They remind us of darker times... They remind us of things we do not want to remember. It is the bane of mankind, to forever be haunted by the things he wants to forget.
If f:A->B maps a basis of A onto a basis of B, and the preimage of a basis element in B is a basis element in A, does that enough to conclude the map is continuous?
@JM None of the current questions on derangements strikes me as satisfactory. Next week I might write a CW question that attempts to collect together all the known identities and stuff, plus links to proofs. Sounds good?
@Srivatsan Yeah, it's a bit scattered. I also had an answer where I showed that the exponential partial sum and the incomplete gamma integral are the same. I'm looking for it now...
@Srivatsan That does seem to confuse people often. There ought to be some nice named standard principle about one-sided limits at poles that one could just cite.
No, as I said, I cannot do it here (and I am a bit frustrated, so I am giving up for now). I will try again on my desktop machine and see what happens. Thanks @JM.
Originally I thought that bookmarks only appear on my "chat profile page" (or how should I call it). I noticed only later that if I click on the room info, there is a conversation tab.
As I am looking through them, I guess I should delete a few of them. (Those ones which are of interest for me, but not useful for other people.)
Well it starts out by talking about the "crisis of Fourier series" and I'm still (a few years since I learned it) wonder when these things actually converge so this does look interesting
I am not sure what argument you have in mind. I would just say: if f is continuous in [a,b] (with a<b) and f(x) -> -infty as x -> a+ and f(x) -> +infty as x -> b-, then f is surjective by IVT.
> The landing site contains a rock type that is very dense and very bright colored; it is unlike any rock type previously investigated on Mars. It may be an ancient playa lake deposit, and it will likely be the mission's first target in checking for the presence of organic molecules
@Srivatsan, that bugs me sometimes too: People post "comments" that happen to completely solve the question - it stops the person from accepting them!
You see, if I understand an answer, I can upvote it (I know that it's correct.)
If someone posts an answer which is two pages long and uses two theorems I never heard about before... should I upvote an answer which I do not understand?
@MartinSleziak Well, I guess you are right. I would upvote a correct (let's add "good" too =)) answer. But being on the receiving end, it feels... different.
I remember that I had in my hands German translation of some book, the translator was obviously not a mathematician. E.g. he used "Feld" instead of "Koerper".
But I can't recall the name of the book at the moment.
@JM Nice. Conversely, Germans used "Feld" for "field" (as in "Galoisfeld", something which is nowadays widely considered an anglicism but actually appears e. g. in Witt's works).
@JonasTeuwen I think that is the main problem here. That answer is forever going to appear at the top of the thread just because the OP clicked the green tick mark.
[And surely the OP would've accepted the answer because (1.) the numerous errors there would not have been noticed then, (2.) this was the only answer then.]
@QED If you would like a small prelude... Remember that sequences have limits. Also functions have limits at a given point. Is there a reason to give the same name to both these things? Does this idea generalise beyond the two examples I mentioned?
What's the deal about limits misusing the equals sign? In my experience, one is not allowed to use the \lim notation at all unless one knows that limits are unique for the topological space in question.
BTW Henning I've recently found out that you're pretty active wikipedian. (I've noticed that you've edited one of the articles I have on my watchlist.)
I guess some of your edits are related to the things discussed here at MSE.
@MartinSleziak I used to be a fairly active wikipedian a handful of years ago, reloading watchlists several times a day and getting involved in editorial arguments, etc. Nowadays I just fix problems when I come across them for another reason.
@AsafKaragila The terminology was not Kelley's invention, though. Kelley had wanted to call such an object a way. However, nets have subnets, which Kelley would have dubbed subways. Norman Steenrod talked him out of it. After some prodding by Kelley, Steenrod suggested the term net as a substitute for way.
I'm supposed to give a 30-minute talk and I already have 2.5 pages of definitions, and I'm not even halfway yet. Very tempted to use Beamer or just talk through everything instead of writing on the board...
@ZhenLin What is the audience for this talk? Can you get away with just presenting the intuitive sense of the definitions and skip the details such that you can get to the good stuff quickly? "Read the paper for details" is a powerful rhetorical tool.
@Henning: It's an expository talk, "Bicartesian closed categories and logic". Unfortunately, I promised in the abstract that no knowledge of category theory or logic will be assumed...
You will have to make copious use of "it can be shown" and "it turns out that there's a sensible definition that makes everything work here, such that (insert simple example)"
Oh, I'm not proving anything. The point of the talk is to make the definitions and draw attention to certain parallels...
Hm, I just realised I don't really need to talk about functors and adjoints. So I'll cheat and unfold the definition of adjunction into the definition for exponential objects...
You can only do so much in 30 minutes. If you try to make anyone understand the details of more than one definition they didn't know when they walked into the room, you'll break your neck.
But there's that promise in the abstract. You might want to make a virtue of necessity and not show any auxiliary definitions at all. Just sketch one or two simple examples, and assert that they generalize to the full whatever.
Huh. It seems that the question was copied from A-M wrong :-)
The book says that every open and compact set is a finite union.
What is interesting is that I do not yet have a clear visual interpretation of the Zariski topology, but I certainly cannot see it as a topology on R or C or whatever.
Well, then that's just as well, isn't it? The Zariski topology doesn't say very much about the geometry of an algebraic variety. It's just there so that we can define more complicated gadgets which do say something interesting.
