as counting the ("r" − 1)-dimensional subspaces of ("m" − 1)-dimensional projective space by fixing a hyperplane, counting such subspaces contained in that hyperplane, and then counting the subspaces not contained in the hyperplane; these latter subspaces are in bijective correspondence with the ("r" − 1)-dimensional affine subspaces of the space obtained by treating this fixed hyperplane as the hyperplane at infinity.