Should there be tags and (synonyms)?

The relevant queries, as of this writing, yield respectively 949 and 70 results.

Currently, many of these questions are tagged with the very generic , and some of them with , , or similar tags. (Admittedly, some of these will be off better under just the tag.)

Given the volume of these questions (and the fact that there is no easy other applicable tag other than ) there seems to be enough justification for introducing this synonymous pair of tags.

NB. I am aware of the subtle difference between Darboux (a.k.a upper and lower) sums and Riemann sums (which may take intermediary values as well) but the distinction is not big enough to merit separation -- not to mention the ubiquitous confusion between the two.

Edit in reply to user79365's answer (it was far too long for a comment):

It seems that the origin of our disagreement lies in our perceptions of the "help in searching" (this tag will admittedly not be marked as favorite by many) it will have.

I contend that the words "Riemann sum" are at best likely to occur in the questions I imagine under this tag, and since "Darboux sum", "upper sum" and "lower sum" are all different terms closely tied together, one is likely to miss out on search results when restricting to only one of them (or, for that matter, by combining them all).

Moreover, there are instances of Riemann sums being computed before the word "integral" is introduced, questions about the existence partition refinements with certain properties, and sums that give rise to an obvious "Riemann sum interpretation". A tag to unify them all still makes sense to me, because it ranges over a considerable array of currently existing tags.

This all in addition to the fact that tags have an enormous impact on the "Related" list, and as such make the localization and subsequent identification of duplicates a lot easier (when used properly). At present, there seems to be no good way of locating duplicates to questions that would fit in this tag, and the trouble this has generated for me at certain times has certainly played its part in the creation of this proposal.

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    $\begingroup$ If "Riemann Sum" does not exist, it is a good suggestion to create it. I have noted several questions where such sums have arisen, not always identified by the person who made the post - and not always obviously to do with integrals. I can imagine a person who receives a Riemann Sum answer to such a question might look for other questions in order to get a better understanding of the scope of the method. $\endgroup$ – Mark Bennet Jun 13 '13 at 21:05

Questions about Riemann/Darboux sums fall under "the definition of the integral" in the tag wiki:

All aspects of integration, including the definition of the integral and computing indefinite integrals (antiderivatives).

More importantly, they should be tagged or depending on whether the question is about constructing a proof about Riemann sums or about computation-driven conversion between a sum and integral for a concrete function.

Why I don't support the creation of a :

  • It will not be of much help in filtering. Filtering is naturally done by users' areas of interest, not by particular mathematical objects. E.g., a user can "I am interested in multivariable calculus", but probably not "I am interested in partial derivatives". (Some area happen to be named after objects, e.g., ). Proliferation of tags actually makes filtering more difficult, because there are more of them to sort into favorite and ignored.
  • It will not be of much help in searching. A question about Riemann sums is very likely to have the words "Riemann sum" somewhere in it. The likelihood is higher than that of the OP choosing as a tag.
  • $\begingroup$ The OP was asking about synonym-izing the two sum tags. The already exist. Are you suggesting burnination? $\endgroup$ – apnorton Jun 13 '13 at 2:02
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    $\begingroup$ @anorton The OP was asking about creating and then synonym-izing the two sum tags. They do not exist at present. $\endgroup$ – ˈjuː.zɚ79365 Jun 13 '13 at 2:04
  • $\begingroup$ oh. duh. (That's what I get for guessing I saw the tag before, and not verifying. :P) Sorry. $\endgroup$ – apnorton Jun 13 '13 at 2:10
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    $\begingroup$ Are you the reincarnation of user75064 who once came out of nowhere knowing already everything about meta just to disappear 30ish days after? I see you have already answered 13 questions on meta in 20 days of existence...What a mysterious coincidence... $\endgroup$ – Julien Jun 13 '13 at 4:21
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    $\begingroup$ Two examples of questions where neither the word Riemann or Darboux is used: 1, 2. You wrote: The likelihood is higher than that of the OP choosing (riemann-sum) as a tag. Well, the OP is clearly not the only person, who can add tag to a post. $\endgroup$ – Martin Sleziak Jun 13 '13 at 5:20
  • $\begingroup$ @user79365 I think your assessment of the help in searching is off by quite a bit. I have edited the question to include a detailed reply on your answer. $\endgroup$ – Lord_Farin Jun 13 '13 at 10:47

It seems that the tag has already been created. I've added a very short tag-excerpt and tag-wiki mentioning that it is for both Riemann and Darboux sums. (If you have some ideas how to improve the tag-wiki, please, do so.) I have also created .

Since both tags are new (have less then 5 question), there are no users who have sufficient rep to vote for synonyms. Maybe some of the moderators could be so kind and make the two tags synonymous.

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    $\begingroup$ I've merged darboux-sum into riemann-sum and set up a synonym. $\endgroup$ – Willie Wong Aug 14 '13 at 8:48

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