if I could interrupt shortly, I'd like to calculate the intersection between two vector subspaces U1 and U2. U1 = [v1, v2, v3] and U2 = [w1, w2, w3], where $v_1, v_2, v_3, w_1, w_2, w_3 \in \mathbb R^5$. Is this the way to do it? a*v1 + b*v2 + c*v3 = d*w1 + e*w2 + f*w3
@tb Actually, it's not a parallel edit, because you have edited it 19 mins before. But I can swear I in fact added the Banach-spaces tag to the post. Not sure what's happened. Sorry anyway.
@JM Oh :-). Nothing in particular but I'm trying to solve some physics problems where I have needed stuff like Bessel functions. I just want to know what a modern reference book for this subject would be.
(I don't remember any of them treating Zernike polynomials, though. Those seem pretty localized to optical applications. But you can use Jacobi identities for those.)
@Srivatsan One's from me. I'm not really here, I had to lie down for a while after eating a piece of chocolate cake which seems to have upset my stomach. Either that or I'm coming down with something.
I see. I'm more used to them as a. stuff related to the error function, b. their roots being helpful with Gaussian quadrature, and c. part of the analytical treatment of the harmonic oscillator.
@tb That thread reminds me of a variant of "you miss one [traffic] light, and you miss them all" that I told my son (when he was 8): "You miss one stop sign, and you miss them all" This really bothered him because he knows that you miss (have to stop at) all stop signs. I guess he was inferring a causality implication from my variant. The truth of the vacuousness was lost on him.
@JonasTeuwen That is elliptic close to the origin, is that the OU operator?
@JM I guess when first learning the informal logic in language, we infer causality where there is none. I think that is why the variant seemed amusing to me and why it was bothersome to my son.
hey guys, can someone help me understand an answer? http://math.stackexchange.com/questions/25371/how-to-find-basis-for-intersection-of-two-vector-spaces how did he solve it? for example for x, how did he find x=1?
