Can anyone elucidate a comprehensive list of rules regarding the usage of 'no' and 'not'? I've found rules of thumb, such as 'no' for nouns and 'not' for everything else, but then there's the case of "there are no kids" and "there are not any kids" — what's the rule for that? And are there other rules lurking?
closed as not a real question by Jasper Loy, FumbleFingers, Mitch, simchona♦, JSBձոգչ Nov 30 '11 at 13:29
It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, see the FAQ.
The difference is simply that not is an adverb, while no is an adjective. (Specifically, no is a determiner, meaning it functions like the; it comes at the beginning of the noun phrase and each noun phrase can only have one. For example, you can say "there are the kids" and "there are no kids", but not "there are the no kids".)
Your example doesn't invalidate the rule of thumb you stated, because "not" in "there are not any kids" is not modifying the noun kids. Depending how you analyze it, it could be modifying the verb are or the adjective any; either way it is an adverb.