Right now, the tag is a synonym of . I do not think this should be so. Rather, I propose to make a synonym of . I further propose to remove all references to in the definition of . In my perfect world, unless the fundamental theorem of calculus is being used, pure antiderivative calculations should not be using the tag.

The reason I feel strongly enough to post this is that I am teaching my son calculus and he is being confused by the concept of an integral as the limit of a sum. We of course may define different limits over different summands to define different types of integrals (e.g., Riemann, Lebesgue,...), but we never do any such limits on sums when taking antiderivatives. Thus, I am no longer using the nomenclature "indefinite integral" because I feel it is misleading.

Are there users who would agree with my proposals?


@MartinSleziak points out, quite rightly, that there are 1360 questions with both and tags. There may be several questions that should have both tags (e.g., questions about evaluating integrals using the fundamental theorem of calculus), so it may be very difficult to do this editing.

I also realize that, logically, this may mean the merging of the and tags. Not sure how people feel about this, but I am OK with it if we need to make the system logically consistent.

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    $\begingroup$ If it helps, you can imagine Abraham Simpson saying all of this, with a few choice "in my day" and "you young people" phrases thrown in. $\endgroup$ – Ron Gordon Jan 31 '16 at 16:57
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    $\begingroup$ I suggest we make them duplicates of primitives, which is the proper name for the concept. $\endgroup$ – Daniel Fischer Jan 31 '16 at 17:09
  • $\begingroup$ @DanielFischer: Fine with me. I do think that "antiderivative" is the clearer nomenclature, but you are indeed correct. $\endgroup$ – Ron Gordon Jan 31 '16 at 17:10
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    $\begingroup$ It's a terrible non-word. I could accept antederivative, but antiderivative is just all wrong. $\endgroup$ – Daniel Fischer Jan 31 '16 at 17:11
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    $\begingroup$ @DanielFischer: <stares at comment with head tilted>. "anti-" = "opposite of, against. "ante-" = "before". Note sure why "anti-" is terrible. $\endgroup$ – Ron Gordon Jan 31 '16 at 17:14
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    $\begingroup$ One point: mixing Greek and Latin is shatnez. And a primitive of $f$ is a function that we have before differentiating, resulting in $f$ after differentiating. And a primitive is not the opposite or enemy of a derivative. But mostly, it's shatnez. $\endgroup$ – Daniel Fischer Jan 31 '16 at 17:19
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    $\begingroup$ "mixing Greek and Latin is shatnez." I will take that lesson to my grave. Still, I think "ante"- in this context is a bit convoluted. Not an enemy, just the opposite, er..., direction. $\endgroup$ – Ron Gordon Jan 31 '16 at 17:21
  • $\begingroup$ I second Daniel's proposal of making them duplicates of primitive. $\endgroup$ – achille hui Jan 31 '16 at 23:40
  • $\begingroup$ If some consensus about this is achieved and it is in favor in this proposal, how much post do you estimate will be in need of retagging? Something like 1k or 2k? There are currently 1360 questions tagged integration+indefinite-integrals. $\endgroup$ – Martin Sleziak Jan 31 '16 at 23:52
  • $\begingroup$ @MartinSleziak: I realize that that proposal may cause some waves. This has happened before with the redefinition of the integration tag a few years back and yet the earth maintained its rotation, etc. Let's get some agreement and consensus with eyes wide open. I'll edit my post to include your observation and see how people feel. However, it doesn't change the fact that taking a primitive is not the same thing as evaluating an integral and our tagging system should reflect that. $\endgroup$ – Ron Gordon Jan 31 '16 at 23:57
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    $\begingroup$ By "redefinition of the integration tag" you mean when the tags (integral) and (integration) were made synonyms? I think that it is a bit different from the viewpoint how much work was needed. Since in that case, no manual retagging was necessary. A synonym was approved and that was all. $\endgroup$ – Martin Sleziak Feb 1 '16 at 0:06
  • $\begingroup$ I don't know if my opinion matters, but I don't particularly like the idea of narrowing the definition of the integration tag. I think most users would find that highly confusing. And "primitive" might be the more proper name, but I personally prefer "antiderivative." $\endgroup$ – Random Variable Feb 2 '16 at 0:33
  • $\begingroup$ @RandomVariable: Your opinion matters, at least to me. $\endgroup$ – Ron Gordon Feb 2 '16 at 1:17
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    $\begingroup$ I agree with you. In my classes I use the terms antiderivative and integral. $\endgroup$ – JP McCarthy Feb 10 '16 at 15:57

