This is false.
One example: consider the origin, (0, 0) in Cartesian coordinates. In polar coordinates, any point with [tex]r=0[/tex] will result in the same point, since [tex]r[/tex] is the distance of a given point to the origin. So for infinitely many values of [tex]\theta[/tex], the point [tex](0,\theta)[/tex] will always be 0 units away from (0, 0).
