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I've seen several cases of other users editing a question to change all instances of an asker's $\mathbb{Z}_n$ to $\mathbb{Z}/n\mathbb{Z}$, saying that the former is an incorrect notation. I don't want to call specific people out if they are genuinely trying to improve the site, but it is really the policy to enforce notation on those who come to ask questions?

Specifically in this example, $\mathbb{Z}_n$ is a quite old, well-established, and space-saving notation for the ring of integers modulo $n$. Yes the symbol does have other meanings, but so do the symbols $+$ and $0$ have multiple meanings. We aren't machines, so we can understand from context what is meant. In fact, the alternative meanings for the symbol $\mathbb{Z}_n$ are so comparatively advanced that I doubt anyone running into $\mathbb{Z}_n$ as the ring of integers mod $n$ would fail to realize what the notation means from context of the question.

It does not help the asker to rewrite his own question to make it more difficult for him to read or understand. Moreover, what is the message we are sending to the asker? "We don't care what convention your teacher or book uses; if you don't write math in the correct notation we will make sure you do"? Aside from being factually wrong (there is no one correct notation, there are only competing conventions), isn't this exactly the kind of arrogant attitude we should be discouraging if we want people to embrace the subject, and come here to ask stimulating, thought provoking questions?

If this is not policy here, then what should we do or say when we see someone doing this?

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    $\begingroup$ +1, and I strongly agree with the complaint here. I will normally reject proposed edits that drastically change the notation when they appear in my queue, and hope others do as well. If there's someone who's making serial edits that are radical changes to a post's content and they're getting approved, you can leave a comment on the post addressed to the editor, or as a last resort flag a moderator. $\endgroup$
    – user61527
    Dec 1 '13 at 19:43
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    $\begingroup$ I agree. The $\mathbb Z_n$-means-what-I-want-to-mean mafia is particularly notorious :-) $\endgroup$
    – Mariano Suárez-Álvarez
    Dec 1 '13 at 19:46
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    $\begingroup$ I prefer $\mathbb{Z}_n$ to $\mathbb{Z}/n\mathbb{Z}$ any day. (But I like $C_n$ even better.) These are all standard notations, and people absolutely should not edit one into another. $\endgroup$
    – Alexander Gruber Mod
    Dec 1 '13 at 19:46
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    $\begingroup$ I agree. I use both notation interchangeably (unless I happen to also be talking about the $n$-adic integers which isn't too common an occurrence). When editing someone's post I try to make my edit reflect the user's intended notation - so if they have an un-mathJaxed Z/nZ I'll change it to $\mathbb{Z}/n\mathbb{Z}$ and if they have an un-mathJaxed Zn or Z_n I'll change it to $\mathbb{Z}_n$. Of course some people may say this is imposing my preference for blackboard bold instead of regular math bold but then we can't know the user's preference in this case. $\endgroup$
    – Dan Rust
    Dec 1 '13 at 19:55
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    $\begingroup$ @DanielRust, I will sometimes go a bit further than that to reinforce conventions that are almost universal on the site (changing $Z$ to $\Bbb Z$ if the integers are intended, for example, seems to improve clarity without much risk of confusion), but obviously a choice like $\Bbb Z_n$ vs. $\Bbb Z/n\Bbb Z$ should be left alone unless there's a very good reason to change it. $\endgroup$
    – dfeuer
    Dec 2 '13 at 8:04
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    $\begingroup$ @AlexanderGruber "I prefer $\mathbb Z_n$ to $\mathbb Z/n\mathbb Z$ any day". Probably not on the days when you want to stress the structure of quotient group, though. (I agree with the rest of your comment.) $\endgroup$
    – Did
    Dec 2 '13 at 10:14
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    $\begingroup$ There is a difference though between $\mathbb{Z}_n$ and $\mathbb{Z}/n\mathbb{Z}$. In many texts the former is used to denote the integers modulo $n$ (i.e. the symbols $\{0,\ldots,n-1\}$ witht clock arithmetic) and $\mathbb{Z}/n\mathbb{Z}$ is the quotient group. It is then a theorem (not too hard of one) that they are actually the same. $\endgroup$
    – Alex Youcis
    Dec 2 '13 at 11:37
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    $\begingroup$ @dfeuer I'm always wary of assuming there is a community standard for things like notation. See this old thread for why imposing a convention is seen as not ideal by some in the community. $\endgroup$
    – Dan Rust
    Dec 2 '13 at 14:11
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    $\begingroup$ Maybe to avoid having your notation changed, include a phrase saying what you mean by $\mathbb Z_n$ right in the original question. $\endgroup$
    – GEdgar
    Dec 2 '13 at 14:39
  • $\begingroup$ Perhaps another symptom. Those who prefer $Z$ or $\bf Z$ instead of $\mathbb Z$. $\endgroup$
    – GEdgar
    Dec 2 '13 at 14:40
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    $\begingroup$ I routinely change $R,N$, and $Z$ to $\Bbb R,\Bbb N$, and $\Bbb Z$ when those sets are clearly intended; I don’t care for $\mathfrak{R}$ for the reals, but I would not change it, as it’s clearly an intentional choice, and the same goes for plain boldface. I generally change $[x]$ to $\lfloor x\rfloor$. I follow some of my own preferences when typesetting something that was posted in ASCII. Otherwise, though, I leave people’s notation alone unless it’s flat wrong, and then I’m more likely to leave a comment asking about it. $\endgroup$
    – Brian M. Scott
    Dec 2 '13 at 19:24
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    $\begingroup$ I've done a few edits to improve readability, either by changing $ to $$ or by inserting \Large in the $\TeX$ expression. An example of the latter: $$\int \frac{e^{\frac{ax^2+bx+c}{dx+e}}}{\sin \pi x}dx \implies \Large{\int \frac{e^{\frac{ax^2+bx+c}{dx+e}}}{\sin \pi x}dx}$$ What's your stand on this? (I might add that to the best of my knowledge all such edits have been approved, but I think that the reviewers' decisions weren't unanimous.) $\endgroup$
    – Daniel R
    Dec 3 '13 at 9:17
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    $\begingroup$ I thing you'd better localise the \Large: $$\int \frac{e^{\frac{ax^2+bx+c}{dx+e}}}{\sin \pi x}dx \implies {\int \frac{\Large e^{\frac{ax^2+bx+c}{dx+e}}}{\sin \pi x}dx}$$ $\endgroup$
    – user1551
    Dec 3 '13 at 11:02
  • $\begingroup$ @DanielR I like those sorts of edits (but more like user1551's that isolate the \Large), but I would be hesitant to approve if it was the only change on a post that was really old... (because the edit would bump the question) $\endgroup$
    – apnorton
    Dec 3 '13 at 14:08
  • $\begingroup$ @anorton Good to know, then I will continue doing them. And, of course, stay away from necrobumping. (And I agree about the isolation of \Large, this was just a fictious example.) $\endgroup$
    – Daniel R
    Dec 3 '13 at 17:20
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Given the comments thus far, I feel justified in writing my thoughts as an answer (seeing as I am not the only one to think this way).

