# "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?

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.

• By the way, I'd rather say "The polynomials F and G are related..."; It sounds less complicated :D Commented Apr 24, 2011 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….” Commented Apr 25, 2011 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! Commented Apr 25, 2011 at 0:25
• The statement is about the relationship between the two individual polynomials that make up the pair, so is seems more appropriate.
– user184130
Commented Jul 26, 2018 at 16:14
• @James Random so you do agree with this answer? Because I received a downvote and if it was you, I am confused. Commented Jul 26, 2018 at 19:36

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)".

• If you could say 'a pair' then it would need the singular 'is'. In first example, you can't say "The pair ... are related...". Commented Apr 24, 2011 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
Commented Apr 24, 2011 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'. Commented Apr 24, 2011 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
Commented Apr 25, 2011 at 4:19

answer is 'is' according to me, because pair represents a collective noun or verb of something, and there is a single pair of polynomials

• This adds nothing to the accepted answer. Commented Jul 26, 2018 at 16:53