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I'm writing a section about some mathematical properties and have trouble with the use of articles (indefinite/definite/no).

I could come up with the following variants, but don't know which one is the correct one. What I want to say is that if we pick any values for A and B, considering they are integers, there will be items such as (A, B, 2), (A, B, 3), ..

Which article should come before item?

  • For any A and any B, there will be an item (A, B, C) such that C > 1.
  • For any A and any B, there will be item (A, B, C) such that C > 1.
  • For any A and any B, there will be the item (A, B, C) such that C > 1.
  • For any A and any B, there will be items (A, B, C) such that C > 1.
  • For any A and any B, there will be items of the form (A, B, C) such that C > 1.
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  • Is (A, B, C) functioning as a single item, such as a specific point in a 3-Dimensional plane? If so, use the first variation. If it is a group of three items, such as item A, item B, and item C, then use "For any A and any B, there will be items (A, B, C) such that C > 1."
    – user97641
    Commented Nov 17, 2014 at 20:45
  • What exactly do you wish to convey? Surely it makes a difference if there will always be exactly one, sometimes more than one, or always more than one item satisfying the condition. It's somewhat "domain-specific" whether item (A, B, C) validly identifies such an item, as opposed to calling it an item of the form (A, B, C).
    – FumbleFingers
    Commented Nov 17, 2014 at 21:00
  • I updated the question.
    – Wickoo
    Commented Nov 17, 2014 at 21:08
  • 5
    None of the above. Use mathematical language. "For any integers A and B, there is an integer C>1 such that ...". And I don't know whether to complete this with "an item of the form (A,B,C) exists" or "(A,B,C) is an item" because I don't understand exactly what you want to say. Is the triple of integers an item, or are items something that is associated with a triple of integers?
    – Peter Shor
    Commented Nov 17, 2014 at 21:38
  • @PeterShor - you should make that into an answer. These words have specific meanings in mathematics, which may or may not be related to the general usage. All of his examples make sense, but they have different meanings.
    – Jasmine
    Commented Nov 17, 2014 at 23:52

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The correct article to use is "an". However, the fact that people don't actually understand what any of your sentences mean indicates that you are not being precise enough. Put the sentence in more mathematical language.

I think that what you mean is either:

For any integers A and B, there is an integer C > 1 such that an item of the form (A,B,C) exists,

or

For any integers A and B, there is an integer C > 1 such that (A,B,C) is an item.

Which of these you should use depends on the exact definition of an item, which we cannot deduce from your question.

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