According to the Java Comparable.compareTo(T o) documentation:

It is strongly recommended, but not strictly required that (x.compareTo(y)==0) == (x.equals(y)). Generally speaking, any class that implements the Comparable interface and violates this condition should clearly indicate this fact. The recommended language is "Note: this class has a natural ordering that is inconsistent with equals."

If this rule is violated, weird and unpredictable failures can occur. For example, in Java 5 the PriorityQueue.remove() method relied on compareTo(), but since Java 6 it relies on equals().

Noncompliant Code Example

public class Foo implements Comparable<Foo> {
  @Override
  public int compareTo(Foo foo) { /* ... */ }      // Noncompliant as the equals(Object obj) method is not overridden
}

Compliant Solution

public class Foo implements Comparable<Foo> {
  @Override
  public int compareTo(Foo foo) { /* ... */ }      // Compliant

  @Override
  public boolean equals(Object obj) { /* ... */ }
}