A data type consists of a set of values and a set of predefined operators on those values. For example, in integer arithmetic the values are {..., −2, −1, 0, 1, 2,...} and the operators are {+, −, *, /}. The selection of these operators is arbitrary in the sense that other operators such as mod and abs could be added to the set. The definition of the operators is not arbitrary because these four are interesting, and suffice for defining and proving theorems in arithmetic and for manipulating arithmetic expressions in practice. It would be possible to reduce the number of operators by defining multiplication and division as repeated addition and subtraction, respectively, but convention and convenience dictate this choice of operators.