I can't understand Russell's paradox. What I understand is that Russell's paradox arises because the set of all sets that are members of themselves is empty. That it's impossible to find a set that's a member of itself, but one can define the set of all sets of the universe that clearly contain itself. Does it mean that there is no set of all sets of the universe?
Please, make answers as simple as possible, I'm nearly ignorant in set theory.