There are many ways to define a set. Here are some examples:
List the members: The set {1,4,5}
Give a property: The set of all integers n such that 3n is greater than 5
We introduce a new method, called a recursive definition. It has three parts: basis, recurrence, and extension.
The basis gives some members of the set in some old way, such as listing the members or giving a property.
The recurrence defines membership in terms of other members of the set.
Extension states that nothing is a member of the set unless it can be proved to be in the set using the basis and recurrence rules.
Here is an example:
Basis: 1 is a member of the set S.
Recurrence: If n is a member of S, then n+n is a member of S.
Extension: If n cannot be proved to be in S using the above rules, n is not a member of S.
Can you give another name for the set S defined above?answer