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.
Answer
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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