can be embedded isomorphically in
Affine points can be recovered from projective ones with
by the mapping
However, these mappings and definitions are affine rather than projective concepts. They are only meaningful if we are told in advance that represents ``normal'' affine space and xn+1 is a special homogenizing coordinate. In a general projective space any coordinate (or linear combination) can act as the homogenizing coordinate and all hyperplanes are equivalent -- none is especially singled out as the ``hyperplane at infinity''. These issues will be discussed more fully in chapter 4.