But the notation could also be used to think of a group $G$ acting on some kind of Cartesian product.
I mean, it is a little awkward to discuss rigorously, but if $(x,y,z)$ is a tuple and $k$ is a thing which reasonably acts on each of $x$, $y$, and $z$, then the notation $k(x,y,z)$ ought to be clear.
Also, I hate HATE that so many elementary calculus texts confuse points and vectors.
It is nice that the tangent space of $\mathbb{R}^n$ over a point is isomorphic to $\mathbb{R}^n$, but points live in the base space, and vectors live in the tangent space. Different animals. :\
I mean, at some level, most of modern mathematics come from physics. But I would say that the formalism of vectors come from mathematics---physicists have used and abused vectors for ages, but it is the mathematical formalism which makes them work.
@amWhy Template text is easy enough. Make the following a bookmark after editing the sample text to what you want:
> javascript:document.execCommand("insertText",false,"This is a sample text.");void(0);
Note that if you want to use a double-quote or backslash inside the text, you need to add a backslash in front of each of them (this is called escaping).
Wait a minute, such javascript is not allowed to run in bookmarks. Gah. You'll need GreaseMonkey or TamperMonkey then. Sigh..
@amWhy @TeresaLisbon @XanderHenderson @ParamanandSingh: I realized I was using the wrong function (for editable textareas instead of textboxes)... Try this bookmark:
> javascript:text="This is a sample text.";active=document.activeElement;v=active.value;p=active.selectionStart;q=active.selectionEnd; r=p+text.length; active.value=v.substr(0,p)+text+v.substring(q); active.setSelectionRange(r,r);void(0);
Question: Check whether the polynomial $x^4 - 20 x^2 + 16$ is irreducible over the rationals.
Eisenstein's criterion cannot be applied here and I couldn't come up with any other method to check whether this is irreducible or not. Any help in getting this done is much appreciated.
@ParclyTaxel: that irreducibilty question has many dupe targets specified. One of them deals with a similar question and the answer by Jyrki uses same technique.
@ParclyTaxel As for this question, I mean, the attempt is literally just one step ahead although the factorization 37*41 is super useful. There's a couple of answers, if you wish to illustrate something beyond what the others have done then maybe go for it, although it feels to me like that's difficult.
@Euler2 I mean, these are fun questions but NOT here! For example, 478994326880221257733489964321 is a semi-prime, the product of a ten digit and a twenty digit prime, both of whose last three digits are 389. If you typed that randomly, you should join some crypto firm!
@XanderHenderson you r wakking? What, exactly, are you cooking in a wok? ;P
@ParclyTaxel Please be careful about accusations against others you name in this chatroom. It seems you're mainly upset because you answered it and want it to remain open?
@soupless That is a complletely orthogonal issue. Before you even get to the "why" or ""how", the questioni is funddamentally about ising WA. It is off-ttopic, even if it were asekd wwell.
I agree that iit is too broad for rMath SE, but don't ccurrently ahve a functiional keyboard with wwhicch tto respondd to the asker, and d am ini cclass fo the next three horus (startiinig in 10 minutes). II will close t he questoin for beinig too broad, bu iit woudl be ccooll if someone eellse took some time to interact witht he askker.
close? reasoning: answer is a one liner, already answered in the comments -> closing prevents rep hungry users to answer and the answer can be found with 10 if not 5 seconds of online research
Regarding the structure of duplicate question links: is it better to have the dupe tree shallow or deep? (Shallow means there are a few big questions which have many duplicates)
@ParclyTaxel That would make a better Meta question. And you don't really articulate how you distinguish "shallow, vs. deep." E.g., the question, What are the roots of $x^2 -1$, is a dupe of the more abstract question "What are the roots of $x^2 - a^2$? In the first case, a = 1. which means $x^2 - 1^2$. Ahaa! difference of squares, which means it can be factored into $(x+a)(x-a)$, so when a=1, we have $(x+1)(x-1)$. The roots being $\pm a$, or in the original case, the roots being $\pm 1$.
Imagine the questions as vertices, and there is a directed edge from a question to its duplicate (there may be more than one). If we take a question that is not a duplicate as the root, then shallow means I only have to click at most once to get to the root, while deep means two or more
My mind is not large enough to make all the correct generalisations to identify a duplicate, even after searching. As mentioned on my profile, I do My Little Pony art as well, and I'm only a week out from this semester's final exams in maths and computer science
I just feel so weak against the 100K+ users of this site because they have more time on here than me. (Right now I'm watching MSI 2021, and I have a commission to do)
@ParclyTaxel How is rep relevant to how much time a user has or how intimidating they are? Also you're not so far away from 100k yourself. (I genuinely can't understand what you mean.)
@Peter Aber das war schon Ewigkeiten her... Werde selber reingehen :)
(MSI is League of Legends's Mid-Season Invitational.) I am actually just jealous. They answer questions I can't, but the questions I do answer, sometimes one of the following happens: (1) I'm not fast enough, (2) it gets closed as duplicate by a gold tag badge user (and I get scolded for making a duplicate answer)
@ParclyTaxel For the first point I can relate. It often happens that if I want to write a long and clear answer another user writes a one-liner and the answer immediatly get's many upvotes. (This is of course not against the mse policy, it's just a little bit frustrating.) And for the second point, just try to search duplicates in MSE, google, Approach0 etc. If the rare case happens where you cannot find a dupe but it actually is, it's not a problem.
