# Use of articles in mathematical writing

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.
• 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
Nov 17 '14 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). Nov 17 '14 at 21:00
• I updated the question. Nov 17 '14 at 21:08
• 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? Nov 17 '14 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. Nov 17 '14 at 23:52