# How general should an answer be?

Questions are usually about concrete problems. They frequently have easy concrete answers that sometimes only work for that instance. (Some would call them tricks.) But they frequently also have more or less easy general answers that work for that instance and much more. Sometimes it is clear what level of answer the OP will appreciate. Should we give both kind of answers, even when the general answers are unlikely to be appreciated or even understood by the OP? Some other people reading the thread later may appreciate the general answers.

I don't really have a hard rule for this and I'd like to hear what other people think about this issue, which I believe relates directly to the quality of this site (and other sites of this type).

• Perhaps it would help to give some specific examples, to help focus the discussion. – Gone Apr 4 '12 at 19:00
• @BillDubuque: math.stackexchange.com/questions/128044/… (don't take it personally) – lhf Apr 4 '12 at 19:02
• @BillDubuque. I love your answers. I learn a lot. – lhf Apr 4 '12 at 19:03
• Thanks. I suspected you might refer to that question. Please do elaborate on this specific example, and I'll be happy to explain my viewpoint. – Gone Apr 4 '12 at 19:12
• @BillDubuque, in that specific question, the OP seemed a bit lost on what to do. A more general answer like yours might not be what he needed. Or it just might, one never knows. Hence my question here. – lhf Apr 4 '12 at 19:25
• As long as there is at least one good answer that uses only material at the presumed level of the OP, additional answers at a higher level are enriching. – André Nicolas Apr 4 '12 at 19:29
• Is this question a duplicate, or am I confusing that with a discussion from chat? – The Chaz 2.0 Apr 4 '12 at 19:30
• @BillDubuque, OTOH, in that specific question, your more general answer is at just the right level of generality for those who can appreciated it. Of course, ideally, the OP, having seen or worked through the concrete answer, would then ask himself just what was special about 2 and 5, if anything. – lhf Apr 4 '12 at 19:31
• Related to meta.math.stackexchange.com/questions/652/…. – lhf Apr 4 '12 at 19:34
• Alas, the OP didn't supply any context or partial work, so it may not be the best example for discussion. The reason I added the general answer is that, in my experience, many students have great difficulty going from a specific answer like yours to the general case, esp. phrasing it in a way that works for the inductive step in the case of $n$ square-roots. There are prior questions here and elsewhere which make it clear that the OP has no clue how to tackle the induction. Phrasing the Lemma in structural form makes it easier to gain the key insight to handle that and related generalizations – Gone Apr 4 '12 at 19:40
• @lhf Thanks for reminding me of that old thread. I just bumped it to help encourage more feedback now that the meta community is much larger. – Gone Apr 4 '12 at 19:48
• There is a case (maybe a joke) where some student asks a question on elementary differential calculus, but then someone posts an answer in terms of jet bundles. – GEdgar Apr 5 '12 at 12:22
• "A method is a trick that has been used at least two or three times." – Phira Apr 7 '12 at 20:22
• See also this question. – Gone Jun 3 '12 at 20:58

As general as you want it to be. The system benefits from having answers at multiple levels of generality.

• It may be good for the system, yes, but does the OP benefit? Or is this site just not (entirely) about the OP? I'm fine with both kind of answers, and those in between as well, but I worry about the OP not getting an answer he can use or being shied away by complicated answers. – lhf Apr 4 '12 at 21:45
• @lhf: answers are not only for the benefit of the OP, they are also for the benefit of anyone else who finds the question somehow (e.g. Google) and is curious about the answer. Having a wide spread of answers is conducive to helping a greater percentage of these people. – Qiaochu Yuan Apr 4 '12 at 21:47
• @lhf: Questions and answers are not just for the OP but for the readers. Be prepared, though, for the possibility that people will tell you that your answers are "self indulgent" and completely "over the head of the OP". – Asaf Karagila Apr 4 '12 at 21:47
• Sure, I said as much in my question. – lhf Apr 4 '12 at 21:48
• @AsafKaragila, they sometimes are way over the head of the OP and not only him. :-) – lhf Apr 4 '12 at 21:49
• @Lhf: If you see that no other answers answer OPs question at the level OP seeks, you can always do that, and then add to the same answer, a general method is so and so etc. – Aryabhata Apr 4 '12 at 21:51