There are 1,732 questions tagged both elementary-number-theory and number-theory

As you can see here, there are currently 1,732 questions tagged and . (For the record, there are respectively 9,252 and 10,636 question in these tags, so that's not insignificant)

It's always been my impression that these sort of tags are mutually exclusive: set-theory vs elementary-set-theory, abstract-algebra vs algebra-precalculus, probability vs probability-theory... In any case it makes zero sense for a question to have both tags, it's just redundant; they can always be tagged just elementary-number-theory.

I believe the differentiation between abstract-algebra and algebra-precalculus works because they are names of actual classes in standard curriculums in the US, and there are very active users (user?) dealing with set theory questions. However, things didn't work out so well for probability theory, as we can see in the question I linked at the top, and number theory is going the same way.

Rather than dealing with specific cases, I'd like to ask general questions:

• Is differentiating tags by level useful?
• Is differentiating tags by level feasible? How?
• How to decide when a tag needs to be split like this? How to decide what the threshold should?
• Yeah, we dealt with this mess (although on a much smaller scale) with a large intersection of set theory and elementary set theory. – Asaf Karagila Jan 1 '15 at 12:44
• In the case of set theory the tag info does the good job. If you look at the tag-info for elementary-set-theory and set-theory you will see that a list of topics which are covered by the tag. Of course, the lists are not exhaustive, but they cover a lot of questions and help to decide which tag to use. – Martin Sleziak Jan 1 '15 at 13:55
• I have noticed this, too. I occasionally hunt these down, and edit the tags. My conservative estimate (no actual data I'm afraid) is that in 90% of the cases I either removed the NT tag, or replaced it with ENT. The rule of thumb is that if I can answer the question without rubbing the three grey cells together real hard it is ENT. Not foolproof, and the algorithm is still evolving – Jyrki Lahtonen Jan 1 '15 at 14:16
• @Martin I doubt it's the tag wiki. Look at the case of probability: it's explained right in the tag excerpt what tag covers what, people still confuse the two. – Najib Idrissi Jan 1 '15 at 14:16
• New users frequently tag their question NT, because they learned about the material in a course titled (Intro to) NT. If we could make them actually read the tag excerpts, the problem would disappear. Not holding my breath. – Jyrki Lahtonen Jan 1 '15 at 14:18
• Two unrelated points: .) If elementary-number-theory is intended only as "low level number theory" than elementary-number-theory is not a good name. .) I do not see the issue with redundancy in itself. Is is also a problem if something is tagged analytic-number-theory and number-theory? This is inherent to the tagging system. – quid Jan 1 '15 at 14:19
• @quid Regarding redundancy, I guess I could have said that better: number-theory is explicitly for higher level than elementary-number-theory. I assume users ask elementary questions then add both tags because they both seem to apply, but they don't. You're right that redundancy is not the right word, what I mean is that if elementary-number-theory can apply (and OP thought so by tagging the question that way), number-theory cannot apply. It's different from, say, tagging a question homotopy-theory and algebraic-topology. – Najib Idrissi Jan 1 '15 at 14:25
• @NajibIdrissi What I meant is that in the case of the two set theory tags, the tag-info does a good job in explaining what belongs to which tag. (The other question is whether the users actually apply the tags correctly.) In the case of number theory, the tag-wikis for elementary-number-theory and number-theory are more-or-less identical. So they do not help much when deciding which tag to choose. – Martin Sleziak Jan 1 '15 at 14:26
• I will just mention that also elementary-general-topology tag was discussed. This older post is also to some extent related to the general questions asked at the end of your post. – Martin Sleziak Jan 1 '15 at 15:31
• As @Martin mentions, such issues have been raised before. Tagging questions with "sophistication" leads to various problems, e.g. in the thread Martin cites see this answer and its comments. As in the example linked there, questions often receive answers of various levels of sophistication - which is pedagogically desirable since it often motivates students and plants in mind seeds of important generalizations that they will later need. It would help to have the ability to tag the level of the answer. – Bill Dubuque Jan 1 '15 at 16:24
• @Bill And yet the issues are still there, a significant number of number theory questions are mistagged, and it's even worse for probability. Rather than dealing with the issues on a case by case basis, it would be nice to have a discussion on how to prevent them from happening again: giving proper names to split tags, having a clear policy on what belongs to where... – Najib Idrissi Jan 1 '15 at 16:56
• [cont] I dislike the idea of meta "sophistication" tags (or meta tags at all) And I don't believe I'm talking about sophistication in this thread: this seems to apply to answers, not questions. Even if it's possible to answer an elementary question with a great amount of sophistication using very advanced notions, it still remains an elementary question. – Najib Idrissi Jan 1 '15 at 16:58
• @Martin (Part of my previous comments addresses one link you cited) As for the tag wikis, I think my point is that I don't believe people read tag wikis at all, and hardly read tag excerpts (example: probability tags have descriptive tag wikis/excerpts, but the situation is even worse than for number theory). I don't think it's the deciding factor (tag names seem more important than anything), and I think the concerted effort mentioned by Asaf earlier has been more decisive in the relative cleanliness of set theory related tags. Of course cleaning up the tag wikis would be important too. – Najib Idrissi Jan 1 '15 at 17:01
• @MartinSleziak Yes of course, you're right, that's not what I'm saying. Fixing the tag wiki is important. But I believe that it would be great if the need for retagging questions was alleviated by having users tagging them correctly in the first place, and it seems to me that the tag name is more important in that respect than the tag wiki. – Najib Idrissi Jan 1 '15 at 19:19
• @Najib I was under the impression that "elementary number theory" is number theory other than "algebraic number theory" or "analytic number theory." So no imaginary numbers, no algebraic integers, no asymptotics or heuristics. – Robert Soupe Jan 4 '15 at 19:20