-2
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$$\gcd(N/q^\alpha,\sigma(N/q^\alpha)) = \begin{cases} \dfrac{N}{q^\alpha \sigma(q^\alpha)}, & \alpha \equiv 0 \pmod 2 \\[8pt] \dfrac{2N}{q^\alpha \sigma(q^\alpha)}, & \alpha \equiv 1 \pmod 2 \end{cases}.$$ $$\gcd(N/q^\alpha,\sigma(N/q^\alpha)) = \begin{cases} \dfrac{N}{q^\alpha \sigma(q^\alpha)}, & \alpha \equiv 0 \pmod 2, \\[8pt] \dfrac{2N}{q^\alpha \sigma(q^\alpha)}, & \alpha \equiv 1 \pmod 2. \end{cases}$$

The style of sentence-ending punctuation in the first display above strikes me as plainly incorrect by any standard, and yet it is frequently seen on MathOverflow and elsewhere on the internet, and that in the second seems reasonable to me.

If you look at something in one font and the same thing in another font and think that one looks aesthetically pleasing and the other hideous, the cause is a large number of little details of design of characters and their relative positions on the page, and it is probable that you don't notice what any of those little details are. When correction of one of those details in a posting was proposed a few years ago, one MathOverflow user said he doubts anyone would even notice the difference. I don't know that anyone has ever missed the point more completely. TeX and LaTeX were obviously designed to make attention to that kind of detail possible and easy.

I did an edit in which, among other things, I changed the first punctuation format above to the second.

Are there consensuses or policies about the appropriateness of such corrections?

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    $\begingroup$ Such corrections are absolutely appropriate. The first version is clearly wrong punctuation and quite ugly. The OP should be glad that you corrected it. Good job! $\endgroup$
    – Todd Leason
    Nov 5 at 22:31
  • $\begingroup$ It's a pitty that moderators are insensible to correct punctuation. Some time ago there has been a discussion on meta meta.mathoverflow.net/questions/5770/… about different line breaks in the preview and the final text. So there are definitely users on MO who care for style and correctness. I hope they step in and support your issue. $\endgroup$
    – Todd Leason
    Nov 6 at 13:36
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    $\begingroup$ I absolutely agree with your aesthetic choice in this instance, but generally speaking about grammar and orthography, expect there to be no consensus on whether your preferences are "correct". Many users insist on not punctuating at all in display lines (no full stops, for example). As for policy, there's no rule against editing made in good faith, so go right ahead as you wish, but as you may know, experience shows that many an OP will vehemently resent it. $\endgroup$
    – Todd Trimble Mod
    Nov 6 at 14:21
  • $\begingroup$ $\ldots\,$that that is malicious disruption of the site's purposes. $\endgroup$
    – Michael Hardy
    Nov 6 at 16:43
  • 2
    $\begingroup$ Speaking to the commenters: there are two things worth keeping in mind here: (1) MO and Math SE are different sites with different cultures and it is perhaps not appropriate expect the standards on one site to be the same as the standards on another site, and (2) the presentation above reflects only one side of the story and should, perhaps, be read with a grain of salt. $\endgroup$
    – Xander Henderson
    Nov 6 at 19:34
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    $\begingroup$ @XanderHenderson : You may notice how the other side expresses their disagreement by (in this particular instance) downvoting the question but without verbally explicating their position. For that other side to be represented here in a way that is comprehended by the use of language, in the form of sentences made up of words, would be useful. $\endgroup$
    – Michael Hardy
    Nov 6 at 20:47
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    $\begingroup$ @MichaelHardy I have no interest in having this conversation here, which is why I was not responding to you, but to the other commenters, instead. This is not an appropriate forum for you to air your grievances with the Math SE moderators. I will note, however, that I do not have sufficient reputation on MO to cast downvotes, hence whatever prompted the downvoter(s) to vote is well beyond my ken (and responding to me to complain about the downvotes is well beyond my ability to do anything about). $\endgroup$
    – Xander Henderson
    Nov 6 at 21:28
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    $\begingroup$ @XanderHenderson : You are the one who brought up that subject that you say you do not want to discuss here. $\endgroup$
    – Michael Hardy
    Nov 6 at 21:59
  • 1
    $\begingroup$ @XanderHenderson I'm well aware of the difference in cultures, and I also agree that Mathematics StackExchange policies aren't relevant here at MO meta. My answer to Michael Hardy was that edits of this nature are generally condoned at MO Main and MO meta, and since MH is not reporting any problems of this type here at MO, it would seem all is well in this regard and his question has been answered. $\endgroup$
    – Todd Trimble Mod
    Nov 6 at 23:50

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