 They can be called infinitely near to "P" as way of visualizing them on "S", rather than "S"*.More generally this construction can be iterated by blowing up a point on the new curve "C", and so on.An infinitely near point (of order "n") "P""n" on a surface "S"0 is given by a sequence of points "P"0, "P"1...,"P""n" on surfaces "S"0, "S"1...,"S""n" such that "S""i" is given by blowing up "S""i"–1 at the point "P""i"–1 and "P"i is a point of the surface "S"i with image "P""i"–1.