What is meant by natural ordering of objects in the context of the collections framework?

Java documentation refers to the natural ordering of objects when describing various algorithms and data structures in the collections framework. Object ordering is obviously needed by the sorting algorithms. It is also needed by the specifications of the interfaces such as SortedSet, SortedMap, etc., and the data structures used for container classes such as TreeSet, TreeMap, etc. Unless instructed otherwise via a Comparator object supplied as an argument to the constructor, the default behavior of a class such as TreeSet is to store its objects in an ascending natural order.

The objects of a class exhibit natural ordering if the class has implemented the java.lang.Comparable interface. Such a class must provide an implementation for the compareTo method -- referred to as the class's natural comparison method -- that can then be used by the algorithms and the data structures for comparing data objects. The compareTo method must return a negative integer, a zero, or a positive integer if the object on which it is invoked is less than, equal to, or greater than the argument object.

It is strongly recommended that a class's natural ordering as dictated by the implementation of the compareTo method be consistent with equals. This consistency is achieved if and only if e1.compareTo( (Object) e2 ) == 0 has the same boolean value as e1.equals( (Object) e2 ) for every pair of objects e1 and e2 of the class. Lack of this consistency could elicit strange behavior from the data structures that need to compare objects.

Many of the system supplied classes possess natural ordering. These include String, Integer, Float, Double, Date, File and many others. For the String class, the natural order is lexicographic; it is chronological for the Date class; lexicographic on the pathname for the File class, etc.