I have the impression that it's a tacit convention that when there may be one or more objects in concern, we can just use a plural noun, but now I'm dithering.
I wrote the statement "every integer greater than 1 is expressible as a product of positive primes" in an article for an audience of people just beginning learning math, and one reader suggested changing it to "every integer greater than 1 is expressible as a product of positive primes (which includes just one prime)".
Is there an authoritative mathematical writing style that addresses this issue?
Edit: removed subjective parts of the question so that it only asks for a mathematical writing style guide that addresses this issue. Whether or not such a guide exists is an objective matter and not opinion based.
If we disregard that the word 'product' indicates multiple inputs, then the above sentence as well as the sentences "the parents' subsidy amount depends on the ages of their children" and "how many degrees of freedom does blah blah have" are generally—even in mathematical writing—understood to include any single-object case.
However, for the sake of absolute clarity, especially due to abovementioned issue with the word 'product', how about:
The parentheses make this clunkier than each of the above bulleted suggestions, while these additional suggestions are both very awkward as it feels wrong both to include and to exclude that indefinite article: