The powers of a function f: A → A are defined recursively byDefine a sequence {an} recursi...

The powers of a function f: A → A are defined recursively by

Define a sequence {an} recursively as follows:

Prove that an ≤ 20n for all n ≥ 0. (Recall that [x] denotes the floor of the real number x. See paragraph 3.1.7.)