Sorry if I write something stupid, but I am just a student. I really want to understand why the rejection of Cantor´s Set Theory. Considering the Cantor´s set concept, can a set be member of itself? Although I suppose that the answer is yes, my intuition answer no, it can´t! "A set is a collection into whole of definite, distinct objects of our intuition or our thought. The objects are called the elements of the set." The elements of a Set have to be definite to Set exists. When I imagine a Set as a element of itself, it have to be definite to my intuition. This Set is not definite to my intuition, cause I need first imagine his definite elements. It never ends! Thats why a set cant be member of itself. Would someone explain where my affirmation is wrong? thanks.