Group: Let G be a set. When we say that o is a binary operation on G, we mean that o is a function from GxG into G. Informally, o takes pairs of elements of G as input and produces single elements of G as output. Examples are the operations + and x of addition and multiplication on R, the set of real numbers.
This de nition implies that we could use standard function notation for o, and write
o:G x G → G;
and represent the result of applying o to g; h ≡ G as o(g; h), but in the present context, we normally use in x notation, and write g o h instead.