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This question has been on my mind for a while now. Not being a native speaker and coming from a country, where grammatical cases are used to modify nouns and nominal parts of speech, the use of articles does not come naturally to me. Nevertheless, when it comes to definite and indefinite articles in math papers, I see many mistakes, not only grammatical, but also from a pure mathematical perspective.

Two examples from the top of my head:

  • An empty set $\emptyset$, should really be the empty set, since there is only one empty set.
  • A unique solution, should be the unique solution (although I am not so sure about this one, e.g. "We assume that Eq. (1) has a? unique strong solution")

What are some other common examples where you see the articles being misused?

xan
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    This is not really a question of mathematics but rather English. The definite/indefinite distinction is subtle and there is more to it than uniqueness or lack thereof. For instance, "... has the unique solution." is ungrammatical but "... has the unique solution $3.141592535\ldots$." is grammatical. – Zhen Lin Aug 14 '21 at 10:35
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    I would disagree. As I mentioned I am much more interested in the mathematical perspective and I highly doubt any linguist knows what a null set is for example. Finally, the "article-writing" tag seems quite appropriate. – xan Aug 14 '21 at 10:49
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    "These equations each have a unique solution" and "the unique solution of this equation is..." are both grammatically correct. [ In any case, concerned about ambiguity, I typically rephrase away from this word: in the two sentences that I quoted, do the equations each have a single solution, or is it that their solutions differ from the solution of the other equations (i.e. are distinct)? ] But like Zhen Lin, when trying to be careful in mathematical writing, I often find that the choice between a/the is quite nuanced. – ryang Aug 14 '21 at 10:51
  • Note that ${\varnothing}$ is not a null set. Also, ${\varnothing}$ is not the empty set. (For some reason this is the way I find it natural.) – Arthur Aug 14 '21 at 10:52
  • @xan And I would doubt most mathematicians, or for that matter native speakers of English, have adequate training in linguistics to be able to give a proper analysis of the use of "the". Here is another tricky example. Both "... has a unique solution property." and "... has the unique solution property." are grammatical but have different nuances. The former will likely be followed by an explanation of how the unique solution property under discussion is different from the obvious one. – Zhen Lin Aug 14 '21 at 11:00
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    @Arthur ${ \emptyset }$ could be a null set, if we were considering a measurable space $X$ such that $\emptyset \in X$ and the measure of ${ \emptyset }$ is zero. But anyway... – Zhen Lin Aug 14 '21 at 11:01
  • The existence of a tag doesn't mean that any question meriting that tag is on-topic here. E.g., there is a "physics" tag, but a physics question with no math angle would be off-topic on this website. – Gerry Myerson Aug 14 '21 at 11:28
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    I feel this is getting very of topic (and quite a bit unfair to be frank), since both are just examples I thought of on the fly to illustrate my point. I think there is a high chance to find people on math stackexchange, that have given this a lot of thought througout their careers. Mathematicinas have to think about the language while writing papers, linguists don't have to care about math at all. – xan Aug 14 '21 at 11:29
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    Mathematicians have to think about the language; they don't have to overthink. – Gerry Myerson Aug 14 '21 at 11:32
  • "...where you see aricles being misused": Xan, a mathematical article written by a native English speaker is not going to get these things wrong. You should accept that perhaps it is your own understanding of English grammar that is faulty. – TonyK Aug 14 '21 at 11:52
  • It definitely is, that is why I am asking in the first place ... – xan Aug 14 '21 at 12:03
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    I hope this question doesn't get closed. Instead of asking for examples of misuse (many readers don't notice such usage oddities partly because their attention contextually autocorrects them away), perhaps expand the post (with a shifted focus and more details)? Anyhow, here's a related question. – ryang Aug 14 '21 at 14:13
  • xan, that is not how your question comes across. "I see many mistakes...": no you don't! You imagine many mistakes. – TonyK Aug 14 '21 at 17:02
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    Also see this comment: https://math.stackexchange.com/questions/513317/is-the-present-king-of-france-is-bald-studied-by-maths#comment1101614_513732 – ryang Sep 25 '21 at 15:38

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