@Peter Same old, same old, but the curves are moving faster. Next time, I should consider combining smaller numbers (~C500) with bigger numbers (~C5000).
The same applies to quadradics in general: $ax^2 + bx + c =0$. We don't want a flood of "how to factor this one particular quadratic with specific a, b, and c. In all such questions we have $x= \frac{-b \pm\sqrt{b^2 - 4ac
@Peter I wish I had a free window, but that's what I'm missing. I'm thinking of aborting one of the searches, but then I'm thinking I'm already 20 days in , nothing to lose and so on. Just praying for a miracle, then.
PSQ (I informed user of EoQS some time ago : flag if needed)
@Peter and @vitamind Let's all stick with English in this chat room. It's a tad rude to have ongoing exchanges in a chatroom in a language in which other users cannot participate.
Feel free to make your own chat: Chatroom for Peter and vitamind, e.g.?
@ParamanandSingh Looking at the comments and answers, it seems that there is no translation. I'll try to find one and I'll notify you but I'm not very optimistic. But if you have the book (Not sure if it's free) and there are some parts which are not clear, please ask me whenever you like.
@ParamanandSingh Rewarding to learn new languages occasionally, I picked up some Russian terminology and stuff to read Matiyasevich's paper on completely enumerable sets being diophantine.
Question : The delete button for an answer is visible from a mobile device, right? A user is having trouble deleting answers from their mobile device, perhaps it will be good to at least give directions.
@TeresaLisbon : I use the site on mobile device, but I use the "full site" version which gives all the features. There is also a mobile site which is with less features. Maybe that is the problem with that user.
This needs to be done once for each site like mathse physics se and whatever se and the setting is stored via some cookie for a long time (few months or so).
@TeresaLisbon It's a terrible question. Some answerers are getting more desperate (the higher rep users), while other answerers are beginning to steer a bit from answering VLQ questions.
Look at just the profile written here, @Teresa. I think one problem on this site is that some retired users get a second wind on this site, earning rep, and they have little else to do.
I'm not condoning that any way whatsoever. They could easily choose to guide new users, all users, and contribute to site quality, rather than indulge themselves only in self-glorification, at the cost to this site.
@amWhy Correct, that's the attitude I'd like them to have : the shining guiding lights. They still are guiding lights, but not in the way one'd imagine.
@vitamind HOW is that question for a seventh grader? Having said that , I have no clue what goes on in some of those countries, in Romania it'd probably be fourth grade.
Let me remind everyone, particularly newer users here, that we try to set a limit of twelve close requests per user and 12 delete vote requests per user; otherwise we risk not having sufficient votes to go around. So everyone posting close vote or delete post requests, please limit the number to 12 each per close/per delete in any given day. Since we have more contributers than when we set it at a dozen of each, we may to curtail that to ten of each per day, per user.
But for now, I trust each user to keep this limit in mind, and abide by it. We want to allow everyone here the to suggest posts for closure and/or deletion, and when a few eat up others votes with too many requests, we risk letting some users requests getting lost. Thanks!!!
@amWhy To be sure: 12close and 12delete together so max=12 or 12close and 12delete seperately so max=24? In any case, I posted 8 comments with a link to PSQ questions so I'll stop for now. Thanks for notifying, I wasn't aware of a limit.
@vitamind 12 of each, but a request to close, then delete, counts as one of each. I'm just suggesting that we allow everyone the opportunity to suggest, and have some success. If we all had unlimited close votes, down votes, and delete posts, I'd say: The more suggestions, the merrier! Since users are most active at various times of the day, we don't want to burn up a lot of users votes, leaving them unable to assist a user's request. This was not directed at anyone, really! ;-)
It seems to me that the OPs in the first question and the second question are the same. The second question, TheSimpliFire said that the (second question) OP had a history of editing questions after they got answers, and the account was deleted
@ParclyTaxel Their attitude is obnoxious, asking a commenter to answer a previous question. I have voted to close that question, and flagged as low quality.
Please flag the answer with the information you've shared with me, both posts. Seriously! Mods can find the deleted account, and see any previous patterns.
@ParclyTaxel Yes (oops sorry, I meant flag the question). Something seems fishy there, with that user. The mods may not know whether it's the same user since then (second post), but they can see more than you or I.
@ParclyTaxel Thanks for your alert. We can use all the help we can get, and you've made it clear you want to do right, and you're also bringing to attention possibly nefarious OP's! We couldn't ask for anything more!
@ParclyTaxel I flagged the post posted as Kia, with a link to the previous user id of the account that was deleted, as well. Mods usually say, the more flags the better, but there is something really fishy going on with that user.
Are you baaaack, @Xander? Nothing urgent. Just checkin' ;D
Please explain how to solve this.
f(X) = X or f(X) = 1 - X ...or 10-x. Or f(X) = 1/x
I think these are the only functions to count but how?
Question: Check whether the polynomial $x^4 - 20 x^2 + 16$ is irreducible over the rationals.
Eisenstein's criterion cannot be applied here and I couldn't come up with any other method to check whether this is irreducible or not. Any help in getting this done is much appreciated.
