Precise definition of "functional interface" in Java 8

Question

Recently I started exploring Java 8 and I can't quite understand the concept of "functional interface" that is essential to Java's implementation of lambda expressions. There is a pretty comprehensive guide to lambda functions in Java, but I got stuck on the chapter that gives definition to the concept of functional interfaces. The definition reads:

More precisely, a functional interface is defined as any interface that has exactly one abstract method.

An then he proceeds to examples, one of which is Comparator interface:

public interface Comparator<T> {
    int compare(T o1, T o2);
    boolean equals(Object obj);
} 

I was able to test that I can use a lambda function in place of Comparator argument and it works(i.e. Collections.sort(list, (a, b) -> a-b)).

But in the Comparator interface both compare and equals methods are abstract, which means it has two abstract methods. So how can this be working, if the definition requires an interface to have exactly one abstract method? What am I missing here?

Answer 1

From the same page you linked to:

The interface Comparator is functional because although it declares two abstract methods, one of these—equals— has a signature corresponding to a public method in Object. Interfaces always declare abstract methods corresponding to the public methods of Object, but they usually do so implicitly. Whether implicitly or explicitly declared, such methods are excluded from the count.

I can't really say it better.