It can be shown that orthogonality of functions is a generalization of the concept of orthogonality of vectors. Suppose we define V to be the set of variables on which the functions ''f'' and ''g'' operate. (In the example above, ''V'' = {''x''} since ''x'' is the only parameter to ''f'' and ''g''. Since there is one parameter, one integral sign is required to determine orthogonality. If ''V'' contained two variables, it would be necessary to integrate twice—over a range of each variable—to establish orthogonality.) If ''V'' is an empty set, then ''f'' and ''g'' are just constant vectors, and there are no variables over which to integrate. Thus, the equation reduces to a simple inner-product of the two vectors.
