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Is it possible that a high reputation (>50K) user post a completely wrong answer? or its answer contains some lines that shows the user is misunderstanding that topic in math?

If so, how we can trust that answer if nobody up-vote it?

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    $\begingroup$ People even with incredible skills can make mistake in their area of skill. The mistake does not diminish their skill and should be considered more as part of our fallible nature. I have sometimes fixed my mistakes in answers here on being pointed out and in certain cases keep the original (in striked out form) mistaken argument intact. $\endgroup$ – Paramanand Singh Aug 10 at 4:59
  • $\begingroup$ No, my question is not about "mistake". $\endgroup$ – C.F.G Aug 10 at 5:39
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    $\begingroup$ Writing a completely wrong answer is a bigger mistake than just having some mistake in part of an answer. I don't see it differently (ie I can't imagine a scenario where a high rep user intentionally posts a completely wrong answer just to see how MSE reacts to it). $\endgroup$ – Paramanand Singh Aug 10 at 5:41
  • $\begingroup$ I saw an answer that was correct but in the last line s/he added some extra information about asked topic that I shocked and s/he continuously was emphasizing that his/her argument is correct. Is this a normal "mistake"? $\endgroup$ – C.F.G Aug 10 at 5:47
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    $\begingroup$ OK in that case one approach would be to engage in discussion via comments or chat and convince the user that there is an issue of mathematical correctness. Also such discussions can be painful (I have had one and it took me 2 hrs to convince). $\endgroup$ – Paramanand Singh Aug 10 at 5:49
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    $\begingroup$ Also in such discussions being polite is absolutely essential even if other party is getting a bit aggravated. Convincing is not just about the math being correct, but also about being nice and not confrontational. $\endgroup$ – Paramanand Singh Aug 10 at 5:52
  • $\begingroup$ I wonder how this can happen for 50k user? $\endgroup$ – C.F.G Aug 10 at 5:54
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    $\begingroup$ Well, for one 50k+ users are also humans. $\endgroup$ – Asaf Karagila Aug 10 at 5:56
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    $\begingroup$ Learn to believe that this can happen. I don't know what to say. World is full of wonders and consider this also as one of the wonders (even if a bit annoying one)! $\endgroup$ – Paramanand Singh Aug 10 at 5:56
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    $\begingroup$ "I wonder how this can happen for 50k user?". And me, I'm sitting here wondering where you got the idea that collecting a high reputation might mean a person no longer gets things wrong. $\endgroup$ – JonathanZ supports MonicaC Aug 10 at 13:22
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    $\begingroup$ I spend more time on some "advanced" tags, so quite frequently I see high reps users drop in and post wrong answers. It is more common than you imagine. $\endgroup$ – Arctic Char Aug 10 at 14:32
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    $\begingroup$ Let's suppose that high-rep users posting an incorrect answer is an impossibility.. Is reputation necessary for an answer's validity? It's like saying that low-rep users' answers contain flaws.. $\endgroup$ – Omar S Aug 10 at 20:02
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    $\begingroup$ 50k is more a measure of how much time a user spends here than of how brilliant the user is. $\endgroup$ – Gerry Myerson Aug 11 at 7:34
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    $\begingroup$ It could also be possible that a high rep user got lucky with a great question that received lots of upvotes, but has relatively little skill/knowledge. Conversely a new user could be a professor who's only just discovered MSE and wants to engage in the online community. Reputation shouldn't be a marker for skill in mathematics. Even if someone is highly skilled that doesn't make them immune from mistakes. Take me for example, I'm doing a PhD, so on paper I'm "good" at maths, but I make mistakes on this site with an embarrassing amount of regularity. $\endgroup$ – SeraPhim Aug 12 at 13:11
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    $\begingroup$ You might be interested in this userscript that hides the reputation, badges, etc. in every user’s flair so that such data does not influence your view of the quality of their posts: stackapps.com/q/3105/61479 $\endgroup$ – user279515 Aug 13 at 15:52
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Yes. That is possible, and it certainly happens.

This is why you should usually be critical and vote after reading and understanding an answer.

And yes, sometimes people will vote a wrong answer because they trust the user. But hopefully someone will actually read it, and point out the mistakes. At least on my end as a high reputation user, that worked out pretty well every time I made a mistake (that I know of, anyway).

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  • $\begingroup$ Thanks. what do you mean by "mistake"? $\endgroup$ – C.F.G Aug 10 at 5:48
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    $\begingroup$ Mathematical mistakes. Not typos. $\endgroup$ – Asaf Karagila Aug 10 at 5:55
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I'd like to tackle the second part of your Question:

If so, how we can trust that answer if nobody up-vote it?

The ideal for Math.SE is to have problems solved by reasoned mathematical argument. By this I mean the correctness of the solution should be evident by following the logic (reasoning) of the Answer. In particular we should avoid asking Readers to accept proof by authority.

Naturally a great variation occurs in the ability of Readers to follow arguments when the subject matter, and even the terminology, may be unfamiliar. This is one of the motivations for wanting context in the presentation of a Question, so that a willing Reader can try to respond in an accessible way to the OP. But in many cases a problem can be solved in various ways, and it is desirable to see that the lines of argument, done correctly, come in the end to the same conclusion.

My advice in posting Questions is therefore to ask about what you will be able to judge for yourself of its correctness. Pushing beyond this limitation may lead to a failure to learn the mathematics. So in such a case it is likely better to step back and ask a more fundamental "threshold" Question, to prepare for next steps in understanding.

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    $\begingroup$ +1 for the mention of "proof by authority". $\endgroup$ – Paramanand Singh Aug 11 at 1:30

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