@Srivatsan Ah. Both answers are nice, but they are from different directions with respect to how things are to be broken up. One breaks up the function, the other breaks up the set. I think the method that breaks up the set is more easily generalizable, but that is a matter of opinion.
No, not to do with the complication. I knew there's a proof that keeps the function as it is and approximates the set. I couldn't figure out the details.
My motivation is this: can you prove the following generalization:
For a reasonably well-behaved (quantify this) phi:[0,1] -> R, we have: lim int_F phi( sin nx ) dx = average value of phi(sin x).
The trouble is, phi could be in C^\infty, and yet its Taylor series might not converge to the function. So Zarrax's approach will not work here [unless I am making a mistake somewhere].
Ok. May be you can include such a statement as an addendum to your answer =) ... I would very much like to see that.
And I think the OP will also appreciate that; they seemed to like my guess at the answer. Such a statement will make the guessing part even more transparent.
I recently took my Honors Pre-Calc. exam. Wanting to get as many points as I possibly could, I circled and skipped several problems. However, I forgot to do this one, and wanted to know if I'm on the right track, because the answer I get for x doesn't work correctly. I've come up with a separate ...
Indeed. And somewhere along the way, I lost track of which he was doing. All in all, it's not a big deal. I would like to be a substantial contributor to this site one day, so I will not discourage helps that only irritate me.
@TheChaz Not at all. I was annoyed as well. Completely irrelevant edits that added nothing but resurrecting old ghosts. And what's more, they ware almost all completely uninteresting questions (to me)
I thought that first statement might have been facetious! Indeed, I weigh the "let it lie" factor as more valuable than the "one character should be changed for aesthetics" factor.
What personal life? Seriously: My main concern was to reduce the number of unsolicited email I receive and I succeeded in that respect. SE and MO are the only sites I participate in that can be connected to me in any way. I feel pretty uneasy about broadcasting personal stuff on the internet.
Well, I used to be at ETH mostly for the past 14 years, studying, completing my Ph.D. and doing a lot of teaching. At the moment I'm taking a break and try to figure out what's to come next.
Let's see if I can come up with a query involving another user whose name is a homonym...
And speaking of great comments, it's a shame that my "Arturo: MSE :: Chuck Norris:the universe" (paraphrased) comment was deleted along with the question that prompted it.
So has any of you done the Trivium? Are the problems meant to be done by every graduate or are they like challenge problems only the top few students can manage?
@Srivatsan Ah, I didn't see the title of V's question, but the answer is still no. But why does this guy have to reach for (the) high(est)-hanging fruit? He'd rather learn some basics first. Learn to walk before trying to do rope-dancing and all that.
I'm not aware of the existence of such an etiquette beyond what common sense dictates. It would certainly be okay for me to say that the third guy said "what's (some notation)? Seems to me you do not even understand your own question.", but it wouldn't be quite okay to say who that was, right?
I read that the reason that things in complex analysis work out so nicely is because the Cauchy Riemann equations are the solution to a certain elliptic PDE. Where could I read about this further?
@Srivatsan: No, they will be upset because I might wake them up when I go to bed. We live together in a normal flat, not in a dorm, like a married couple, just not married : )
@Ilya It is possible, I was a hobbyist photographer. However it is also not too likely since I worked hard to remove my photographic footprint off the web.
