I've been a fairly active member for about a month, and I first of all want to say that this is a terrific site for someone like me that loves to mess around with challenging problems for no reason but the pure joy of it. Thanks to the moderators and others that make this site hum.

That said, I would like to ask about some ethics in answering some of the questions, driven by the (understandable) goal of increasing one's rep score. I am finding that, on more than one occasion, I may post an answer, and then, not 1 or 2 minutes later, but more than 10 minutes later, a nearly identical answer is posted, with nearly identical insights. Answer collisions - even collisions in additional insights - are understandable when there are questions in elementary subjects such as calculus. But after 10 minutes or so, when the duplicate answer has been posted either without even looking to see that a proposed answer has already been posted or even without caring, seems unreasonable to me.

My question is: shouldn't there be some responsibility of the users to check answers already posted so that those who answered first get proper credit?** And, if the incentive for rep score is too strong to be trusted to us users, shouldn't some moderators do a check of questions with many answers to make sure that duplicate answers are removed? (With an explanation sent to the answer-er, possibly with a path to appeal.)

**I understand the irony of this statement given my "pure joy of it" comment. But the joy is removed when you feel usurped.

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I checked some of your recent answers, but I can't quite see what you are getting at. Could you give some examples? –  Thomas Jan 14 '13 at 20:19
Here is one: math.stackexchange.com/questions/278747/…. You probably saw this and wondered what the problem was. The problem was in stating precisely the same insight I had, although I had answered > 10 minutes earlier. I suppose that this example makes me seem petty, but this is not the first time I have felt this way. Perhaps I should shrug and get a thicker skin. But have I raised a legitimate problem? Have any other members felt this way? –  Ron Gordon Jan 14 '13 at 20:24
By the way, I'm not saying that one should stop writing when an answer appears. Just that, when there are already answers, that users read them to make sure that they are contributing new material. Also, it's not just about rep scores for the answer-ers, but clarity for the people who asked the question. –  Ron Gordon Jan 14 '13 at 20:44
@RonGordon: Julien is here "Rude van Nistelrooy" :-) –  B. S. Aug 22 '13 at 7:58

I have to disagree with you that the motivation for posting answers after others have done so is related to reputation hunt.
I am a slow typer and a perfectionist ( others would say a nitpicker!), so that it takes me a long time to compose my answers since I do a lot of checking and try to write a well-formulated answer, of which I won't be ashamed in a year's time.
Add to this that English isn't my mother tongue and that I have some linguistic checking to do, and you will understand why, when I post my answer, I often see other answers which are mathematically isomorphic.
I can't deny that it sometimes is a bit embarrassing but more often than not I don't delete my answer.
One reason is that I'm vain enough to believe that it might add something to the other answers.
Another reason is that I can't resign myself to the idea that I have spent a not negligible part of my time for nothing : this might not be a very noble motivation but, hey, I'm a human being not a saint!

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Fair enough. Perhaps it is I who has the problem and needs to see better motivation in people. –  Ron Gordon Jan 14 '13 at 21:16
Dear rigordonma, speaking of "linguistic checking", I'm happy to see you use the elegant expression "it is I who..." instead of the more usual "it is me who..." :-) –  Georges Elencwajg Jan 14 '13 at 21:56
Georges: thanks. Of course, I write for a living, so I hope I get these things right! –  Ron Gordon Jan 14 '13 at 22:00
How interesting! What do you write, if I may ask? –  Georges Elencwajg Jan 14 '13 at 22:26
Patent applications. That and all sorts of correspondence with the US Patent Office so that my claims get allowed. –  Ron Gordon Jan 14 '13 at 22:27
Thanks for your quick answer. You are in good company: as I am sure you know, Einstein was working at the Patent Office in Bern the year he revolutionized physics (1905). –  Georges Elencwajg Jan 14 '13 at 22:33
Beautiful answer. –  user38268 Jan 16 '13 at 4:05
Thank you, @Benja. –  Georges Elencwajg Jan 16 '13 at 6:22
It's not elegant, it's grammatically correct. –  asmeurer Jan 21 '13 at 7:21
@asmeurer: Now I just spent 5 minutes trying to figure out whether it actually is grammatically correct. I think it may actually be "it is I who have the problem and need to..." Some opinion supporting this. –  Tara B Mar 8 '13 at 20:55
Oh, good point. I just meant the I vs. me part. I didn't even notice the verbs. –  asmeurer Mar 8 '13 at 22:58

The linked question illustrates why having more than one answer to the same question is a good thing, even when they are similar (for some value of "similar"; on some level all calculus problems and solutions are similar to one another).

The first-posted answer has a line "Use the fact that $\sqrt{x+h}-\sqrt{x} = \frac{h}{\sqrt{x+h}+\sqrt{x}}$" but does not explain where this fact is coming from. How would one think of this identity on their own? The second-posted answer makes a general point: when the difference of two roots is present, one should consider multiplying them by the sum of the same roots.

Both answers are of value. I would upvote both, but I'm all out of votes at this time.

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Thanks for answering. Not to get defensive, but a) there is a 3rd answer which is the one that set me off, and b) I write to the presumed level of the questioner. Perhaps that questioner would not have dreamed up that identity, but (s)he should easily verify it using the difference of two squares; if not, (s)he'll ask. –  Ron Gordon Jan 14 '13 at 21:19
@rlgordonma The 3rd answer is different; it invokes the derivative of $1/\sqrt{x}$, which, as noted in comments, is most likely to fall into circular reasoning. The observation about circular reasoning adds some value too, and it would not appear without the answer being there. Anyway, now that the new UTC day has dawned, I upvoted the answers given by you and Bruce. –  user53153 Jan 15 '13 at 0:07
I don't see the comments about circular reasoning. But anyways, for the sake of torturing analogies, the nice thing about a circle is that there are two ways from point A to point B -- while one may be interested in the derivative of a square root and is using such a limit to find it, one could also very well be interested in that limit, and use the derivative of a square root to find it. (the power rule could be derived from the chain rule, without any knowledge of manipulating roots in limits) –  Hurkyl Jan 15 '13 at 15:05