Why std::hash<int> seems to be identity function

Question

#include <iostream>

int main() {
    std::hash<int> hash_f;
    std::cout << hash_f(0) << std::endl;
    std::cout << hash_f(1) << std::endl;
    std::cout << hash_f(2) << std::endl;
    std::cout << hash_f(3) << std::endl;
}

I compile with "g++ main.cpp -std=c++11" and then the result is :

0
1
2
3

Why is this happening? I don't use any library and I don't have a specialized hashing function.

Addendum : I wanted to define the hash for an unordered_set of unordered_set of int with the hash of a set being the sum of its components hashs, but if it's just identity it's not cool because the hash of {2,4} is the same than the hash of {1,5}. The simplest way to avoid that is may be to use the std::hash double function.

Answer 1

It seems its identity, its allowed as its distinct.. From cpp reference

The actual hash functions are implementation-dependent and are not required to fulfill any other quality criteria except those specified above. Notably, some implementations use trivial (identity) hash functions which map an integer to itself. In other words, these hash functions are designed to work with unordered associative containers, but not as cryptographic hashes, for example. ....