2

I know that it is correct to say

There is 1 composition of n.

but what if instead of "1", I use an expression that evaluates to 1? For example, what is the grammatical number in these sentences?

There is/are 20 composition(s) of n. (two to the zero)

There is/are 3 - 2 composition(s) of n. (three minus two)

There is/are 20=1 composition(s) of n. (two to the zero, which equals one)

There is/are 1=20 composition(s) of n. (one, which equals two to the zero)

This problem comes up somewhat frequently for me when describing the base case in a proof by induction.

1

The general pattern is:

  1. If the phrase does not end in "1", use plural: "There are 1=2^0 compositions of n."
  2. If the phrase does not equal "1", use plural: "There are 2^1 compositions of n."
  3. Otherwise, use singular: "There is 2^0=1 composition of n."

I do not have a link to any particular style guide on this and am going entirely by ear. I suspect the primary debate would revolve around (1) but only because the phrase also starts with "1". The following sounds completely incorrect to my ear:

INCORRECT — There is 2^0 composition of n.

0

If the result does not trivially evaluate to 1 then use plural, which is proper for unknown numbers of items.

-1

I think if you convert these problems to word problems you will find your verb agrees with your noun for each part of the equation. There are 2 items which are powered to the zero, so 1 item results. There are 3 items and 2 are removed, so 1 item remains. 1 is the result when 2 items are powered to the zero.

However, if you are referencing the number as the subject, a number is singular no matter its value and the verb should reflect that. When 1256 is powered to the zero, 1 is still the result.

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