11. Flat objects may be identified by the point at infinity being included in the solutions. 12. This corresponds to the situation that one of the fixed points is the point at infinity . 13. In the real case, a point at infinity completes a line into a topologically closed curve. 14. The neutral element is then given by the point at infinity ( 0 : 1 : 0 ). 15. This corresponds to a point at infinity in the Euclidean plane, no corresponding intersection point exists ). 16. The point " O " is actually the " point at infinity " in the projective plane. 17. These lines are sometimes thought of as circles through the point at infinity , or circles of infinite radius. 18. Thus we define as the homogeneous coordinates of the point at infinity corresponding to the direction of the line. 19. The domain of a complex-valued function may be extended to include the point at infinity as well. 20. This definition for addition works except in a few special cases related to the point at infinity and intersection multiplicity.
