Consider a set defined on the universe of integers. It contains a large number of subsets. These subsets include the empty set and sets which contain multiple integer elements. However our set does not directly contain any integers.
Is it correct to say that our set does not contain any elements (despite the large number of subsets it contains)?
After all, these subsets are not elements but simply subsets. And their elements are not elements of our set, but merely elements of the subsets.