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You see an answer which is incorrect in formatting or content, but is easily fixable. What do you do?

I see three reasonable (active) options:

1) Add a comment explaining the issue and the suggested correction.

2) Directly correct the error using the edit tool.

3) Downvote and move on (especially applicable if there are other correct answers and/or it was a content error).

Let's disregard the downvoting option for now assuming for some reason you are feeling motivated enough to make this answer right.

My tendency so far is to directly edit if the answerer is a relatively new user (especially if the error is formatting), and comment if they appear to be a more experienced user (especially if the error is content). I see the following advantages -

Commenting: Is more deferential, and allows the possibility of the suggested edit being incorrect.

Editing: Is simpler and quickly resolves the problem.

However, directly editing seems preferable for all parties in terms of efficiency, but it appears that experienced users typically find this action offensive, and even sometimes follow up with a trivial edit of their own (I presume so that the answer appears wholly theirs again).

In short: If there is definitely a mistake in an answer and you are sure you can fix it, is it preferable to leave a comment or just to fix it yourself?

A few examples of the types of errors:

a) In the context of taking a derivative: $\sin^3 x=3\sin^2 x \cos x$

b) In the context of defining a polynomial basis: $\{x^i~|~0\le 1 \le n\}$

c) Multiplying $a$ and $b$: $a.b$

Note that I am asking particularly about answers - which somehow seem more sacred to users than questions.

A related question: is there any etiquette to be observed when editing a question or an answer

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    $\begingroup$ Please do not use MathJax for formatting. And, Markdown even supports lists. $\endgroup$ – quid Mar 25 '15 at 19:38
  • $\begingroup$ @quid Sorry about that. I am unfamiliar with the standards on the meta. $\endgroup$ – Peter Woolfitt Mar 25 '15 at 19:53
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    $\begingroup$ If the mistake is a typo or TeX error, editing seems best. $\endgroup$ – André Nicolas Mar 25 '15 at 20:09
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    $\begingroup$ Thanks for the edit. This standard is however not unique to meta. One should not use MJ for formatting on the main site either. MJ is for typesetting math, and only this. $\endgroup$ – quid Mar 25 '15 at 21:08
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    $\begingroup$ See this edit on an answer of mine by @Lord_Farin. I don't know if I qualify as a "more experienced user" (~ 4 months, 7k rep), but I definitely did not take offense to that edit. In fact, I thanked him in a comment. I didn't make a trivial edit to make it look like my own again. If the edit is useful and corrects something the poster clearly did not intend (which I think is evident in my post and why Lord_Farin corrected it), then I would expect more mature behavior out of more experienced users than simply making a trivial edit. $\endgroup$ – Daniel W. Farlow Mar 25 '15 at 21:08
  • $\begingroup$ @quid Ah, then I suppose I should generalize my statement to I am unfamiliar with standards. Thanks for the info. $\endgroup$ – Peter Woolfitt Mar 25 '15 at 22:23
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    $\begingroup$ @quid One should use MJ as one sees fit (and one should not attempt to force one's formatting opinions on others). E.g. I use MJ to generate newlines in comments (as do others). $\endgroup$ – Bill Dubuque Mar 25 '15 at 22:51
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    $\begingroup$ @BillDubuque this has nothing to do with formatting opinions but is about preserving correct semantics, which can be important for the accessibility of the site, for example via screen-readers. $\endgroup$ – quid Mar 25 '15 at 23:09
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    $\begingroup$ @quid My remark concerns your unqualified statement "Please do not use MathJax for formatting". I do so frequently and your arguments against such are far from persuasive. $\endgroup$ – Bill Dubuque Mar 25 '15 at 23:13
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    $\begingroup$ @BillDubuque the opinion of the developer of MathJax on the subject seems clear enough. "MathJax should be used only for mathematical content, not for adding white space, or italics, or colored text, or background colors, or line breaks in comments, or other display hacks, to textual (non-math) content." (source) $\endgroup$ – quid Mar 25 '15 at 23:25
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    $\begingroup$ @quid So what? People are free to use the tools in whatever way works for them to effectively present mathematics. The purpose of the site is not to compose perfect markdown and TeX (nor to critique such trivial syntactic matters). Rather, the prupose of the site is to communicate mathematics. $\endgroup$ – Bill Dubuque Mar 25 '15 at 23:27
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    $\begingroup$ @BillDubuque the point is precisely that misusing MathJax can be detrimental to the goal of communicating mathematics, especially towards users accessing the site via non-standard means such as screen readers. Please refer to the answer where the comment was made, and other writings on the meta-board by the developer of MathJax. I defer to his expertise, and encourage others to do likewise. $\endgroup$ – quid Mar 25 '15 at 23:32
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    $\begingroup$ @quid Arguments from authority are hardly persuasive. In any case let's agree to disagree. $\endgroup$ – Bill Dubuque Mar 25 '15 at 23:36
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    $\begingroup$ Refrain from correcting formatting that is a matter of opinion. Do not change $dx$ to $\mathrm{d}x$, or vice versa, for example. $\endgroup$ – GEdgar Mar 28 '15 at 14:13
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    $\begingroup$ See also: Is it incorrect to make edits to math mistakes? $\endgroup$ – Martin Sleziak Feb 29 '16 at 8:21
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I use edits on answers almost exclusively to fix typos - that is, to fix things which the poster probably didn't intend originally. Obviously, misspelled words and obvious grammatical errors should be fixed by edits (it'll be far harder to communicate where the error is than to just fix it anyways). This does include mathematical errors - however, one should limit the scope of this; if a single equation is in error and the error is not referenced elsewhere in the post (i.e. it is not copied into further equations, or talked about in the text), one may as well fix it with an edit.

