Yeah to add to this when you study probability at a more advanced level, you learn that really what a probability is "just" an integral ie P(x) = integral{Indic

Yeah to add to this when you study probability at a more advanced level, you learn that really what a probability is "just" an integral ie P(x) = integral{Indicator function(X)}. So it's actually not a crazy object to pop up when you're thinking about integrals and integral approximations.