Is it consistent to define the position of a particle in some frame as a vector or is just an informal representation? Velocity and acceleration can be added up and multiplied by real numbers and still have physical meaning (they live in tangent spaces). But what is the physical meaning of adding a position to another or, in relativity's domain, does adding two events have any sense? If this has no sense, then defining the position of a particle as a "vector living in a vector space" is surely wrong?