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I believe that question/answer of this form:

Q: Is there an online repository of basic identities/results about topic X?
A: Many of such identities can be found with the proofs at math.SE, I'll give here a list with links

is a valid question and a valid answer for this site.

We already had some questions of this type, e.g. this one: A comprehensive list of binomial identities?

I've tried to make such a post for basics of cardinal arithmetics here, but I can imagine such post being useful for other topics, too: combinatorial identities or perhaps identities involving binomial coefficients (we have plenty of more-or-less duplicate questions asking about a proof of Chu-Vandermonde identity here), trigonometric identities, basic limits, sums of series, basic facts about image and preimage, basic facts about injective/surjective/bijective functions, etc. (Probably many of mathematical topics that have "list article" at Wikipedia would qualify.)

Nevertheless, I've cheated a little, because I've tried to use this questions and answer to "organize" posts at this site a little - in this way we (hopefully) get list of questions/answers relevant to given topic. (So my main intention was not to ask a question and get an answer, but to make an "organizer" post - I was not able to think of better name for this type of post.)

I think that post like this might be useful mainly for the reasons that:

  • It helps when searching for duplicates. (It's probable that such a basic question has already been answered here, but it's not always easy to find it.)

  • It helps askers to avoid adding duplicate question.

A few more minor notes.

  • Obviously this would make a post more suitable for wiki-format then Q&A-format but Stack Overflow has elements of wiki in its hybrid design, says this blog post.

hybrid design of stackowerflow

  • I do not suggest that we should start right now massively doing this, but I think this is worth considering for topics, where duplicates of some basic questions appear very frequently. (Once an "organizer" post exists, it is not too much work to add links to it, whenever a new duplicate question, which is not covered in the post, appears.)

  • I am not doing this hunting for points (although in my post about cardinal arithmetic, I link to some questions I've answered). I hope you'll take my word for this.

  • Two questions, which lead me to thinking about posting something like this were How do you search for duplicates? and a very recent Compiling an introductory resource for (say) Abstract Algebra, from MSE answers. - which has a somewhat similar flavor to this question of mine.

I'd be glad to hear the opinion of other users, whether such format is good for this site and whether they think such posts might be useful.

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    $\begingroup$ Regarding the "hunting for points", I can easily see your desire to help the community as a primary motivator. If you believe your answer(s) on a particular topic(s) to be a good fit for a particular "Overview", then by all means include it! $\endgroup$
    – The Chaz 2.0
    Commented Apr 13, 2012 at 16:45
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    $\begingroup$ And really... if one of your answers is chosen for an Overview, then it will necessarily be a high-quality answer. As such, it should receive much attention and many votes. I don't think anyone is opposed to that! $\endgroup$
    – The Chaz 2.0
    Commented Apr 13, 2012 at 16:49
  • $\begingroup$ I believe this is (almost) a necessity. However, this opens the door for the obvious question: Can users still post questions about topics covered in this huge database? i.e. Will it become inappropriate to ask a question with hopes of it being personally explained? I would hate to see this site go that way--I believe the personal and informal explanation is conducive to learning and very, very productive for the community. $\endgroup$
    – 000
    Commented Apr 15, 2012 at 5:55
  • $\begingroup$ Furthermore (I make this a separate comment due to its complete different focus), if this were to be a list, I would hope it would either A) be hosted offsite and have no particular "author" or name attached to it or B) be hosted in the site and as a direct-url somewhere on the website's interface. I assume B requires consulting Stackexchange's programmers, but it would certainly be worth it. I would suggest the URL be located in a very prominent area (e.g. as a banner, perhaps?). $\endgroup$
    – 000
    Commented Apr 15, 2012 at 5:58
  • $\begingroup$ Martin, do you have plans for another "Overview" Q&A? I'd love to help (and might even be able to contribute some of the content if the level is low enough!). $\endgroup$
    – The Chaz 2.0
    Commented Apr 22, 2012 at 1:33
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    $\begingroup$ @Limitless I don't think that there is any problem with "organizer posts" being posted among ordinary questions/answers. The purpose of this is similar to List of Generalizations of Common Questions with the exception that these post are specialized to one topic. That question is not hosted off-site. $\endgroup$
    – Martin Sleziak
    Commented Apr 30, 2012 at 10:09
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    $\begingroup$ To your another concern - I do not think that there will be problem with asking new questions, or even about details about the questions from this list; but this could help to find out whether the question was asked before and avoid the same work being done by the users again and again. $\endgroup$
    – Martin Sleziak
    Commented Apr 30, 2012 at 10:10
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    $\begingroup$ @TheChaz The elementary-set-theory tag is among my favorite tags and I've been following questions there relatively closely, so I've seen which questions reappear there quite frequently. Maybe I'll post one more overview question from elementary set theory; but I do not think there's another area of mathematics where I'd be able to do a similar thing. (Simply for the reason that this requires to follow which question from this area appear at MSE at least for some time.) $\endgroup$
    – Martin Sleziak
    Commented Apr 30, 2012 at 10:18

2 Answers 2

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  1. There is nothing wrong with this, and I strongly support your efforts so far.

  2. I will contribute in any way possible.

  3. Users who don't like seeing such questions on the main page can downvote or vote to close (maybe as Not a Real Question??), but I will upvote and vote to reopen!

To elaborate...

  1. Having such a resource (i.e. collection of such Q&A's) will benefit the community, as it will engage students in the learning process, and teachers in the teaching (or at least organizational/pedagogical) process. A tag such as "overview" should be created.

  2. While my math level is relatively low, I would like to help with finding the "answers" in certain topics, and creating answers/transitions between answers when possible.

  3. People have differing opinions about what they want to see and what they want to do when on MSE, but I can't imagine such a useful resource being poopoo-ed. Let's go for it! If you are serious about proceeding, I'd love to create a chat room dedicated to this, so contributors can organize their thoughts.

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I consider 7 upvotes for my question and 3 upvotes for the answer by The Chaz being sufficient to consider this a consensus. Although I do not expect this list to become populated too quickly, I think it's good to keep track of the question of this type that have already been posted.

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