# Difference between [definition] and [terminology]

What is the difference between the tags and ?

At the moment, there are 678 questions with the tag, and 278 questions with the tag, and only 31 questions with both, so there seems to be perceived difference.

I'd like to point out that there was a different question (I think the most recent incarnation of this question, http://meta.math.stackexchange.com/questions/825/how-should-we-handle-tags-terminology-notation-definition, that was raised on meta two years ago. But as I read through, I thought there was a focus on keeping separated from the others (which I agree with - notation is different).

The wiki for says:

Questions on the usage and meaning of words in mathematics, the names for mathematical entities, and other such questions.

Interestingly, the tags and are tag-synonyms for . I see a big difference between etymology and definitions.

The wiki for is longer, and says:

Definitions are the core of mathematical precision; they come to answer "what is X" in mathematics. Into this category fit questions regarding equivalence of definitions; clarifications regarding complicated definitions; as well questions with purposed definitions for mathematical notions with requests for improvements or comments.

Perhaps these are clearly different to someone, but when I see something about "the meaning of words in mathematics... and other such questions" compared to looking at "what is 'X' in mathematics", they look about the same to me.

• I am not sure what way to go. (Whether they should be separated or synonyms.) But one type of questions that, in my opinion, fit terminology but does not fit definition could be something like this: "I am interested in partially ordered set such that for every countable set there is an upper bound. Is there a name of such posets?" – Martin Sleziak Aug 18 '12 at 5:59
• I have a deja vu (not the file format, although I also have these), didn't you ask this somewhere before? I remember answering you as well. – Asaf Karagila Aug 18 '12 at 7:56
• I do see a difference between the two: For example: Why are rings called rings? or where does the term “integral domain” come from? are questions about (origins of) terminology where the definitions themselves are entirely clear. On the other hand the recent On the definition of the Hausdorff distance is a question about details of a specific definition and doesn't take issue with the terminology at all. – t.b. Aug 18 '12 at 10:08
• @Asaf Did you mean this answer? – Martin Sleziak Aug 18 '12 at 10:28
• @Martin: Ah, yes. I didn't write an answer per se, as it seems (although I still retain a memory of writing an answer to this question before...). – Asaf Karagila Aug 18 '12 at 10:31
• I don't see how this is a different question from «How should we handle tags: [terminology] [notation] [definition]?». In particular, my answer there applies to this question verbatim, no? – Grigory M Aug 28 '12 at 12:35
• I see the two tags as duals. Terminology is, "what do you call a relation that is reflexive, symmetric, and transitive?" Definitions is, "what's an equivalence relation?" – Gerry Myerson Jun 22 '17 at 5:45

At least to me, the two texts describe a different meaning. My understanding is as follows:

• is for asking questions about the terms themselves, how they are defined, or conversely if there is an established term corresponding to a concept.

• on the other hand is for asking about definitions in general, their relations to each other, what a definition is to begin with, and stuff like that.

To make an analogy with visual perception: is about the things you see. is about the process of seeing.

I'll give what I believe is an example demonstrating the difference between definition and terminology.

Definition. Let $X$ be a nonvoid set and let $\mathfrak{F}(X)$ denote the set of filters on $X$. A preconvergence structure on $X$ is a nonvoid subset $p$ on $\mathfrak{F}(X) \times X$.

Terminology. Let $p$ be a preconvergence structure on $X$. We will write $(\cal{F},x)\in p$ as $\cal{F}\to x$ and read it as "$\cal{F}$ converges to $x$" or "$\cal{F}$ $p$-converges to $x$" or "$\cal{F}$ converges to $x$ in $p$" or "$\cal{F}$ converges to $x$ in $X$", etc.