# How to properly ask a definition question?

Quite often, I find myself having to ask a definition question. I define a definition question as a question which main object’s name and/or definition is not known by the asker (common case) or by the community (much rarer).

These questions are challenging because, by definition, asking them properly with well-defined names is difficult (in the common case) or demonstrably impossible (in the rarer case).

This is a perfect self-fulfilling prophecy of failure: these questions tend to be misinterpreted or to be judged imprecise, therefore get downvoted and eventually put on indefinite hold.

This is unfortunate, because many such questions could lead to useful clarifications (common case) or occasional discoveries (rarer case).

Adding the definition tag could be an elegant way of addressing the problem.

Best examples from various sites:

• A popular question related to something probably deserving a better name.
• A closed question related to something that is possibly interesting.
• A solid question related to something that is imprecisely defined by the community.
• A solid question related to something that is not defined yet by the community.

More examples from Mathematics only:

• A solid question to something that has yet to be named by the community.
• A solid question to something that has yet to be named by the community.
• A solid question without any reaction so far.
• A trivial question that was properly answered in a comment.
• A poor question with a clear answer.
• Almost all your examples are taken from the stats website. Did you mean to post your question to a stats meta? or are you aware of more examples here on math? – Gerry Myerson Jan 10 '19 at 15:44
• @GerryMyerson I find myself struggling with the issue on multiple SE sites, including this one, MO, and CV. I added examples from CV because this is the site where I had the most relevant examples, but the patterns are the same. I had similar cases on Mathematics recently and I will add them to the original question, but I have deleted some of the questions in order to reduce the noise level and preserve my shaky reputation. Taking the role of friendly contrarian on SE is not easy, as attested by the unexplained downvote. – ismael Jan 10 '19 at 16:26
• @GerryMyerson I have added 5 mores examples from my own questions on Mathematics. – ismael Jan 10 '19 at 16:36
• Just to start: Any question asking about the definition of a mathematical term on this site needs to include the definition one has encountered in a text, or has researched for on the internet, even if merely including Wikipedia's definition of the term. If the searched for definition is confusing, such a question needs to include an explanation regarding "what about the definition do you not understand?" Alternatively, some questions about definitions are asked after the asker has encountered two different definitions that they cannot reconcile. In such a case, both definitions ... – amWhy Jan 10 '19 at 18:48
• ... ought to be included (in entirety) in the question, citing the source of each, respectively. What are not welcomed are questions which show absolutely no research effort on the part of the asker, nor any sources cited as to where the definition(s), if included in the post, were found. – amWhy Jan 10 '19 at 18:50
• @amWhy Obviously. I hope that my questions did not fall into the last category. If some of them did, please point them to me and I will clarify them. – ismael Jan 10 '19 at 18:52
• I've looked at, and answered, two of the math questions you post. This site is no shortchanging you; rather, in one case you fail to recognized that your proposed "subtraction operator" can be better described in terms of the addition operator and all the familiar properties of addition, multiplication, associativity of addition, commutativity of addition, and the distributivity of multiplication over addition. – amWhy Jan 10 '19 at 19:51
• In the second question I answered, there is no such an entiity as "an abelian group without the closure property of the group under its binary operator." So it is not a meaningful question. – amWhy Jan 10 '19 at 19:51
• @amWhy I accepted your answer for the second question, and I updated its introduction in my original meta question. You are absolutely right, the question was ultimately meaningless, but getting it answered like you did still helped me develop a better understanding for the question’s object. There is no denying that it was valuable to me, and I like to believe that it could be valuable to others as well. – ismael Jan 10 '19 at 20:12
• My only other suggestion is that you remove posts about your questions on Cross Validated from Mathematics Meta (specifically from this question), as they are off topic on this math site. You are free to post them to the other site's meta Cross Validated Meta. (I say that your concern about your questions to Cross Validated is off topic on Mathematics Meta because questions posted to Mathematics Meta are on-topic, provided they concern the Mathematics site only. We don't have the authority here to represent the entire SE network, and its site, in general. – amWhy Jan 10 '19 at 21:22
• I get the feeling that you are expecting too much. Not all conceivable ideas have a name. It's not like there exists a Grand Tome of All Mathematical Definitions that we can look up things from. Many definitions have become standard because they come up so frequently, and the chance of misunderstanding is high if they are misapplied. But, by and large, definitions are local. Think: the various meanings of normal. The pragmatic concerns are overriding. If a concept occurs frequently in your context, make up a word describing it. – Jyrki Lahtonen Jan 11 '19 at 8:09
• (cont'd) It then behooves you to communicate that to your readers (or whoever you communicate your thoughts with). If others find your concept (and the word you picked to call it) useful, they may begin to use it as well. That's all there is to it. – Jyrki Lahtonen Jan 11 '19 at 8:11
• Of course, there's no harm in asking others if they have seen a name for some operation/identity/concept/whatnot, but you should be prepared for the possibility that no answers come, simply because no one has seen the need to make a definition. Also, even seasoned mathematicians don't agree on all the definitions. Ring being a notorious example (some heretics think it does not need a multiplicative neutral element), natural number is another (it is anybody's guess whether a given author includes zero or not). In longer texts we include our definitions and stick to them. That's all. – Jyrki Lahtonen Jan 11 '19 at 8:15
• @JyrkiLahtonen Thank you so much for all these comments. They make a ton of sense and are really helpful. – ismael Jan 11 '19 at 15:28

