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I have the impression that it's a tacit convention that when there may be one or more objects in concern, we can just use a plural noun, but now I'm dithering.

I wrote the statement "every integer greater than 1 is expressible as a product of positive primes" in an article for an audience of people just beginning learning math, and one reader suggested changing it to "every integer greater than 1 is expressible as a product of positive primes (which includes just one prime)".

Is there an authoritative mathematical writing style that addresses this issue?

Edit: removed subjective parts of the question so that it only asks for a mathematical writing style guide that addresses this issue. Whether or not such a guide exists is an objective matter and not opinion based.

Long Horn
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  • The suggestion seems worse to me. The thing that seems to trip people up more (when addressing a non-expert audience) is the idea that you can have a product of one prime; they expect a product to involve at least two factors. If you're talking to mathematicians then you don't need to worry about that either. Who is the writing for? That could make a difference. – David K Jul 07 '23 at 03:21
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    The sentence "every integer greater than one which is not a prime is expressible as a product of primes" should withstand the critiques of all audiences. – Kurt G. Jul 07 '23 at 03:41
  • @DavidK That's a good reminder: The audience are beginners in math, so I should probably also explain that products can involve a variable number of operands. However, my question is more about specifically the plural noun "primes". I wonder whether I ought to write something like "prime(s)". This is a more general question. – Long Horn Jul 07 '23 at 03:51
  • @KurtG. That's a great way to phrase it. I do wonder if there's a general rule regarding plural nouns though. – Long Horn Jul 07 '23 at 03:52
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    My personal rules are: 1. Human language is not a programming language that needs an authoritative committe to standardize it. 2. A few extra words that add clarity never hurt even if the audience has math PhDs. – Kurt G. Jul 07 '23 at 03:58
  • If clarification is needed then I would write this as "expressible as a product of one or more primes". I have never heard of negative primes so I probably would leave out the word positive. – John Douma Jul 07 '23 at 04:41
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    Once your audience attacks English, your reaction should be to write it in pure and rigorous math lingo and highlight its advantage over English. Also gives them a glimpse of what's awaiting them. – Piita Jul 07 '23 at 08:08
  • I realize I did not address the main question in my first comment; that's why it was a comment, not an answer. There is an actual answer below. What I meant was that this particular "correction" was itself ambiguous and potentially confusing. This is one of those cases where a radical rewriting of the sentence is called for, which makes it not a good example for your more general question. Perhaps you should add other examples to the question. – David K Jul 07 '23 at 11:19
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    @Piita Mathematicians are educated people. If your English is that bad then your mathematics is probably worse. – John Douma Jul 07 '23 at 12:41
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    @JohnDouma You misunderstood. Learning to write maths in a formal way is valueble precisely because it eliminates many sources of doubt and misinterpretation, so when beginner students are raising such an issue of vagueness, it's basically asking for it. – Piita Jul 07 '23 at 18:00
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    @LongHorn "Is there an authoritative mathematical writing style that addresses this issue?" The fact that it is standard practice—even in mathematics—to ask "how many solutions.." when "one" is a valid answer almost certainly means that any such style guide would have no issue with using the plural form of the object/noun (boldfaced in the current answer below) in such cases. The actual reason your given example is biased towards the plural case is due to the word "product" connoting (even denoting) multiple primes, rather than the word "primes" being presented in its plural form. – ryang Jul 09 '23 at 16:02
  • @ryang I really appreciate your answer and upvoted it. I was a bit hesitant to accept it yet as I was still hoping to see if someone can find a widely adopted writing stylebook/guide that addresses this issue in general. For now it looks like no one is able to find one, so it looks fair to consider that too difficult and to accept your answer. – Long Horn Jul 11 '23 at 17:28

1 Answers1

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"every integer greater than 1 is expressible as a product of positive primes"

If we disregard that the word 'product' indicates multiple inputs, then the above sentence as well as the sentences "the parents' subsidy amount depends on the ages of their children" and "how many degrees of freedom does blah blah have" are generally—even in mathematical writing—understood to include any single-object case.

However, for the sake of absolute clarity, especially due to abovementioned issue with the word 'product', how about:

  • Every integer greater than 1 is expressible as the product of one or more primes. ✅
  • Every integer greater than 1 is either prime or expressible as a product of primes. ✅✅
  • Every non-prime integer greater than 1 is expressible as a product of primes. ✅✅

"every integer greater than 1 is expressible as a product of positive primes (which includes just one prime)".

The parentheses make this clunkier than each of the above bulleted suggestions, while these additional suggestions are both very awkward as it feels wrong both to include and to exclude that indefinite article:

  • Every integer greater than 1 is expressible as a product of prime(s).
  • Every integer greater than 1 is expressible as a product of a prime(s).
ryang
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