If the error is deeper - that is, it's fairly clear that the author intended it as it was, but was wrong - then a comment is likely better. If nothing else, a comment is more likely to convince the author that they were wrong than an edit (which could be alarming), but it also offers the author the chance to determine what else in the post is wrong. I would definitely advise comments if the problem is stylistic in nature, as this requires major changes, but could go in lots of direction - so it really ought to be the author providing the creative energy for it.

Personally, I've only once undone an edit on one of my posts - and I did so because it added superfluous explanations to my answer. As a somewhat experience user, I consider it pretty surprising to receive an edit to an answer (since it's rare - not to brag, but my answers are perfect), but as long as the edit is correct, I'll appreciate it.

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    $\begingroup$ We’re in substantial agreement. I occasionally correct typos and obviously unintentional minor mathematical errors in answers or improve formatting if the user is new, but in general I prefer to leave comments and very much prefer to have comments left for me. I don’t generally correct misspellings, save of names and techical terminology that might be subjects of searches, or grammar and usage, because I’d be doing nothing else. (E.g., it’s anyway, not anyways. :-)) I very occasionally correct foreignisms that are genuinely hard to understand. $\endgroup$ – Brian M. Scott Mar 26 '15 at 5:19
  • $\begingroup$ I too use occasional edits of answers to fix typos. I think I've twice edited answers of people with substantially more reputation than me - normally I leave a comment as courtesy and hope that the answer will be edited and the comment can be deleted. My two occasions involved very obvious typos (one was the letter for an index in a sum) where the intended answer was mathematically correct, but the typo might actually be misleading if someone was reading quickly. Just today I left a comment on a very good answer which had a mistake and OP corrected - result - and OP gets the credit. $\endgroup$ – Mark Bennet Apr 4 '15 at 21:33
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The standard that I try to adhere to is this: is it clear that they meant to write the correct thing? If a small adjustment is all it takes to make the answer correct, then editing the answer is the proper course of action. But if you'd have to rewrite the answer from scratch to make it correct, then that's what a downvote is for.

For example, an answer repeatedly refers to $\mathbb{Z}[\sqrt{-5}]$ and then at one point mentions $\mathbb{Z}[\sqrt{5}]$ but it's clear they're still talking about a domain of complex numbers. Clearly they're missing a minus sign, so editing is what should be done.

