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?