I am reading Introduction to Set Theory (Jech & Hrbacek) and in one of the exercises we're asked to prove that the complement of a set is not a set. I get that if it were a set that would imply that "a set of all sets" (the union of the set and its complement, by the axiom of pairing) exists and that leads to paradoxes. However, does that mean that the sample space is not considered a set? I always thought it was a set (and a quick check on Wikipedia confirms that). So, understandably I'm confused. Any help? Thanks!