I do not agree with this part of the proposal:

I further propose to remove all references to in the definition of . In my perfect world, unless the fundamental theorem of calculus is being used, pure antiderivative calculations should not be using the tag.

My main objections are:

  • I consider current system fine. The questions about calculation of s are differentiated by and , which I consider subtags of main tag integral.1
  • I expect this change to cause confusion for new users. From the past experience it seems that new users typically apply tag to the questions of this kind.2
  • Perhaps the proposal could work for computation question. But do not forget that there are also theoretical questions in the tag . 3
  • This would require great amount of work going in individual evaluation and manual retagging of many questions.4

1Certainly, not all questions asking about calculation of definite or indefinite integral are currently tagged as such. But I think that there are many users who make effort to help with correct tagging of questions. I would certainly prefer the workload be directed towards improving tagging of incorrectly tagged questions rather than to retags connected to substantial changes of the tagging systems.

2In fact, this would also probably cause some confusion also among experienced users, which are used to the current system. If the consensus to change the current usage is reached, it would take some time until the users who do not visit meta too often learn about this. Definitely, if we go through with this, it would be good idea to create a comment template for this issue.

3This is probably the main objection against merging and . But I suppose that the proposal does not actually suggests that these two tags should be merged or synonymized. The comment about merging added in the edit of the original posts - "this may mean the merging of the integration and definite-integral tags" - should probably be interpreted as saying that these two tags might have big overlap.

In the past there was some discussion that we should try to keep computational and theoretical questions separate. There was a proposal to change the names of the tags in such way, that some of them would clearly indicate that they are for questions about computation/evaluation of integrals rather than about properties of integrals and results about them. However, this suggestion was later abandoned and the tags and were synonymized.

4A very conservative estimate is about 1k questions, since probably large part of the questions tagged integration+indefinite-integrals would have to be retagged. But seeing that the tag has 24k questions and calculation of indefinite integrals is quite frequent category, I think that there might be even more. (However, if we keep the current system, questions in of this type should also have . So they are incorrectly tagged both under the current scheme and under the proposed new scheme, so they do not really count.)

Of course, this would need a lot of effort and time, since we cannot retag too many questions at once.

If we compare this with the removal of (algebra) tag, which is probably the largest retagging effort on this site so far, it took quite concentrated effort of several users to get from 700 questions in October 2011 to 0 in February 2012. And the effort to remove this started probably earlier. This was discussed already in June 2011, when there was about 600 questions in that tag.

The removal of (algebra) is also cautionary tale from another viewpoint. We still have now and then some comments on main and meta (and occasionally even posts on meta) objecting to removal of this tag and replacing it with and . So we should perhaps not be too hasty about drastic changes in tagging system - it is good to leave some time for people who disagree with the proposed changes to put forward their arguments.

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    $\begingroup$ Thanks Martin, I really appreciate your detailed comments. It gives me a lot to think about. $\endgroup$ – Ron Gordon Feb 1 '16 at 1:49
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    $\begingroup$ @Martin Retagging 1,000 questions doesn't have to be a problem. On chem.SE, we retagged 200 questions with 7 users within 1.5 hours. But since we have a lot more users on this site, we might get it done in two sessions of 1.5 hours. After that, we of course need to pay attention to the questions asked in that 1.5 hours, which will be a bit more than in Chem.SE. $\endgroup$ – wythagoras Feb 3 '16 at 8:43

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