@t.b. I have succeeded applying your hints to the problem, and indeed the two axioms are already enough to characterize a group!! Thanks for your generous hints here.
And we can then argue that if x is a left identity and y is a right identity, then they coincide, and hence we can prove that every left identity is equal to x. C.Q.F.D.
But in the arithmetic with which so far I have ever had acquaintance, we are interested in the equation, and hence to guarantee the solvability of some equations might appear easy to understand?
and the existence of the inverse is also natural because it reflects the fact that often we don't want to consider transformations that lose some information
@awllower don't tell me you never had calculus or linear algebra before 0_o
I am only a sophomore, therefore I am still learning some of the important theories like the measure theory for locally compact groups, and is reading the book by A.Weil to learn it. Maybe I will need your help again afterwards. Nice to meet you!!^^
it's very interesting to contrast this with real numbers
two integers are close to each other wrt euclidean norm if in any base they have many of the same digits 'counting back from infinity' (in the sense that |x - y| is small if x - y is small)
and two integers are close to each other wrt p-adic norm if they have many the same digits counting from zero 8)
My tutor (guy who grades homework) is not as evil as I thought. In one of the questions when I got fed up with calculating derivatives I wrote "What follows are some very long calculations which you cannot see as they are written in invisible ink. Basically, (explanation of the argument)" and I got full marks : )
@Skullpatrol A beta site is an experimental site where things are meant to be tested. The Meta site here is a site which discusses issues about the main sites.
And overflow is just a name. Stack Overflow (the programming QA) was the original Stack Exchange -style site, and Math Overflow is a research-level mathematics site
The Tam'O'Shanter has been around for a long time (longer than Lawry's), but Lawry's bought it. Walt Disney used to eat at The Tam'O'Shanter back in the day.
@JM Wait: if you write about a dead and famous person you have the guts, while when you write about someone you know, you wouldn't? I would think the bon ton would be the other way around...
That's what would be fine and that's what I was trying to point out. But it's JF Adams he writes about (and I think he intends to say that he knows JD quite well)
@JonasTeuwen oh, so you get your first salary? that means that I should have also received mine. And congrats to you! that was a good idea to drink before you receive the salary )
What is the most general category for which differentiation and integration are adjoint functors?
Well.. maybe you can narrow it down to at least picking the objects as subsets of \mathbb{R}
Taking the morphisms as analytic functions obviously works, but anything more "general" than analytic functions seems to break down somewhere, as then differentiation is no longer a "total" functor.
@Ilya if you do (-1)^n * 1/n, then you can apply, and you get that it's convergent but not absolute convergent. that's my question. is there any alternating serie that is absolute convergent?
@Ilya Ashok's answer only uses the purely measure theoretic fact that for an increasing sequence A_n of sets the measure of the union is the limit of the measure of A_n, so I don't understand why you go via a cdf.
@AsafKaragila I read your discussion with Victor, I know that it is impolite and you I guess know that I'm not interested in the answer. Just that was the only reason for Clash's behavior
@tb sorry, his intentions confused me a bit. I was also wondering what are the strict bounds on the convergence
quick question, I have proved with the alternating test, that a series is convergent. Can I show that it's not absolute, by doing the comparison test on the |series| and showing that it's divergent?
@tb nice ) his answer is perfect also due to its generality, though I was interested in more information - that's why I had to use c.d.f. Do you mean you see more simple way?
@Ilya Well, the point is it isn't real fog we're having here. Just a grey curtain about 500 m above the city, this is going to last for about four more months now, at least...
@Matt What's not true? I see no fog in the city and none around my place (over the hill), but a few hundred meters right up, but I'm bad at estimating the distance.
@tb Well, here is still part of the city but the fog is right here, you can touch it. Feels nice to walk in it, especially in the morning. I can't argue if you were only referring to the city centre...
@Matt one friend told me the criteria how to realize where is the border between Belgium and the Netherlands, but I won't sound it here because it's not only about the cows, but also about the girls
@Matt I see. Well, I sort of understand the appeal. When I lived in the mountains, it was beautiful to have real thick fog (and we had snow from early November until May, too). Next time I see St. Peter, I'll see what I can arrange for you :)
@Matt not at all, we are not in the army (aren't we?) I personally prefer cats much more, but recently my father appeared to have black Labrador. Amazing guy
@MartinSleziak I'm taking no objection (no downvote on the suggestion I made either) as a go-ahead. If people should happen to raise valid objections, we can then still merge (lattice-order) into (order-theory).
@MartinSleziak Even if integral lattice would be somewhat more tech-savvy, I believe that we already have enough confusion with the many "integral" tags, so I'd go for "integer-lattice".
I guess retagging should go slowly, so that I do not flood front page - perhaps if the last question I rettaged is no longer on the first page, I might retag a new one. Does it seems a correct rate?
@Martin: Links do not work in tag-wiki excerpt, so I wouldn't add them. I edited the link out from one of them. That rate sounds very reasonable. You could easily do two or three at the same time, I don't think that this would be perceived as flooding. And thanks for the effort!
Hello. I solved numericaly a stochastic equation 10000 + t = 1000N(t), N(t) --- Poisson process(0.01) and found it's minimal root. It's probability density has 3 local maximums. I can't interpret this :(
@MartinSleziak I would say it also depends on what you want to do with these algebras. Maybe modules-algebras would encompass what you're looking for. For example ring-theory, representation-theory contain questions that would fit that tag (and yours).
I see :) I share that feeling that doing something about it would be useful (maybe even necessary), however I couldn't come up with a tag proposal that I really liked.
