Random personal comment, since we're talking about the Philippines: @J.M., did I ever tell you that I lived in the Philippines? It was for about two years - all before I turned three. So, unfortunately, I don't remember any of it. I wish I did.
@JM Good guess! Air Force, actually. Dad was stationed at the air base near Manila that I believe was destroyed by a volcano about 20 years ago. My sister was born there.
Dad got out of the Air Force about three years after leaving the Philippines and spent the next few years as an engineering prof.
It's all just various algebraic structures anyway, the ones sufficiently closely connected with our original idea of numbers and the trend of expanding generalizations get the label "numbers" in the end.
@Henning: may I suggest that you add links to the words you mention? That might make your answer much more useful (a click is easier than entering the words in Google, which, in turn, is harder than asking a question here, but I like to think the click is still the easiest among the three)
OMG! I had looked at Does this question even have an answer? when it was first asked. I just looked and saw that it had 77 upvotes, 22 favorites, and Henning got 85 upvotes.
@robjohn They capped out the first few days, but have been coming steadily since then. My eyeball estimate is the there's a 50/50 chance that the tail-end upvotes will bring it to 100 eventually.
this is weird (the 'result' part in particular): wolframalpha.com/input/?i=Sum%5B1%2F%28z^3-n^3%29%2C{n%2C30%2C30}%5D*Sin%5BPi*z%5D*Sin%5BPi*%28-1%2BSqrt%5B-3%5D%29%2F2*z%5D*Sin%5BPi*%28-1-Sqrt%5B-3%5D%29%2F2*z%5D
I am considering asking math.se to "Describe all ideals of k[x,y]/(xx,yyy)." I've described them all, but I'm a little worried I've missed the point. Anyone here want to describe them?
@Jack: There are some grammar problems, too. I think I'll just edit the entire thing, since I'm stuck in my attempt to find the exact expression wanted.
@anon: That's what I'm doing. The >=2 bins case is the difficulty. But I just saw another problem I'm going to tackle. If you want to answer that one, go for it!
@Mike: Note that if every bin in (C) has >=2 you can count the possible configurations by taking the number of balls available, subtracting 2 for every bin in C, and then acting like the leftover number is how many balls you put into #C bins with no restrictions.
(of course the no. of bins in C will have to be the index in a summation, I think)
Oh yeah. There should be a couple of questions there. Including the famous sigma-algebra where Qiaochu answered the plain question, I introduced the hierarchy and Arturo just wrote another book.
I also need to badger someone to add elementary set theory in there.
But that was about Lebesgue but not Borel! Now it's not quite clear to me what the guy actually asks, I guess one should treat him to some Borel-hierarchy in...
The precise answer would be along the lines of: well, the Borel hierarchy can be described by transfinite induction on the level < \omega_1 by the operations you have. Just check that you get a sigma-algebra...
But I don't really understand what makes him ask about the unit square instead of the unit interval, so there seems to be some confusion.
Drat! The window didn't tell me that Sasha had answered the question before I posted.
Usually, a banner appears saying that an answer had been posted, but two were posted and no banner appeared. I would have posted earlier, but I was checking out numerical examples.
@robjohn: I made the experience that if I have an editing window open in a tab and an answer is posted while I'm fooling around doing something else in another tab then the system does not notify me. I guess there's small bug in the script that triggers that notification only when the tab's active.
What's happening here? The question seems somewhat "subjective and argumentative" to me but closing it as "not a real question" seems somewhat harsh, especially without any explanation and with a brand new user (member for 10 days).
@JonasTeuwen ok, if your surname is Wiener and you like the name Norbert, why not name your son in that way? Though you may not understand, your surname if different )
Okay, I think they are now all removed. It takes about three clicks for each message, and my internet connection is not that fast (or my computer has too many windows), thus it took some time. Next time please stop earlier :-) (@t.b, @Gortaur)
@tb ) sometimes I think that this smile is a Cheshire Cat's smile. It's a pity that Mariano has already used that avatar - sometimes I use it too in other places. Like that Cat
Interesting, I'm reading a paper that refers to another one to invoke a theorem, but the space they use is slightly different from the one they refer to. At least, I'm not able to prove they are equivalent. I hope they are 8-).
No, I think you misunderstood. I am asking you a question (and guiding you to the solution). Remember that you need to prove (A union B)' subset of (A' union B'), and vice-versa.
