Hello! I am reading some introductory differential geometry and they define the vector space associated to a point of a manifold as the tangent plane at that point. Intuitively it makes sense to call these vectors (just as the speed is the tangent to the trajectory), but why are those called vectors and the one in the dual vector space one-forms. Is this just a convention, or it is a deeper meaning? Like the dual vector space is still a vector space, so its members can be considered vectors, while the real vectors can be considered one forms, right? Thank you!