Dr. J introduces the idea of a subset and set comparisons. Set A is a subset of set B if the elements of A are all in the set B. The set A is a proper subset of B if there is at least one element in B that is not in A. Thus subset is really a set comparison and is related to the mathematical inequality less than while a proper subset is related to the mathematical inequality less than or equal to. The opposite set comparison is a superset and proper superset.