Is there actually a notation and + operator for which 1 + 1 = 2 is ambiguous? Only being semi-rhetorical, I'd be interested to know if there is one. (Modular arithmetic is not considered ambiguous, at least not in the math neck of the woods.)
Not really answering your question, but more to the point of the discussion in my opinion, a() + b() could be ambiguous if a() and b() are functions with side effects and the evaluation order of the +-operator is not specified.
> 1 + 1 = 2 Is fairly unambiguous until you introduce operator overloading (and why i despise overloading).
What is it specifying—or, perhaps a better question, what would an implementation look like? It might be more precise to say "I have yet to encounter an implemented spec that was not in some way ambiguous."
That's not how addition works. You're either adding the vectors or you're adding the magnitudes. You don't get to sleight of hand by writing one and adding the other.