# “Is” vs. “Are” when using the word “Pair” in a mathematical setting

I've seen equally good arguments for and against using "is" for this sentence.

The pair of polynomials (f,g) is/are related by the reciprocity law.

Which verb is used correctly?

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## 2 Answers

You should use the singular, because it refers to "Pair" and not to "polynomials". The pair in this case is one, so "is".

If it was "three pairs of polynomials...", for example, then you would have used "are".

Like:

A pair of shoes is in my bedroom. - VS - Two (three, four, five, etc) pairs of shoes are in my bedroom.

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By the way, I'd rather say "The polynomials F and G are related..."; It sounds less complicated :D – Alenanno Apr 24 '11 at 17:03
I would also avoid using the word “pair” in the example in the question because introducing the pair itself does not seem to add anything. I would write “The two polynomials f and g are related….” – Tsuyoshi Ito Apr 25 '11 at 0:16
It is difficult for me to remember that “a pair of Xs” takes a singular verb whereas “a couple of Xs” usually takes a plural verb. Confusing! – Tsuyoshi Ito Apr 25 '11 at 0:25

If the mathematical statement is about the two objects in the pair then "are" is appropriate, however if it is about the pair as a mathematical object of itself then "is" is in place. Thus "The pair of polynomials (f,g) are related by the reciprocity law" but "The pair of polynomials (f,g) is equal to the pair (h,q)".

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If you could say 'a pair' then it would need the singular 'is'. In first example, you can't say "The pair ... are related...". – Mitch Apr 24 '11 at 17:21
One sometimes uses "the pair of Xs" just meaning "the two Xs". E.g. the following example from answers.com seems right to me: "A pair of numbers that are used to locate a point on a graph is called a ordered pair and is expressed as (x,y)..." Read more: wiki.answers.com/Q/… – noam Apr 24 '11 at 17:41
grammatically, in your example, "...the numbers are..." but "A pair ... is...". In the example "...[to be] related by", the copula is governed by the singular 'pair', not the plural 'polynomials'. – Mitch Apr 24 '11 at 17:48
A single item can not be just "related" (except to another thing), thus when saying that "the pair is/are related" the meaning is that the two items in it are related to each other, and not that the pair object itself is something. – noam Apr 25 '11 at 4:19