- 601

- 7

Also, why is it that we can compare vectors at different points, and also add/subtract points in Euclidean space? For points, is it simple because the coordinate map is the identity map and so adding/subtracting the coordinates of points is equivalent to adding/subtracting points in Euclidean space. And for vectors, is it because Euclidean space is affine and so the tangent spaces at two different points in Euclidean space are naturally isomorphic (with the isomorphism given by parallel translation).