set-theory

A set theory library for Java, including the ability to create sets (collection-like structures with no duplicates) of any type. These sets support a wide variety of widely-used set operations including union, intersection, complement, difference, Cartesian product, and subset detection. Additionally, sets support elementhood tests and discrete/uncountable cardinalities. Discrete sets can also be converted into arrays.

The Set Class

The set class is an abstract class that contains a variety of basic methods that all sets have (though infinite sets may not be able to perform all these methods in all circumstances). Sets contain elements of some singular type. These methods (for a Set of type T) are as follows:

Method	Return Type	Description
cardinality()	int	Finds the cardinality of the set (the number of elements).
unionWith(Set a)	Set	Gives a set with all the elements of either of the two sets.
intersectionWith(Set a)	Set	Gives a set containing all the elements that are in both of the two sets.
differenceWith(Set a)	Set	Gives a set containing all the elements of the receiver that are not in the argument.
productWith(Set a)	Set	Gives the Cartesian product of the two sets, that is, a set containing ordered pairs where the domain of the points is the receiver, and the range of them is the argument.
complement()	Set	Gives a set containing exclusively all the elements not in the original set.
powerSet()	Set	Gives a set containing all the subsets of the original set.
contains(T e)	boolean	Tests whether the set contains the argument.
isSubset(Set a)	boolean	Tests whether or not the argument is a subset of the receiver set.
equals(Object a)	boolean	Tests if the sets contain exclusively all the same elements.
existsElementSatisfying((T)->boolean c)	boolean	Tests if there is an element in the set that satisfies the condition.
allElementsSatisfy((T)->boolean c)	boolean	Tests if all elements in the set satisfy the condition.
toArray()	T[]	Gives an array with all the elements of the set.
isDiscrete()	boolean	Tests if the set is discrete or not.

The DiscreteSet Class

This class inherits Set and represents sets containing discrete elements. In addition to all the methods listed above, DiscreteSet also has the following constructors for a DiscreteSet containing elements of type T:

Constructor	Description
DiscreteSet(T... elements)	Makes a DiscreteSet containing all the arguments.
DiscreteSet()	Makes an empty DiscreteSet.
DiscreteSet(ArrayList<T> elements)	Makes a DiscreteSet containing all the elements of the argument.

This class also has two additional methods:

Method	Return Type	Description
add(T e)	void	Adds the argument to the set.
remove(T e)	void	Removes the element from the set.
toString()	String	Returns a String formatted as a list of the elements of the set, seperated by commas, inside brackets

The Complement Class

Complement inherits from class and represents a set that is defined as some other set's compliment, a set which exclusively contains elements that the original does not. Because these sets are defined by what they don't include, not by what they do include, they have infinite cardinality. The Complement class has the following constructor

Constructor	Description
Complement(Set a)	Creates a complement with all the elements not in the argument.

This class also inherits a toString method from Object:

Method	Return Type	Description
toString()	String	Returns a String formatted "complement: " followed by the string representing the complemented set.

This class has no additional methods beyond what it inherits from Set and Object.

OrderedPair

OrderedPair is a class that contains an ordered pair, or two ordered values. These two values are the domainVal of type T and the rangeVal of type S, which are the only two instance variables. This class exists to support the productWith() method. This product has the following constructor:

Constructor	Description
OrderedPair(T _domainVal,S _rangeVal)	sets the domain and range values to the arguments

This product has/overrides the following methods:

Method	Return Type	Description
getDomainVal()	T	returns domainVal
getRangeVal()	S	returns rangeVal
setDomainVal(T e)	void	sets domainVal to the argument
setRangeVal(S e)	void	sets rangeVal to the argument
toString()	String	returns a string of the format "("+domainVal+","+"rangeVal"+")"
equals(Object ob)	boolean	returns whether the argument object is an OrderedPair with identical domain and range values

Condition

Condition is an interface used to support the use of condition lambdas on elements of type T in the Set class. It has one method, satisfiedBy(T element), which returns a boolean.