Well, to start, we actually already do have a tag; however, in the case where you don't know the name of what you're looking for, it's probably better to use or . Let's compare and contrast.

A canonical question for would be something like

I'm reading the paper A Treatise In Frustration (A. Gruber, Journal of Fake Group Theory, January 2019), and I'm having trouble understanding the following definition.

Def. A group $$G$$ is said to be annoying if $$[G,G]\ne\{[a,b]:a,b\in G\}.$$

I've looked everything up, and I understand that $$[G,G]$$ is defined as the subgroup generated by $$\{[a,b]:a,b\in G\}$$, not just the set $$\{[a,b]:a,b\in G\}$$. But in every example I can think of, these are equal, how is it possible that they couldn't be? What is an example of an annoying group? What does it mean?

A canonical question for would be something like

Hi Math StackExchange. I'm a programmer whose job is to abelianize groups for the reputation-backed securities market, and boy do I have an irritating problem. Sometimes I run into these groups where I calculate $$\{[a,b]:a,b\in G\}$$ and it turns out not to be a subgroup, so my program crashes! Some examples include $$\operatorname{SL}_2(\mathbb{R})$$, the free group on $$2$$ letters, and a couple of finite groups with order 96. Is there some kind of established term for these groups so that I can avoid them in the future?

A canonical question for would be something like

I met a math major at the bar the other day and after texting her 36 times in a row, she sent me this:

$$\emptyset \ne [G,G]\setminus\{[a,b]:a,b\in G\}$$

I can't begin to unpack this because I don't even know what those brackets mean. I'm in way over my head here, you guys. What do $$[a,b]$$ and $$[G,G]$$ mean?

It's also a good idea to pair these tags with in the case that you're looking for an official source, if you're wondering who came up with something first, or if you're wondering why the definition matters or its relevance in the grander scheme of things. Along with tagging the relevant field(s) of mathematics, this should be draw enough attention to your question to get you what you're looking for.

• Good examples, +1. I do wonder whether the definition tag should exist at all, though: does it actually contribute anything useful to categorizing your example? It seems like it's just a question about group theory (and more specifically, about annoying groups), not really a question about definitions or even a particular definition. – Eric Wofsey Jan 12 '19 at 0:00
• Good answer, and also entertaining! – hardmath Jan 12 '19 at 0:08
• Awww,shucks. Now you've piqued my interest; please provide answers! – amWhy Jan 13 '19 at 14:29