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Suppose that I have a set (S). This set should contain numbers. These number should follow a specific bound. Then,

0 and 20 are the lower and upper bound of the set S, respectively.

or

0 and 20 are the lower and upper bounds of the set S, respectively.

Which one is correct?

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  • You can (but are not required to) say "of set S" rather than "of the set S".
    – TimR
    Commented Jan 9, 2019 at 14:30

2 Answers 2

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As you have written the sentence, you should use the plural "bounds".

0 and 20 are the lower and upper bounds of the set S, respectively.

"0 and 20" is a plural subject, with a matching plural verb "are". 0 is one bound and 20 is another, so "bounds" is most appropriate.

You are free to include or to omit the definite article before "upper". I think omitting it (as in your example) is the better choice, but that is an assessment of style rather than grammar.

Alternatively, you can use the singular "bound" after both upper and lower:

0 and 20 are the lower bound and the upper bound of the set S, respectively.

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    +1. It might also be worth looking at the sentence without the coordinate adjectives: "Zero and twenty are the bounds of the set". These bounds are countably plural even without attribution.
    – Gary Botnovcan
    Commented Jan 9, 2019 at 15:27
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The first one of yours is correct and the second would also be correct if 'the' was inserted before 'upper' as follows;

0 and 20 are the lower and the upper bounds of the set S, respectively.

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  • I disagree. If the subject is a compound subject ("0 and 20"), then you must use the plural verb are, so your first example is ungrammatical. The only correct alternative is your second example.
    – Canadian Yankee
    Commented Jan 9, 2019 at 14:11
  • I agree to "If the subject is a compound subject ("0 and 20"), then you must use the plural verb are, ..". Eg: "One and one are two." emswriting.wordpress.com/2012/01/12/subject-verb-agreement-24
    – Zeeshan Ali
    Commented Jan 9, 2019 at 14:19
  • I second Canadian Yankee's comment. The first example in the question is not grammatical, and the second "the" is not required.
    – Tashus
    Commented Jan 9, 2019 at 14:42

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