A field is a special set. constituents distinct elements of at least 0 and 1 operations of addition and multiplication requirements closed commutativity associativity identities (both additive and multiplicative) inverses (both additive and multiplicative) distribution Therefore, \mathbb{R} is a field, and so is \mathbb{C} (which we proved in properties of complex arithmetic). additional information Main difference between group: there is one operation is group, a field has two operations.