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
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