 Whereas elementary algebra is conducted in a fixed algebra, abstract or modern algebra treats classes of algebras having certain properties in common, typically those expressible as equations. The subject, which emerged during the 19th century, is traditionally introduced via the classes of groups, rings, and fields. For example any number system under the operations of addition and subtraction forms an abelian (commutative) group; one then passes to rings by bringing in multiplication, and further to fields with division. The common four-function calculator provides the four functions of the field of reals.