Page 150

		Show the following.

		(a) For each , .

		(b) . Observe that this result together with part (a) implies .

		(c)

		(d) For each , .

		(e) For each , .

		A Lim-program for a function may be viewed as a higher-order program for the function. A three argument  j -program i is called a Lim2-program for  h ) just in case for all x . This process can easily be iterated to define Limn programs. The reference [29] considers identification of such higher-order programs for functions.