Branch of mathematics that deals with the properties of sets. It is most valuable as applied to other areas of mathematics, which borrow from and adapt its terminology and concepts. These include the operations of union (), and intersection (). The union of two sets is a set containing all the elements of both sets, each listed once. The intersection is the set of all elements common to both original sets. Set theory is useful in analyzing difficult concepts in mathematics and logic. It was placed on a firm theoretical footing by Georg Cantor, who discovered the value of clearly formulated sets in the analysis of problems in symbolic logic and number theory.