I was reviewing some of the formal definitions of linear algebra and I found this issue. I particularly have difficulty with formalizing some of the more "trivial" definitions and theorems, so maybe this has something to do with that.
A vector is an equivalence class, which is a set, then why can we say that a particular oriented line segment is a vector? Is it just abuse of notation and we should call it a representative of such set? Or is it because the vector is well defined by just one of the oriented line segments in the equivalence class?