Regarding correct (but just not preferred) notation: Changing someone's notation to something they didn't write should be rejected as a suggested edit, as a matter of respect for the author.

For example, I write my integrals $\iint f(x,y)\,dx\,dy$, whereas some users here (one specific user I look up to comes to mind) write integrals as $\int \mathrm dx\int \mathrm dy \,f(x,y)$. Do I change the integrals to match my format? No! Both formats are correct and understandable, and out of respect to the author of the post, I should leave his/her format as-is--who am I to correct it?

That said, I don't think someone other than the post's author should actually roll back the edit because the roll back will bump the question. A caveat could be if the question is really new, edit is substantial, and bumping to the top of the question queue doesn't make too much of a difference--then maybe rolling back is justified.

Regarding notation that is obviously a carryover from computer typesetting: This should be changed if it's obvious the OP was trying, but didn't know enough TeX to convert R (<- using markdown) to $\Bbb{R}$, or something similar. Other instances include the Unicode integral ʃ, excessive parenthesis and / symbols for attempted fractions, or ^ for exponentiation, etc.

Regarding notation that is just plain wrong: This should not be changed (unless it's an obvious typo, like $x^2$ in the first line becomes $x2$ in the second and back to $x^2$ in the third). "Wait!" you say. "Why in the world would we want to preserve bad notation?" Well, more often than not, if someone uses poor notation, their misunderstanding of the question stems from that misuse of notation. We should ask first in these instances before correcting the notation.

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  • $\begingroup$ Regarding notation that is obviously a carryover from computer typesetting: For centuries, users of mathematics have been happy to write and read such notation as $\cos\theta$, $\sin\theta$, and so on. In the last decade or so, it seems to have become de rigueur to write $\cos(\theta)$, $\sin(\theta)$, etc. There is almost no function that may now be written without accompanying parentheses. $\endgroup$
    – John Bentin
    Nov 16 '15 at 16:48

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