For example, the example in the book: the corresponding relationship between the country and the capital, which is a good mapping example.

Function is a special case of mapping, so why is function a special case of mapping? The reason is that the function is a mapping of counting, but in my example above, it is also a mapping, but it is not the corresponding relationship of counting, so it cannot be called a function.

The mapping we usually need is actually a function expression. For example, the mapping between natural numbers and positive even numbers is: F(n)=2n.

I hope my understanding can help you.