ABSTRACT
If we abstract from the identity of their elements, we can still characterize sets with respect to how many elements they have--with respect to their size. If a and b are different objects, we can say that the set {a, b} has two elements, independently of which particular objects a and b are. And if c, d and e are different objects, we can say that the set {c, d, e} has more elements, is bigger, than the set {a, b}, independently of whether any element of one set is identical to any element of the other. We can also use arithmetical notions to compare the sizes of sets. We can say, for example, that the size of the set { c, d, e} is the sum of the sizes of the sets {a, b} and if}, independently, once more, of whether the elements of one of these sets are identical to the elements of the other two.
