I have a (hopefully) quick question about this. Fulton's Algebraic Curve, exercise 7.2.3 on page 85 says:
Let $F$ be any plane curve with no multiple components. Generalize the results of this section to F.
My question is that I don't see how the results don't already apply to any plane curve. As far as I can see, we're only making the assumption that $F \neq x$ and so we aren't accounting for one curve. Is this the only thing we're trying to generalize to? I'd appreciate any help with what I'm missing.
