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I am posting this question as a place where we could collect various examples of good questions together with explanations what makes them good. (Feel free to choose the format you like best. I will post my own suggestion below, mainly to give a better explanation of what I am looking for).

There have been several suggestions to have some example questions showing how good question looks like. (And perhaps also examples of bad questions.) Such things have been discussed, for example, here: Examples and counterexamples of good questions and answers and Standard example of well asked question. (There exists also this list: Compile short list of links to model questions (by type) But it is intended more as a list of exceptionally good questions. As opposed to a reasonable standard, achievable even by new users, which is the point of discussion here.)

However, it would be useful not only to have examples of good questions but also provide explanation what exactly makes these question well-asked. Explanation could be given, for example, in a picture (where important stuff could be underlined or marked by circles together with commentaries) or in an animation or a video (where explanations could be added, for example, as subtitles) or simply as a few paragraphs of text.

We can discuss whether (and how) can this be done technically in a separate discussion. And also discussion whether this would be a good thing would probably be better directed to a separate thread. Or we could discuss these topics in comments. I would definitely prefer answers to this question as a place to collect examples of good questions.

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Note: This is only an example question. An equivalent question already exists on the main site. I have posted the question here (but immediately deleted it) just to see what will be shown in the list of related questions. The post is still visible to users who have privilege to view deleted questions.


Search before asking

It is good to search before asking. It is possible that somebody asked about a similar problem in the past. You can use either built-in search or use your favorite search engine and restrict searching to this site. Various tips on searching can be found, for example, here.

Admittedly, searching for questions on this site might be quite difficult. Searching for mathematical formulas is especially problematic. But the SE software helps you in finding similar questions during the process of writing the question. So we will get back to this.


Descriptive title

It is good to choose the title which describes the topic of your question as well as possible.

  • Bad: How to prove this inequality?
  • Good: How to prove that $x^2+y^2\ge 2xy$?

Search for similar titles

Notice that after you wrote the title for your question, SE software lists questions with similar title above edit box (under the caption "Questions that may already have your answer".)

At this point, you might check whether some of the questions displayed there answers your question. If you found such question, or even several of them, you can read the answers given there. (Of course, if you have problems understanding other answers, it is still ok to ask about explanation. But in such case, you should clearly state what part of the answer you have problems with and you should link to the posts you have already read.)


Add the context to the question

Good question should contain context. In particular, you should include where you encountered the question. And you should also explain what have you tried so far. Do not forget to include all necessary details.

Bad: How can I show that $x^2$+$y^2$ $\ge$ $2xy$?

Note that in the above example, the question does not contain all necessary details. (Are you interested in this inequality for integers? Or for positive real numbers? For any real numbers?) No attempts to solve the problem are shown. And we also do not learn where does the question come from or why your are interested in.

Better: How can I show that $x^2$+$y^2$ $\ge$ $2xy$ for any real numbers $x$, $y$?

I have seen this inequality used in another post on this site, but I do not know how to prove it.

I can see that that this is true if $xy<0$, since both $x^2\ge0$ and $y^2\ge0$.

I tried to change the right hand side to $2xy=xy+xy$. But this did not help too much, since I cannot have both $x^2\ge xy$ and $y^2\ge xy$.


Try to choose correct tags

Before posting the question, you also have to choose tags. (This might be tricky for new users, but eventually you will learn which tags are used.) But also if you do not have much experience with the tag system, the SE system tries to help you. As you start typing in the tag field, you can see all tags containing the string you typed together with their tag-excerpts. Reading the tag-excerpts might help you decide whether the tags are appropriate for your question.

For example, if I have the question described above, I might try to describe what questions contains. There is an inequality. When I start typing this word, I see that the tag indeed exists. I might decide to try to post that the inequality contains squares $x^2$ and $y^2$. So if I type the word square, I see that the tags and exist. However, if I read the displayed tag-excerpts, I see that they are for questions about squares of integers. So they are not suitable for my question.

See also: How am I supposed to use tags?


Look at similar and related questions

Notice that after you filled the body of the question and the tags, the list of similar question on the right is created by SE software. Again you should look among these questions to see whether your question has not been asked before.

And also after you post, list of related questions is shown in the side-bar on the right. You should check those questions, too.

Both similar and related questions are suggested based on tags, title, and various keywords appearing in your post.


Learn from improvements of your question

Other users might edit your question. Maybe they will leave you an explanation of the edit in a comment in the edit summary. But even if they don't, you might learn from their edits. For example:

  • Somebody might add tag to your question. So you learn about existence of this tag and you might read the tag-info to see what questions this tag is suitable for.
  • Somebody might change $x^2$+$y^2$ $\ge$ $2xy$ to $x^2+y^2 \ge 2xy$. You will learn from this edit that you do not have to enter each part of a mathematical formula separately, but you can enter the whole formula as one expression.

