# Should there be distinction between the tags (inequation) and (inequality)?

You might have noticed that the tag has been created recently. (See also a few comments and related links posted after the creation of the new tag in chat: https://chat.stackexchange.com/rooms/3740/conversation/the-inequation-tag.) The tag was created by the same user who posted the question Why isn't the term inequation widely used in English? on the Mathematics Educators site - so the discussion there might be a bit related to this.

Question. Do we need a new when the tag already exists and is widely used?

• The tag creator pointed out that there are two separate Wikipedia articles inequation (current revision) and inequality (current revision). (Merging the two Wikipedia articles was discussed in the past, but it seems that for the purposes of Wikipedia the consensus was to keep the two articles separate.)
• The tag creator also suggested some basic tag-info for the newly created tag. (Although if there are supposed to be two tags, it should be made very clear in the tag-info what exactly is the distinction.1
• On the other hand, the tag is one of the biggest tags on the site with almost 20k questions. So if some of the questions should be tagged with a new tag, it's quite likely to be a rather large retagging effort. So before going to be that, I think that it should be clarified: 1. Whether the new tag is actually needed. 2. What exactly is the distinction.
• Perhaps it's also worth mentioning that the tag has been created (at least) twice in the past, in 2011 and in 2013. The SEDE queries used to find those posts can be seen here.

1Here is the wording suggestion by the tag creator. For the tag-excerpt: "For questions about solving an inequation or a system of inequations." (https://math.stackexchange.com/review/suggested-edits/1195346 https://math.stackexchange.com/posts/3212655/revisions) For the tag-wiki: "An inequality is a question, in the form of an inequality between two algebraic quantities. This inequality contains unknowns. To solve an inequality is to find the values of these unknowns that make inequality true. For example $$3x-2>0$$ and $$(x^2-5x+6)(x^3-1)\leq 0$$ are inequations to be solved." (https://math.stackexchange.com/review/suggested-edits/1195345)

I was a bit hesitant whether to post a separate question or whether to make a post about the new tag in the tag management thread. I decided to go for a separate question, since clarifying what the new tag is supposed to be for will probably need more place than comments under an answer in the tag management thread would allow for.

• Perhaps for the same reason that there is an “equation” tag but not an “equality” tag — it would be redundant – MPW May 4 at 12:43

To avoid being recreated, I have made it a synonym for .

• Thanks. That seems to be the Right Thing (tm) to do. – Xander Henderson May 6 at 4:37
• I have accepted this answer - so that the action taken by the moderators is shown at the top. I will include also the link to the list of synonyms of the (inequality) tag: math.stackexchange.com/tags/inequality/synonyms – Martin Sleziak May 9 at 3:50

No, obviously not. The term "inequation" is not commonly used in English and in my experience its usual meaning is for statements with a $$\neq$$ sign, rather than inequalities that are to be solved as the tag creator seems to intend. In any case, there is certainly no reason to have such a tag to contrast with , since the distinction is not sharp and very few users would follow it in practice.

Update: Based on the overwhelming consensus here, I have gone ahead and removed the tag.

• +1 not commonly used in English. Or, at least not for the past 50 years. – GEdgar May 4 at 9:17

My personal thoughts:

Even from the name, the two seem to carry the same intents (bear in mind, I've always heard "inequality" my whole life). The Wikipedia article doesn't seem to offer any information that would suggest the two are really two, distinct things, either. I don't claim to know why Wikipedia thought the two should remain separate, and I certainly can't see why myself.

So I think it would be best, not to have this as a separate tag, but as a tag synonym - for pretty much the reasons already prescribed:

• At least by my knowledge, they're extremely similar - if not the exact same. If they are different, I'm unaware of any reason why. Even the suggested tag wiki for "inequation" seems to use them interchangeably.

• Retagging a bunch of questions involving this would amount to basically devoting two tags to "inequality". This bears a problem in and of itself: why should we have to retag literally everything involving inequalities, if they're distinct things to begin with? It also sounds like an extreme hassle to retag all those questions, and could possibly worsen searching (since if a question has five tags already, then we'd have to get rid of at least one).

