Old Dominion University: Shunichi Toida's "Recursive Definition"

Read these essays. Notice the similarities between using recursion to define sets and using recursion to define functions. Then answer the four questions at the end of the first essay.

In this type of definition, first a collection of elements to be included initially in the set is specified. These elements can be viewed as the seeds of the set being defined. Next, the rules to be used to generate elements of the set from elements already known to be in the set (initially the seeds) are given. These rules provide a method to construct the set, element by element, starting with the seeds. These rules can also be used to test elements for the membership in the set.