number 50

Consider an inductive definition of a version of Ackermann's function. This function was named after Wilhelm Ackermann, a German mathematician who was a student of the great math- ematician David Hilbert. Ackermann's function plays an im- re at ve portant role in the theory of recursive functions and in the study of the complexity of certain algorithms involving set unions. (There are several different variants of this function. All are called Ackermann's function and have similar properties even though their values do not always agree.) of of 2n If m =0 if m 1 and n =0 ifm > 1 and n = 1 r of (m, n) = A(m 1, A(m,n 1)) if m2 I and n 2 2 Exercises 48-55 involve this version of Ackermann's func- tion 48. Find these values of Ackermann's function. with T: is d) A(2. 2) t the rtices 49. Show that A (m, 2) 4 whenever m > 1. 50. Show that A ( l , n ) = 2n whenever n 1 . 51. Find these values of Ackermann's function. mber ), the a) A(2.3) 52. Find A(3, 4). eb) A(3, 3)