• If indeed they mean ultimately the same thing with no real distinction, and the use of whichever is merely a matter of personal choice/upbringing, it makes sense to add it as a synonym. It doesn't have to be removed altogether if it would serve a valid purpose, but with another tag serving basically that very purpose as far as I can see, better to keep it as a synonym.

So, in short - unless someone can clarify why the two are/should be distinct tags, and whether the two terms mean separate things (and where those differences arise), I think "inequation" has more merit as a tag synonym than either being deleted or being its own tag.

Yes the tag (inequation) should remain; I don't understand why @EricWofsey removed it. Did it take too much space on the server? You do realize that, following your argument, there are many tags that are redundant and could be removed. Some examples are (continuous) and (continuity), (triangle) and (triangles), (congruence-geometry) and (geometry) and (euclidean-geometry), (geometric-series) and (sequence-and-series), (geometric-transformation) and (transformational-geometry) and (mobius-transformation), (integral-transforms) and (laplace-transform) and (mellin-transform),...

I understand that the wikipedia article (inequation) doesn't give enough explanation but you can google-translate the wikipedia article in french or deutsch to understand or you can read the explanations on other sites like this or this. The main difference is that you solve an inequation and you prove an inequality. Most users may not use this tag but few may use it so why not keep it? After all I don't think the aim of this question is to remove redundancy, but to remove this tag specifically for some reason. You can see (cubic-equations), (quadratics), (quintic-equations) and (quartic-equations) can be removed : there's the (algebraic-equations) tag. But @MartinSleziak didn't care to remove these tags.

• To provide context for others, you and I have had this conversation before. The short version is that "inequation" is not commonly used in English. When it is used, there is little to no distinction between "inequation" and "inequality". Most English speakers will not understand a distinction, and this is a primarily English speaking community, hence I don't see any need for the tag "inequation," except, perhaps, as a synonym for inequality. – Xander Henderson May 4 at 16:19
• Thanks for the downvotes. @XanderHenderson To provide more context, @rnd, I (and another user I couldn't find) noticed the lack of this tag. We would like to use it when asking some questions. Are we asking too much? – Paracosmiste May 4 at 17:03
• After seeing your two links about inequation, I still cannot see how it is different from inequality. – Arctic Char May 4 at 17:31
• @ArcticChar After reading about JB-Algebra, I still cannot see how it is different from nonassociative algebras but I didn't ask to remove it. – Paracosmiste May 4 at 17:39
• @BPP I am not sure why you are thanking me for downvotes. I provided only one downvote which, on meta, simply indicates that I disagree with you. Downvotes on meta (where there is no reputation) are different from downvotes elsewhere. – Xander Henderson May 4 at 17:41
• Well, this is not answering the question at all. If you see no lasting value for JB algebra, you can (and you should) go to delete it. – Arctic Char May 4 at 17:43
• @ArcticChar No because other users may use it. – Paracosmiste May 4 at 17:45
• Use it for what? If two concepts A and B are the same, and people are free to choose the tag A and B, then (1) it fails its purpose for classification, (2) it fails its purpose for people to search for those questions. – Arctic Char May 4 at 17:47
• @ArcticChar Just because I or you don't understand the meaning of a concept or its tag doesn't mean we should remove it. Other users may decide to use it. – Paracosmiste May 4 at 17:52
• Well, let me just say if you failed to explain to the community what are the difference between the two, saying something like "I or you don't understand the meaning of a concept or its tag doesn't mean we should remove it. Other users may decide to use it" does not help. – Arctic Char May 4 at 17:58
• You seem to be under the impression that there is no downside to having more tags. If it was true that everyone knew exactly what each tag meant and labeled/searched for things with the correct tag, you'd be right. The problem is that neither of those statements are true. This means it takes continuous effort by the community to avoid the tags being treated like synonyms. If they are treated like synonyms despite being distinct tags, then both the people who care about the distinction and those who don't lose out. It also increases the burden on all askers to decide which tag is appropriate. – Derek Elkins May 5 at 13:24
• It should be made crystal clear that there's no problem in specifications and special cases; as in (geometric-series) and (sequences-and-series), since the former I'd a special case of the latter. The problem comes when we have two tags that mean the exact same thing, which is for all intents and purposes the case for (inequality) and (inequation). If you disagree with this, you should give an argument; at the moment your first paragraph seems rather irrelevant. – YiFan May 6 at 3:34