Hello, I have an aficionado curiosity, so please bear with me. As you know, bags are sets where repeated elements are allowed. Imagine the following funny representation for a bag: instead of repeating elements, we use a set of ordered pairs, containing each distinct item plus a count of how many of its kind there are. (Suppose, for the sake of the argument, that the number of repetitions is countable.) Now the funny part: we can store items which are not in the bag by using a count of zero. The question is, what is the cardinality of such a monster? In order to represent, say, the integers, you save each of them with a count of one. But then you also save the (rest of the) reals with a count of zero, so the cardinality of this set is at least aleph-1; but you also save elements with a zero count from sets of size aleph-2, aleph-3... You might argue that the construction is paradoxical by design, since I am simply asking for a set which is bigger than anything you can construct. But I suspect such rejection would have an interesting consequence. Take, from the example above, the subset of the zero-count elements, from sets of size aleph-1, -2, -3... The individual items are, in themselves, sets (Cauchy series), whose elements have, in turn, being taken from the "previous smaller set": the reals being series of elements from a set of cardinality aleph-0, and so on. So this subset is also a subset of a potentially bigger one, "the sets which do not contain themselves as a member", a phrase which should ring a bell. Would we be saying that the Russell Paradox does not exist, since it's based on a premise which is flawed in the first place?