In this case the plural is also the collective noun. You’re not really talking about *any* amount of apples but rather the concept of apples (specifically your lack of possession).
Or another way: It’s because what you’re *really* doing is saying in one statement that you do not have each and every apple, so you use the plural.
The singular (generally) refers to a specific apple, whether positive or negative.
“I have no apple” is totally acceptable, but it kinda implies (a tiny bit) that you have a particular apple in mind that you lack. :p
I think that, in the context, it means not a single one of many? If you know of something that’s singular but you don’t have it, then you might say I do not have a/n blank. So basically the context changes how they’re used. I have a 0% interest rate for the first 6 months refers to a single thing. I have no/zero interest in this conversation.
Latest Answers