For the case of finite groups, since there is only one binary operation "x" and |x[??]| = |y[??]| for any x, y [member of] [??], we get the following corollary, which is just the Lagrange theorem for finite groups.
(Lagrange theorem) For any finite group G, if H is a subgroup of G, then |H| is a divisor of |G|.
We can interpret the generalized Mean Value Theorem as follows: Assume the conditions of Lagrange Theorem holds for the function f, for each x [not equal to] [x.sub.0] in I, we can find the point c in (x, [x.sub.0]) or ([x.sub.0], x) such that
For n = 0; it follows from Lagrange Theorem that there is a c 2 (x, [x.sub.0]) such that