Right or wrong, this is my take. Rather than being a question of grammar, I believe it is a matter of conceptual and syntactical interpreation. Whether using "none" or "nothing" as an answer is really depending on conceptual mindsets of the people engaged in the conversation.
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AnonymousI taught that none means zero.It is part of this set of grammatical particles: all, some/any, none. I guess they can be called "partitives", but I'm not sure.
AnonymousI taught that none means zero.True, but so does nothing.