I recently answered a question here Limit of Sequence?? And, I got down votes, so I deleted it.

But, I am curious to know what was wrong with my answer. This was my answer for that post:

Because the magnitude of your non-zero values are getting smaller and smaller and it will be zero at the end. Even if you have $−2,0,+1,0,−1/2,0,+1/4,0,…,$ again the limit is $0$.


Could someone please shed some light on this?

Thanks, Nima

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    $\begingroup$ First, the fact that the non-zero terms are decreasing in magnitude is neither necessary nor sufficient in itself to ensure that the sequence has a limit. Secondly, there is no ‘end’, so ‘it will be zero at the end’ is not just wrong, but meaningless. (Note: I did not even see the question, let alone downvote your answer.) $\endgroup$ – Brian M. Scott Feb 10 at 4:45
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    $\begingroup$ @BrianM.Scott I see. Thanks for your input. It makes sense. I should have been more precise in writing the answer. $\endgroup$ – Nima S Feb 10 at 4:52
  • $\begingroup$ @NimaS: You’re welcome. $\endgroup$ – Brian M. Scott Feb 10 at 4:52
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    $\begingroup$ Yep. Your answer is what I would normally say or write in an informal discussion with somebody who understands everything there is to understand about the definition of the limit of a sequence and can easily turn my handwaving into a formal proof. But the OP was clearly rather clueless about all that stuff. On the other hand, while I would not upvote your answer, I would not downvote it either. It wasn't actually "wrong" (unless you want to be really formal) and it would be a reasonable hint if the OP were a bit more knowledgeable. It was just surely directed at a wrong audience :-) $\endgroup$ – fedja Feb 12 at 21:05
  • $\begingroup$ @fedja Thanks for the input. Appreciate it. $\endgroup$ – Nima S Feb 13 at 1:49

first of all let me give you a warm welcome to MSE.

You seem to have warmed to MSE better than most new users. I am sure you will keep growing as a contributor. There will be bumps along the way, but if you learn to enjoy them you will get nothing but pleasure out of the site.

Let me also take this opportunity to appreciate you for asking this question. That you wish to improve yourself is a hallmark of a budding contributor.

Now to your answer. There are two improvements that I would make, and a few other comments.

  • There's nothing wrong with providing intuition, it can even be more helpful than the mathematics itself. But as Brian points out, providing wrong intuition can be misleading for the OP(original poster i.e. the person who asked the question). While I try to see what you intend to say, unfortunately it isn't fully correct, because of the word magnitude. What you mean by magnitude of $x$ is $|x|$, I think. That's not a consistent notion, however : if the user takes it to be $x$ instead of $|x|$ (i.e. retaining the sign) then he/she gets the wrong message. So if you are providing intuition, you will still have to be mildly precise about things.

  • In addition to this, your answer must be tailored to the user, as fedja says above. While we often aim for generality in our answers so that they can be widely applicable, this is often impossible for user-specific issues, particularly a user that is clueless or requires 1-1 attention to get over the line on a question. Intuition is often a way to be general and cover a lot of mathematical ground. However, in the case of OP, it was also important, like the other answerer did, to provide some mathematical details. He/she wrote a complete answer, but you could have written something like he wrote and left it with : "can you find out what $N_{\epsilon}$ works? If you can't, I'll hide the explanation below" and put a hidden box with the explanation below, or address it in the comments if he/she says that $N_{\epsilon}$ could not be computed.

  • For your reputation, you write great answers. I have seen some of your answers, they are long and well-explained. Keep this length as a pattern : for users of low reputation, answers that provide both intuition and mathematical details will be long but rewarding experiences in the future for you. Once your reputation goes up, experience will help you gauge users and see if you can avoid mathematical details and/or intuition, although at my level I rarely avoid either.

  • Finally, please do not give up because one question or answer goes awry. Life itself is full of ups and downs, so if MSE wasn't then it would not be part of so many people's lives. One bad question or answer can be followed by five excellent ones, and then five more.

If you wish to do 1-1 mentoring for your contributions in the future, you can chat with me. But I am sure you will get over these issues in the future and am waiting to read what you write.

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    $\begingroup$ @NimaS This is my chat room here which you can visit and post links to your questions and/or answers which you wish to be assessed by me. Thanks once again. $\endgroup$ – Teresa Lisbon Feb 13 at 7:41
  • $\begingroup$ Hi @Teresa Libson, Thanks for your kind and thorough reponse. I am a grad student in Electrical Engineering who enjoys math. Although my background is good to some extent, I don't have deep knowledge in math like some of the contributor and that's the reason I cannot provide a very-solid answer (with correct definition/terminologies) for the users. But, all in all, it is good. As you said, life is a rollercoaster. I am enjoying it. I appreciate the input you provide. It was very helpful. Thanks. $\endgroup$ – Nima S Feb 13 at 7:58
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    $\begingroup$ @NimaS No problem. If you wish for tips on any answer of yours, please use the chatroom to contact me and I will take a look, possibly edit the answer a little if required. $\endgroup$ – Teresa Lisbon Feb 13 at 8:46
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    $\begingroup$ My goodness but this answer was pleasant and inspiring. $\endgroup$ – Trixie Wolf Feb 14 at 11:25
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    $\begingroup$ @TrixieWolf Thank you for the compliment, I prefer to be encouraging rather than merely critical as you can see with the answer. This is an attitude which I keep in life and wish to retain. $\endgroup$ – Teresa Lisbon Feb 14 at 12:00

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