• What is a set?
  A finite or infinite collection of unique elements/members (in which order may or may not have significance)
  
• How are sets defined?
  Extension - Listing all of the elements/members
  (e.g., \(S = \{1, 3, 5\}\))
  Intension - Describing the properties of the elements/members
  (e.g., \(T = \{t: 0 \leq t \leq 10\}\))
  

• Definition:
  • A definition of a set that is written by listing the elements (i.e., an extensive definition of a set)
  • The set of elements so defined
• Examples:
  • Months of the Year (Jan, Feb, Mar, Apr, May, Jun, Jul, Aug, Sep, Oct, Nov, Dec)
  • Marital Statuses (Never Been Married, Engaged, Married, Divorced, Widowed)
  • Suits in a Deck of Cards (Clubs Diamonds, Hearts, Spades)
  • Cards in a Deck of Cards (Ace, 2, ..., 10, Jack, Queen, King)

• Value Type or Reference Type?
  • Enumerated types are reference types
• Ordered or Unordered?
  • Enumerated types are ordered (though the order may not be meaningful/useful)

• Identify the Elements:
  • List all of the elements in the set
• Identify the Properties of the Elements:
  • Declare the names and types of attributes
• Identify the Behaviors of the Elements:
  • Declare the signatures of methods
• Refine the Design:
  • Think about ways the design can be improved before your start writing code

• Properties of the Instances:
  • Attributes and behaviors of individual instances (in Java, the non-static variables and methods)
• Properties of the enum:
  • Attributes and behaviors of the set of instances (in Java, the static variables and methods)

Though it is not immediately obvious from the documentation for the Java API, all enumerated types have the following methods "implemented for them".

• Static Methods:
  • values() returns an array containing all of the objects in the set
  • valueOf(String) returns the instance with the specified identifier (or throws IllegalArgumentException)
• Non-Static Methods:
  • int compareTo(E other) which uses the order of the elements
  • boolean equals(E other)
  • ordinal() returns the ordinal value of the instance (0-based)
  • toString() returns a String representation of the identifier

• Suppose:
  • We are designing and implementing a product that needs a calendar
• An Obvious enum:
  • The months of the year

• A "Set" of public static final String Objects:
  • They can only be validated at run-time
  • It is impossible to iterate over the group
• An Array of public static final String Objects:
  • They can only be validated at run-time
  • They need to be referred to by index number
• A "Set" of public static final int Values:
  • They can only be validated at run-time
  • They aren't useful for user interaction (e.g., they are meaningless when printed)
• A Mixed Approach:
  • They can only be validated at run-time
  • Inconsistencies can arise