It is convenient to introduce affine and projective spaces by means of linear spaces, as follows. A linear subspace of a linear space, being itself a linear space, is not homogeneous; it contains a special point, the origin. Shifting it by a vector external to it, one obtains a affine subspace. It is homogeneous. An affine space need not be included into a linear space, but is isomorphic to an affine subspace of a linear space. All affine spaces are mutually isomorphic. In the words of John Baez, "an affine space is a vector space that's forgotten its origin". In particular, every linear space is also an affine space.