Learn from comments to your question

After you post a question, you might receive comment from other users. For example, user called Bob might post a comment like this: "Hint: Try to expand $(x-y)^2$." If you can solve the problem yourself using the hint, then you should try to post this as an answer to your question. (Unless an answer based on the same approach has already been posted.) If you have problems to solve the question using the hint, you can try to ask the user posting the hint what they mean. In such case it is good to ping the user, i.e., start your comment by @username, so that the user is notified. For example: "@Bob I get $(x-y)^2=x^2-2xy+y^2$. But I still do not see how this helps me to prove the inequality. Can you elaborate, please?"

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    $\begingroup$ I don't think it's always necessary to show work. If the question is really canonical it seems acceptable to not show any work. Of course any work worth being mentioned is better mentioned, but I just want to make sure that questions won't be getting down-voted because the OP simply couldn't accomplish anything or didn't find the need to do so because the question on itself seems interesting enough (though that'll always be a little subjective). $\endgroup$ – punctured dusk Jun 29 '15 at 17:56
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    $\begingroup$ @barto: I agree. This show work is an annoying stackoverflow thing which people seem to care too much about. Imagine someone having a similar question two months later. The show work portion of the question is now (usually) complete noise and the reader now has to pore through junk to figure out if the question really matches the one have in mind. $\endgroup$ – Aryabhata Jun 29 '15 at 18:46
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    $\begingroup$ I have linked above to provide context part of the FAQ about asking good question. Providing context indeed includes much more things that only showing your own work, there are other possibilities to provide context. $\endgroup$ – Martin Sleziak Jun 29 '15 at 18:50
  • $\begingroup$ @Aryabhata Well I'm not completely against showing work or asking to show work. It's hard to explain but the link in MartinSleziak's comment (thanks, btw) contains more or less the nuance I was trying to express. $\endgroup$ – punctured dusk Jun 29 '15 at 18:58
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    $\begingroup$ @MartinSleziak: Context is great, don't disagree with that. Showing random work done by someone who had that question at some point in the past, and which might well be nonsense is not useful for future readers. Only in very few cases (observer's bias) have I seen the show work portion on a math question to be actually helpful. $\endgroup$ – Aryabhata Jun 29 '15 at 19:01
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    $\begingroup$ @Aryabhata It's very easy for the OP, or later editors, to separate "work" (context) from the actual question (just put it at the top, for example, or in a block quote). So if anyone is simply not interested in what the OP has attempted, where the question comes from, why the question would be interesting and all that, they can just skip straight to the question. $\endgroup$ – Najib Idrissi Jun 30 '15 at 8:01
  • $\begingroup$ A very solid +1 for the last three paragraphs, which are excellent points not usually mentioned in this context. $\endgroup$ – Lord_Farin Jun 30 '15 at 16:51
  • $\begingroup$ @NajibIdrissi: You are perhaps reading more from my comments that I intended. The movitation/what makes the question interesting etc are good to have. It is the incessant "-1: show us your work" which is what I have issue with (which leads to poster quickly adding some noise to the question). In any case, do you really think people will do a cleanup of the question as you suggest? Too much traffic these days. $\endgroup$ – Aryabhata Jul 1 '15 at 16:35
  • $\begingroup$ @Aryabhata: While I do prefer to have some work shown by OP regarding his question (that somehow seems to make the user genuine rather than just some reputation hungry person), the decision to vote is not so much based on work shown but rather on the question itself. Almost every question on evaluation of tough definite integrals receives a huge number of upvotes and most of the questions don't contain any work shown by OP. See math.stackexchange.com/q/155941/72031 for an example. $\endgroup$ – Paramanand Singh Jul 5 '15 at 11:22
  • $\begingroup$ @ParamanandSingh: As long as the questions are good, why should one care about the motivation? Future folks who have the same question definitely won't care. That is one reason I really dislike seeing good questions downvoted because of the supposed motivation of the poster. 2 weeks later the poster is gone and the motivation is moot. All that remains is a possibly helpful question lying around with downvotes and no answers. Anyway, I would prefer not to discuss this issue anymore. $\endgroup$ – Aryabhata Jul 5 '15 at 16:41
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    $\begingroup$ (Since Aryabhata doesn't want to discuss the issue anymore I won't ping.) Questions and answers should also be interesting to everyone, not just people who have the exact same question. In this case motivation is useful, it explains why the question is interesting. Though I agree that it's not strictly required if the question is already interesting on its own, but in general it doesn't happen. I also agree that incessant comments are annoying, votes to close are both more effective and waste less time. $\endgroup$ – Najib Idrissi Jul 6 '15 at 9:28
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    $\begingroup$ @NajibIdrissi: I don't want to discuss further, but do want to clarify that "motivation" is in response to the "reputation hungry person" comment. It is not about the context of a question. A useful context is one way to make a question good. Anyway... $\endgroup$ – Aryabhata Jul 6 '15 at 15:52

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