Great lectures (19/20) but same remark than in lect5, there is great confusion between VECTOR SPACE and AFFINE SPACE, and in particular between the AFFINE ORIGINE (0,0,0) and the 0 VECTOR. The 0 vector is NO WHERE. He's NOT living in affine space. Actualy this aparent paradoxes can only be overcome by driling to the heart of the true definition of a vector space. For the 1-dim vector space, they are by serious definition an EQUIVALENT CLASS of infinitely many parrallel affine lines that fill the entire plane. Similarely a 2-dim vestor space is an equivalent class of infinitely many parallel affine planes that fill the entire 3-space R^3. The key word is thus, REPRESENTATION (Vorstellung in German). An affine line is a particular REPRESENTATION, a "minister" of a "King" which give the DIRECTION : the 1-dim VECTOR SPACE. Similarly an affine plane is a particular REPRESENTATION, a minister of a "King&Queen" which fix the TWO-DIRECTION : the 2-dim VECTOR SPACE####[]