An*operation*(more precisely, a*binary operation*) on a set*S*is a function from*S × S*to*S*. Standard examples are addition, multiplication, and composition of functions.

Elementary texts often emphasize the “closure” property of an operation (or, sometimes, of an algebraic structure): the product of two elements in*S*must be an element of*S*. We have, instead, built this into the definition.

An*algebraic structure*(Bourbaki says a*magma*) is a set equipped with one or more operations. Such structures sometimes come with distinguished elements (such as identity elements) or functions associated with the operation (such