Do cryptographic hash functions reach each possible values, i.e., are they surjective?

Question

Take a commonly used binary hash function - for example, SHA-256. As the name implies, it outputs a 256 bit value.

Let A be the set of all possible 256 bit bina

Answer 1

It really depends on the hash function. If you use this valid hash function:

Int256 Hash (string input) {
    return 0;
}

then it is obvious that C != A. So the "for example, SHA256" is a pretty important note to consider.

To answer your actual question: I believe so, but I'm just guessing. Wikipedia does not provide any meaningful info on this.