I just thought about a problem. Say you have a circle (there is an infinity of radius of the circle), and you want to pick up one radius. If there is a finite number of elements (here radius), the probability to pick up one on n elements is if the probability to pick up one is equal to the probability to pick any other element. I believe that in my example, I can make n tends to . As I will pick up one radius, the sum of all the probabilities to pick a particular radius must be 1. So I can rewrite as tends to . Seems very strange for me. Can someone tell me if I did something wrong?