Consideran inductive definition of a version of Ackermann's function. This function was named after Wilhelm Ackermann. a German mathematician w ho was a student of the great mathematician David Hilbert. Ackermann's function plays an important 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.)

involve this version of Ackermann's function.

Prove that A(m, n + 1) > A(m, n) wheneverm and;; are nonnegative integers.