Recursive definitions are not bad at all. On the contrary, they are the best kind of definitions. It is important to note that recursive defintions are **not** the same as circular definitions - in a recursive definition there is a base case which will eventually be reached. For example, we can define the set of natural numbers recursively:

A number is a natural number if:
a) it is , or
b) it is the successor of another natural number

Do you see the recursion? We can use this definition to determine that 3 is a natural number:

3 is the successor of 2, so 3 is a natural number if 2 is a natural number;
2 is the successor of 1, so 2 is a natural number if 1 is a natural number;
1 is the successor of 0, so 1 is a natural number if 0 is a natural number;
0 is a natural number;
so 3 is a natural number

Recurive definitions can make writing

recursive programs very

natural. Consider the following definition of

factorial:

factorial(n) = 1, if n = 0
factorial(n) = n * factorial(n - 1), if n > 0

This makes writing the factorial

function very easy. Here it is (in

Scheme):

(define factorial
(lambda (n)
(if (zero? n)
1
(* n (factorial (- n 1))))))