Edits should not be used for stylistic impositions, however. For example, someone writes $\textbf{Z}[\sqrt{-5}]$ I'm not going to change it to $\mathbb{Z}[\sqrt{-5}]$. But if someone writes $Z[\sqrt{-5}]$, you bet I'm changing it $\mathbb{Z}[\sqrt{-5}]$. When someone doesn't know $\rm\TeX$ but it's clear what they would have written if they did know, then that's another occasion editing the answer is appropriate.

In between the extremes of an answer incorrect because of a small oversight and of an answer incorrect because of a thorough misunderstanding of the mathematical principles at hand, we have the gray area of those answers that could become correct with several small adjustments. Maybe that's where a comment is called for, but it's going to be a judgement call.

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    $\begingroup$ @crash: That edit was not a good edit. $\endgroup$ – Asaf Karagila Mar 27 '15 at 18:48
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    $\begingroup$ @AsafKaragila I hope the humor was not lost on you--it was a very tongue-in-cheek edit. $\endgroup$ – Daniel W. Farlow Mar 27 '15 at 18:52
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    $\begingroup$ @crash: And with so much going on over the meta site, perhaps it was unnecessary. $\endgroup$ – Asaf Karagila Mar 27 '15 at 18:54
  • $\begingroup$ @AsafKaragila Okay, I can agree with that (the edit being unnecessary in light of the most recent/hot meta posting about site design changes). Too late to do anything now I'm afraid. At a different time, perhaps it would have been more appropriate/amusing. $\endgroup$ – Daniel W. Farlow Mar 27 '15 at 18:58
  • $\begingroup$ @crash You managed to make an utterly pointless edit, to introduce an outdated $\TeX$ macro (\rm) and to make the thing look worse than before. All in one go. Congrats. $\endgroup$ – Najib Idrissi Mar 27 '15 at 20:10
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    $\begingroup$ @NajibIdrissi Apparently the humor was lost on you as well. For one thing, $\TeX$ looks like garbage. It shouldn't be slanted. Another, it really should be $\rm\LaTeX$. $\endgroup$ – Daniel W. Farlow Mar 27 '15 at 20:15
  • $\begingroup$ Donald Knuth's creation is a very deep subject and I must admit I just know the bare minimum for online use, if that. $\endgroup$ – Robert Soupe Mar 28 '15 at 1:46
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    $\begingroup$ @RobertSoupe That's fair. But here's one way to see just how inane Najib's comment is--what looks better? (1) The $\TeX$book or (2) The $\rm\TeX$book? I think Knuth would be rather pissed off at someone using the former. $\endgroup$ – Daniel W. Farlow Mar 28 '15 at 2:40
  • $\begingroup$ Okay, so $\mathrm\TeX$ looks better @crash. Do you believe your edit was necessary, or simply noise? And if it really should be $\mathrm\LaTeX$, why did you use \rm? I understand the "humor" you were going for (Robert is saying not to make trivial edits to posts to conform them to your typographical preferences, this is exactly what you did). Ha-ha. Was that funny? $\endgroup$ – Najib Idrissi Mar 28 '15 at 7:17
  • $\begingroup$ @NajibIdrissi Did you even read Robert Soupe's answer? If you did, then you would know that my edit was tongue-in-cheek, as already explained to Asaf. $\endgroup$ – Daniel W. Farlow Mar 28 '15 at 7:20
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    $\begingroup$ @NajibIdrissi That's kind of lame to edit your post to make it look like my comment was aggressive and nonsensical. "Was that funny?" Obviously not to you. And that's fine. If you, and several others on MSE apparently, cannot take a joke, then that's fine. However, if you want to get into a war about typography, then I'm down for that. For example, did you know that $f : \mathbb{R}\to\mathbb{R}$ is not appropriate? It should be $f\colon\mathbb{R}\to\mathbb{R}$. Anyway, I'm done with trying to justify humor. $\endgroup$ – Daniel W. Farlow Mar 28 '15 at 7:31

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