Section 3.3: Problem 8 Solution
Working problems is a crucial part of learning mathematics. No one can learn... merely by poring over the definitions, theorems, and examples that are worked out in the text. One must work part of it out for oneself. To provide that opportunity is the purpose of the exercises.
James R. Munkres
Let and be representable functions, and assume that Show that is representable.
One way is to use the primitive recursion (catalog item 13). Let , and . Then, , and , therefore, is the function defined by by primitive recursion. Therefore, it is sufficient to show that is representable. is representable, and for , is representable. Hence, is representable (a more general case of “gluing” representable functions together is presented in Exercise 10).