I feel like emanuela and I are arguing semantics at this point rather than mathematics, and it looks like the kind of thing that can just go around and around in circles (thus leading to a discussion of pi, perhaps).

I may be wrong or I may be right; I don't know. I don't claim to be a professional mathematician, and it has been 8 years since my bachelor's degree in mathematics, so the odds are that I'm wrong and emanuela is right. But my intellectual curiosity is not really satisfied. Maybe someone else can set me straight on this. There must be some demonstrable flaw in my logic.