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I recently read an answer regarding L'Hospital rule and I don't even understand a line what this answer is talking about. There are several others of such answers (which have been deleted now):

All of them are related to a magic "Taylor's formula" from non-standard analysis, which can be seen from the first linked answer. I know nothing but the name of non-standard analysis and I have never seen people do calculus this way before.

I was not intending to target one particular user. But all these low-quality answers are from this same person, it seems that I am now.

Are my serial downvotes to such answers inappropriate? If yes, would anyone suggest what one should do?

[Added:] Here is the list of undeleted(deleted now) answers I have downvoted:

(I really want to know if an expert on nonstandard analysis would stand up and shout at me: "go home and learn more math! These answers are all valid!" )

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    $\begingroup$ Series are related, but I think you meant "serial", as in many votes to one user. $\endgroup$ – Simply Beautiful Art Aug 24 '17 at 21:38
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    $\begingroup$ The second deleted answer is outright nonsense, in general, there should be another correction term. $\endgroup$ – Simply Beautiful Art Aug 24 '17 at 21:40
  • $\begingroup$ @SimplyBeautifulArt: Fixed now. Thanks. $\endgroup$ – Jack Aug 24 '17 at 21:40
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    $\begingroup$ Yeah, this user is definitely misinterpreting Taylor's theorem. I don't believe the deletion was bad, despite them all coming from the same user. $\endgroup$ – Simply Beautiful Art Aug 24 '17 at 21:42
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    $\begingroup$ It depends on how one defines "targeting" a user. Focusing in on one user to the exclusion of other moderating actions, may not fare well upon the crunching of numbers, by the daily scripts detecting "serial voting". I am not suggesting you were serially downvoting or deleting for any reason other than enhancement of site quality. You made a lot of good calls; but maybe review such a user's posts less rapidly; as is, many of the posts in question are from a year ago. Bottom line: Your honesty here is applaud-able. And it's a good question, in general!! $\endgroup$ – Namaste Aug 24 '17 at 22:10
  • $\begingroup$ From the viewpoint of non-standard analysis, some of the added answers (the one you just added) do make sense. It is a little bit handwaving but the spirit is mostly correct. $\endgroup$ – achille hui Aug 25 '17 at 3:38
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    $\begingroup$ @achillehui: No they do not. In a lot of those cases the user claims that L'Hopital's rule is false, just because his weird manipulations arrive at a contradiction. Also, he is willy-nilly using the idea of nilsquare elements all over. $\endgroup$ – user21820 Aug 25 '17 at 6:44
  • $\begingroup$ @user21820 I didn't bother to look at all the answers. $\endgroup$ – achille hui Aug 25 '17 at 6:46
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    $\begingroup$ @achillehui: That's okay. I'm just stating it in case people get the wrong impression. I look sufficiently at every single answer that I delete. =) $\endgroup$ – user21820 Aug 25 '17 at 6:53
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    $\begingroup$ @Jack The second answer from the second list has no downvotes at the moment. Perhaps you can check the other answers, but I guess that your votes have been reversed by the automated script which removes serial votes. (Also on the user's profile I see today +8 reversal - Voting corrected. Of course, I cannot see whether the reversed votes were yours - voting is anonymous.) $\endgroup$ – Martin Sleziak Aug 25 '17 at 8:51
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    $\begingroup$ Is it not ironic that the mentioned user's username is "selfawareuser"? $\endgroup$ – Franklin Pezzuti Dyer Aug 26 '17 at 15:17
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    $\begingroup$ Let me add something to the discussion: I had a brief virtual encounter with that user last year, when I detected him using 3 separate accounts; of them, one was for posting, and another one for upvoting his own posts. When confonted with this fact, he quickly deleted 2 out of those 3 accounts. Regarding his posts - some of them are ok, but there is a lot of non-standard analysis in answers to simple high-school questions where the OP is obviously looking for "standard" analysis. I myself have downvoted and voted to delete many of this user's posts. $\endgroup$ – Alex M. Aug 26 '17 at 15:45
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    $\begingroup$ @AlexM. I no longer see it there. I'm pretty sure I saw it when I posted my comment - maybe I should have made a screenshot. (Maybe all the post related to those reputation changes were deleted and that's why we no longer see the reputation changes.) But I guess it is not very difficult to find some other user profiles with voting reversals. Since this seems only tangential to the issue at hand, we can continue this discussion in chat, if needed. $\endgroup$ – Martin Sleziak Aug 26 '17 at 15:55
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    $\begingroup$ @rocksNwaves ?? $\endgroup$ – Simply Beautiful Art Aug 27 '17 at 23:17
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    $\begingroup$ Maybe a recent discussion on meta might be of interest to you in relation to this: Someone is doing “targeted serial downvoting” against me? (Just a guess, but I thought it might be useful to let you know about that discussion.) $\endgroup$ – Martin Sleziak Dec 1 '17 at 5:55
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In my mind there are at least three sides to this, in general not only for this particular case.

  1. At one level the votes are appropriate. They are based on your best judgment of the post. To communicate your evaluation of a post is exactly what votes are for.

  2. At another level you focused your votes on one user. This could raise some red flags and indeed it seems from Martin's comment that a script picked up on the pattern and annulled your votes in part. This is unfortunate for various reasons. This could be seen as a lack of the script, but let me get to the third side.

  3. I do know the situation of stumbling over a user and finding many of their contributions lacking and feeling the urge to take some action. But, ultimately, I mostly try to resist the urge to take actions in bulk. On the one hand, to avoid the second point. On the other hand, and more importantly, I feel it can be better to give the user direct feedback via a comment and to give them some chance (that is in particular time) to fix their stuff.

Sure, sometimes there will be no change in behavior and then the situation changes a bit. Yet to vote massively on one user's contribution is not necessarily the best option.

If there is a massive and persistent problem signal it to the moderators (for example, via a custom flag on one of the concerned posts).

If the problem is not massive the best course of action might actually be not to focus on it. Deal with the posts occasionally if you come across them, otherwise trust that somebody else will take care of them. (Yes, maybe, nobody will do that, but then realistically there are any number of other users' posts that would also require your attention.)

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    $\begingroup$ (+1) I think such an extreme case should be dealt with by moderators. $\endgroup$ – Simply Beautiful Art Aug 27 '17 at 23:23
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I think the community's overreacting on this one. The user under question seems to be basing their viewpoint on calulcus on this book. I haven't looked at the arguments too carefully, but it's not clear to me that the these arguments fall into the category of "plain wrong." In particular, aren't they just working in the dual numbers and then using the phrase "let $\varepsilon \rightarrow 0$" as sloppy terminology for "apply the $\mathbb{R}$-algebra homomorphism $\mathbb{R}[\varepsilon] \rightarrow \mathbb{R}$ defined by $\varepsilon \mapsto 0$?" Really they should find better notation for this, and they should probably disclose that they're not working in the real line, but apart from that, most of the answers I glanced at seemed okay. Obviously if the results they're deducing directly contradict ordinary real analysis that's a problem, and the idea that L'Hopital's rule is "just wrong" is itself just wrong, but nonetheless seems a bit rash to delete all their answers like that. We should restrict ourselves to deleting the blatantly incorrect ones. And, I should add that the whole thing seems to be a device for throwing away "terms that won't end up mattering anyway," so mathematically, the interesting question is: under what circumstances can this device be used safely, without deducing statements about the real line that are already known to be false? I don't know the answer to that question, but surely the answer isn't "never."

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