The set theory approach to arithmetic is defined in terms of the non-negative whole numbers 0, 1, 2, 3, …. These numbers are identified with specific sets based on the placement and number of brackets. For example, mathematicians identify 0 with the empty set { }; 1 is identified with {{ }}; 2 is identified with {{}, {{}}}; 3 is identified with {{ }, {{ }}, {{ }, {{ }}}}, and so on (each bracket an interpretation of the empty set and 1, or {{}}).