I've noticed that our world is believed to be so strongly founded on the idea that possibility of an occurrence of an event increases and levels off at 100%, then the slope of a function to describe Cuil would approach 0 as Cuil approaches 1. The same is true if the possibility approaches 0. If this is true, this limits how we could define Cuil, based on both De Rolles's theorem of differentiation, as well as the Mean Value Theorem of differentiation. If you are not familiar with these, go back to school. Otherwise, if you are as mathematically based as I am, you should notice that this would imply that the graph of an equation which would describe Cuil and its relations would have to always have a slope of 0 on any differentiable point. Taking all of this into account, there would be no way for Fractional Cuil to exist without delving into the realm of imaginary numbers; but we see in everyday life that Fractional Cuil exist. How, then, can we describe Fractional Cuil mathematically without breaking the laws of Calculus? Help!

Mathematically Defining Fractional Cuil