where ∇P is the gradient of P and the second part of the equation is minus the gradient for a function of the Cartesian coordinates x, y, z.[lower-alpha 1] In some cases, mathematicians may use a positive sign in front of the gradient to define the potential.[2] Because of this definition of P in terms of the gradient, the direction of F at any point is the direction of the steepest decrease of P at that point, its magnitude is the rate of that decrease per unit length.