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Often I spend time solving some math problems on my own as exercises and after I'm done I tend to search the MSE site for the same problems or similar ones, as I want to see what are some other possible ideas or solutions. Sometimes it happens that I have solved the problem on my own, but when I find it here on MSE I don't see a posted solution similar to mine. The questions often have nice answers, which are rightfully accepted, but the idea they use differs from mine.

So I was wondering whether I should post my solution too, which I believe is alright and different from all posted solutions, but not necessarily better than the already accepted answer. Will adding a different answer enrich the website or it's just wasting of time, as the OP has already accepted an answer. So what's this site take on this? Are we tend to be a site which gathering as much knowledge as possible or just a medium for people to help each other?

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    $\begingroup$ '..but not necessarily better than the already accepted answer.' Well this 'better' might be ambiguous because it might be a better answer for a not very smart math student (with no mathematical maturity) or might be better for a smart student. I don't know, I always think the more answers I have to my questions the better, if I don't understand the first one, then I would take the second one and so on. $\endgroup$ Commented Nov 19, 2017 at 3:14
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    $\begingroup$ @Michelle I respect your opinion. You're right better is a bit ambiguous and subjective. I was thinking better in my opinion, but as you've pointed out somebody else, even the OP might consider it the other way around. $\endgroup$
    – Stefan4024
    Commented Nov 19, 2017 at 6:01
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    $\begingroup$ yes but the most important is the help you give to the users that are students, you have no idea how helpful the answers from the smartest ones or teachers are for beginners or undergraduate math students. Don't stop answering questions never:) $\endgroup$ Commented Nov 19, 2017 at 6:15
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    $\begingroup$ If you have a unique perspective or technique to offer, then yes. If youre arriving at a different result and wish to be contentious then yes, I think so too, but you should figure out why the other is wrong first. If the answer youre giving is similar to another, then submit it if you are showing more work, citing more information, expanding on methods and techniques, and generally being more helpful and educational. There is no point in offering a new answer that is no better than any other by any measure. You dont have to compete with the accepted best answer. $\endgroup$ Commented Nov 25, 2017 at 18:54
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    $\begingroup$ Sometimes I do this if I think I can make the answer simpler. $\endgroup$ Commented Nov 25, 2017 at 19:20
  • $\begingroup$ @MichaelHardy I agree with your assertation, but my focus was on late answers as I did it here. Is my answer simpler than the others? I would argue no. Is it fundamentally different? Yes, my proof even showed something more. So that's why I decided to post it. I was interested in this site's take on such answers, although the example I gave doesn't have an accepted answer. $\endgroup$
    – Stefan4024
    Commented Nov 25, 2017 at 19:25
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    $\begingroup$ I don't think the timing is essential. Whether you should post an additional answer shouldn't depend on how long it's been since the others were posted. $\endgroup$ Commented Nov 25, 2017 at 23:18

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You can absolutely provide additional answers. It's useful to remember that a big goal of the site is for posts to have lasting value beyond just to the OP. An OP's acceptance of an answer serves as one indication to later visitors what answers are or are not useful to someone considering the same question. Other's votes serve as additional indications.

There is value in additional perspectives or points of view within the answers. If you think you can give this, then it seems likely that some later viewer may benefit. On the other hand, there is not much value in giving the same answer twice. (There's not much lost other than your time, but not much gained).

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    $\begingroup$ Worth nothing that there's a badge for this, so it's definitely in the spirit of Stackexchange. $\endgroup$ Commented Nov 20, 2017 at 0:33

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