Applications Data Structures and Algorithms with Object-Oriented Design Patterns in Java Applications One of the most important applications of partitions involves the processing of equivalence relations.
Equivalence relations arise in many interesting contexts.
In effect, the wires establish an electrical equivalence relation over the nodes of a circuit. A similar relation arises among the classes in a Java program. In effect, the class declarations establish an equivalence relation over the classes in a Java program. That is, for every , . That is, for every pair and , if then .