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By answering the question Does $\sum_{n=1}^\infty\frac{1}{n}$ diverge using an argument of Cauchy sequence I received several downvotes (and of course my question isn't about the downvote but just to understand the reason of the downvote and to open a discussion to explain the policy of this site for this situation).

The downvoter said that my answer confuses the asker since he's probably from the USA, and so he most likely doesn't know about Cauchy sequence. Really I feel this reason is ridiculous, in fact:

  • Should I guess that the OP is from USA or another country, to decide if I have to give an answer using Cauchy sequence or another method?
  • Should the answer be addressed uniquely and only at the OP, or also at any other person can expect to benefit from the answer?
  • Let's assume that the OP doesn't know the Cauchy sequence; then either he asks for understanding this new concept, or he is not interested in this answer which probably interests other readers.

Surely this question will give different opinions since my answer received many upvotes as downvotes and I admit that this is not the first time that this happens, I've had similar cases using the notation of big Oh and small Oh.

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    $\begingroup$ How do you know the person who made this comment downvoted you? $\endgroup$ – Michael Greinecker Nov 23 '13 at 18:14
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    $\begingroup$ @Sami I find your title confusing. $\endgroup$ – user940 Nov 23 '13 at 18:21
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    $\begingroup$ I think this thread is strongly related to the question. $\endgroup$ – user61527 Nov 23 '13 at 21:33
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    $\begingroup$ FYI, I learned about Cauchy sequences in my high school calculus class in the U.S., so that comment sounds utterly absurd. $\endgroup$ – dfeuer Nov 24 '13 at 6:37
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    $\begingroup$ I am opposed to having a policy imposing standards for downvotes. Or for upvotes. $\endgroup$ – GEdgar Nov 24 '13 at 12:29
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    $\begingroup$ Something that may have caused the downvote is that you answered a question which was obviously a duplicate (this is after all a very common question). Personally, I would not want to start downvoting such answers, but it seems from previous meta discussions that a few people do. $\endgroup$ – Tobias Kildetoft Nov 25 '13 at 9:59
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    $\begingroup$ @dfeuer: It’s not, I’m afraid; you were quite fortunate in your high school calculus class. $\endgroup$ – Brian M. Scott Nov 26 '13 at 0:38
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    $\begingroup$ I would not have given your answer, because I would not expect it to be as helpful to someone likely to ask the question in the first place as a more elementary argument from partial sums, and my first concern is always helping the OP. However, I think that it’s a fine answer, and I don’t understand all the fuss. I certainly don’t understand the five downvotes. $\endgroup$ – Brian M. Scott Nov 26 '13 at 0:44
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    $\begingroup$ It doesn't really matter where someone is from, that really sounds like nationalism or Americanophobia. $\endgroup$ – Squirtle Nov 29 '13 at 21:05
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    $\begingroup$ What I am surprised to learn from this discussion is that it seems possible to learn about convergence of sequences (and even advance to series) without learning about Cauchy sequences. Is that a freedom fries thing? $\endgroup$ – Hagen von Eitzen Nov 29 '13 at 21:44
  • $\begingroup$ The fact that you linked to a description of the Cauchy makes the reference fine, in my opinion. $\endgroup$ – JTP - Apologise to Monica Dec 3 '13 at 18:32
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    $\begingroup$ (Sees the answer 20 days later...) 30 upvotes! Yeah, the system works.. $\endgroup$ – Braiam Dec 5 '13 at 18:23
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Your answer is fine. I have no idea why it was downvoted so much. Even if the original person asking the question does not know about Cauchy sequences (we have no way to tell), it is OK for some answers to address more advanced viewpoints. And, surely, the most direct way to show that $\sum_{k \in \mathbb{N}} 1/k$ diverges is to verify that the sequence of partial sums is not Cauchy. That is not really a very "advanced" viewpoint.

In general, if you have 25k reputation and someone with 500 reputation posts comments that seem odd or intemperate, based on your experience with the site, I would trust your experience over that of a new user.

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    $\begingroup$ Strongly seconded (I've had a few of these, too). It may take some off-screen time to be able to do so, but such comments may be safely ignored. $\endgroup$ – Lord_Farin Nov 23 '13 at 22:00
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    $\begingroup$ I would also add that answers on SE sites in general are not just for the question askers, they are also for the countless Googlers that will come for years and years. As such, multiple approaches (some of which are advanced) are good. $\endgroup$ – Reinstate Monica Dec 3 '13 at 3:16

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