sentences:  For example, the rhamphoid cusp "y"2 = "x"5 has a singularity of order 2 at the origin.After blowing up at its singular point it becomes the ordinary cusp "y"2 = "x"3, which still has multiplicity 2.In the previous example it was fairly clear that the singularity improved since the degree of one of the monomials defining it got smaller.