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I don't remember the exact words and perhaps the moderator who removed my comment would care to explain why he did so and paste my comment somewhere on the thread.

In this answer I left a comment saying I didn't understand why Muphrid's comment had two upvotes (which it did at the time) and I added that his comment added nothing to the answer except for naming the notation. Furthermore I mentioned that $\frac{dx}{dt}=x'(t)$ is wrong and that it should be $\frac{dx}{dt}(t)=x'(t)$ or $\frac{dx}{dt}=x'$.

My first remark was more of a request for clarification because I really couldn't see why someone found the comment helpful.

Do moderators have carte blanche to remove comments as they wish?

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    $\begingroup$ Mods can remove comments as they wish. In addition, comments that receive many flags are automatically removed (at least 3, plus 3 more for every upvote - so upvoted comments are harder to remove). Your comment was both multiply flagged and ultimately removed by a mod (i.e. it received multiple flags, but was removed by a mod before it hit 3, and only 3 were necessary since it received no upvotes). $\endgroup$ – davidlowryduda♦ Jun 4 '13 at 7:12
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    $\begingroup$ According to the explanation by @mixedmath, the comment was one flag short of automatic removal. In such a situation, a mod deleting the comment exercises no more power than an ordinary user with the privilege to flag. $\endgroup$ – ˈjuː.zɚ79365 Jun 4 '13 at 8:36
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    $\begingroup$ More interestingly: "my thread has so many downvotes and I don't know why" $\endgroup$ – Sosi Jun 4 '13 at 13:21
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    $\begingroup$ @Sosi That is indeed a good question. Even if for some reason, that I can't even begin to understand, my comment in that answer was unwarranted, just what is wrong with my question? What parts of the FAQ does it violate? This question getting $10$ downvotes, that's what's ridiculous. $\endgroup$ – Git Gud Jun 4 '13 at 15:01
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    $\begingroup$ @GitGud Remember that votes on meta do not work the same way as votes on the main site. In particular, downvotes are used on meta to express disagreement, not to indicate that the question/answer is incorrect or does not belong on the site. $\endgroup$ – Alex Becker Jun 4 '13 at 16:46
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    $\begingroup$ @AlexBecker This community ignores the rules and makes their own way too much. My only problem with that is that (once again) the FAQ and the communities rules are not in accordance. $\endgroup$ – Git Gud Jun 4 '13 at 16:51
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    $\begingroup$ @GitGud I'm not sure what you mean. $\endgroup$ – Alex Becker Jun 4 '13 at 16:52
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    $\begingroup$ @AlexBecker To be honest I had never read that part of the FAQ. My apologies and thank you for clarifying. $\endgroup$ – Git Gud Jun 4 '13 at 16:53
  • $\begingroup$ @GitGud That's alright. It's not immediately obvious that the FAQ for the main site does not apply here. $\endgroup$ – Alex Becker Jun 4 '13 at 16:56
  • $\begingroup$ @AlexBecker The mixup was even greater than that, I had read some parts of the Meta FAQ, just not that one. $\endgroup$ – Git Gud Jun 4 '13 at 16:58
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It does not apply to your case. But here is another reason why a comment could be deleted without notice. I have just learned it from @robjohn.

Assume you comment to mention that a thread is a duplicate. If the question is deemed a duplicate, the system will automatically remove your comment. I believe this applies only if you explicitly used the word "duplicate".

I understand the reason behind such a script. Nevertheless, in certain cases, I think it is not appropriate. For instance, if the duplicate you mentioned is not the one linked to in the end in the box "this question already has an answer here: [link]". In the case I have just witnessed, there were several answers with other approaches not reflected in the chosen duplicate.

Not the best SE script in my opinion. Note however that in the case I mention, the link I had proposed does appear on the right in the box "linked", above "related", together with the chosen duplicate. What is lost is the comment and the bit of algebra that explained why the thread was indeed a duplicate: a modification of the integrand.

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