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See this question: Question on the notation $ds^2=dx^2+dy^2$ : what does it really mean?

The question is really about differential geometry and metric tensor. The asker originally tagged the question as differential-geometry, but later changed it to real-analysis, because he does not seem to know much about differential geometry. I wanted to tag it as differential-geometry and tensors (and remove real-analysis tag), but now I am reluctant, after seeing him change the tag himself.

Should I change the tag in such case?

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    $\begingroup$ It's fine to modify the tags as long as it exposes the question appropriately to those seeking the same question and those seeking to answer such questions. It is important to apply the judiciously to maintain their usefulness. People frequently mistag their posts since they don't understand the subject matter, though. $\endgroup$ – rschwieb Oct 9 '18 at 12:39
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The tags on a question are not only to categorise the content of questions, but also to indicate the level of specificity of the asker's knowledge. A less specific tag tends to indicate less specific knowledge.

Consider, for example, the tags and . These subjects have a very large overlap. Within this overlap, the primary difference is the rigour with which the subject is treated, and the mathematical maturity of the person asking the question. With the tag, we know that the asker is more likely to have seen fundamental tools (such as the three value theorems: intermediate, extreme, and mean), as well as expect more rigour from us in our arguments.

I would remove the tag, personally. Tagging the question with may help others to find the question if they're looking for help with differential geometry, but I think it misleads prospective answerers into giving answers that the asker may not find helpful. My attitude tends to be to help the asker first, and if anyone wants a more specialised answer, they may ask their own question.

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I too was puzzled by the differential geometry tag. for what I perceive as the level of the question, which might be just second semester calculus - not even multivariable.

I'm the author of the relatively elementary answer that (at the moment) has two upvotes; the other two answers have one each. We've yet to here from the OP about whether I guessed his/her level correctly.

I think the purpose of the tags is to alert askers and answerers to questions they might be interested in. So in retrospect I probably should have retagged, or at least added a more elementary tag (calculus?). But since the OP has retagged real analysis I think we should leave it.

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It's a multivariable calculus question. Is Stewart's textbook "Multivariable Calculus" a book on differential geometry?

In a sense, yes. Then again, it would not be normally called that. Same with this question.

Unless, of course, you feel like writing an answer that's entirely over the head of the OP. Then be sure to add tag as well.

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    $\begingroup$ I don't see how the last paragraph helps anybody. If you feel it is subject a, put the relevant tag for a. If it turns out that it is also obviously subject b, it seems reasonable to also tag it as b. You may get answers at different levels, yes, but rather than a priori deciding that this is something bad, the variety may actually be useful in the long term. $\endgroup$ – Andrés E. Caicedo Oct 8 '18 at 20:40
  • $\begingroup$ @AndrésE.Caicedo Maybe the answerer will clarify a bit what they meant, but I'll at least mention that there is a consensus that (within reason) tags could be added also depending on answers that are posted. See: Retagging after an answer is given (and maybe also some of the posts linked there). $\endgroup$ – Martin Sleziak Oct 9 '18 at 6:06
  • $\begingroup$ I would rather write an answer that is correct but takes much effort to understand, than write an answer that makes the asker happy for a while and then confuses him later on. $\endgroup$ – edm Oct 9 '18 at 8:06
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    $\begingroup$ @edm, why not do both? $\endgroup$ – Gerry Myerson Oct 9 '18 at 10:12
  • $\begingroup$ @GerryMerson: I love the idea of an answer that makes the asker happy, is tough to understand, is correct, and later confuses the asker. But I feel that perhaps it's not something to strive for consistently. $\endgroup$ – John Hughes Oct 10 '18 at 18:07
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No. You absolutely should not change the tag. Perhaps adding the tag would be helpful.

The purpose of the tagging system imo is not absolute correctness and a cataloguing of answers (this is not wikipedia.) The purpose of tags is so that answerers, readers, and askers can quickly and efficiently find relevant or interesting questions similar to those that they are thinking about.

In particular, this question might fit more naturally under the umbrella of differential geometry, but the OP's question is not really going deep into this, and neither are the answers, they don't use a complicated language to answer the question.

What would be helpful is adding a comment/answer mentioning that this is a special case of a metric tensor, and understanding this concept would help. Perhaps link a related question in the differential geometry tag. Now, you've directed other users that have not taken DG to a subject and place where the question more naturally sits.

For comparison, I think this is like retagging

  1. "how can I factor complicated polynomials?" with field theory or galois theory.

I just don't see who that may help except for those that already know the latter subjects.

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    $\begingroup$ I don't know... Sometimes a naive question one thinks is about $A$ turns out to require $B$ in essential ways. It is natural to add $B$ as a tag, even if the person originally asking the question was not aware of the connection at all. In fact, it would be a bit of a disservice to not make the connection explicit via tags for future reference. $\endgroup$ – Andrés E. Caicedo Oct 9 '18 at 16:13
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    $\begingroup$ That might be nice, but I see no reason to replace a tag $\endgroup$ – Andres Mejia Oct 9 '18 at 16:14
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    $\begingroup$ Oh, not in the case at hand. (There are cases where replacing tags is appropriate, though, but I do not think the question that prompted this post is an example.) $\endgroup$ – Andrés E. Caicedo Oct 9 '18 at 16:15
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    $\begingroup$ @AndrésE.Caicedo sorry for the late response. I've edited the first sentence to emphasize that adding the tag might be a good idea. I agree $\endgroup$ – Andres Mejia Oct 12 '18 at 1:07

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