Example 2 If for any $x \in A, y \in B (A \subseteq \mathbf{R}, B \subseteq \mathbf{R})$ there is a uniquely determined $f(x, y)$ corresponding to it, then $f(x, y)$ is called a binary function of $x$ and $y$.
Now, a binary function $f(x, y)$ that satisfies the following properties is defined as a generalized "distance" for real numbers $x$ and $y$:
(1) Non-negativity: $f(x, y) \geqslant 0$, with equality if and only if $x=y$;
(2) Symmetry: $f(x, y)=f(y, x)$;
(3) Triangle inequality: $f(x, y) \leqslant f(x, z)+f(z, y)$ for any real number $z$.
Now, two binary functions are given. Please select all that can serve as a generalized "distance" for $x, y$:
(1) $f(x, y)=|x-y|$;
(2) $f(x, y)=(x-y)^{2}$
(3) $f(x, y)=\sqrt{x-y}$.
The correct sequence numbers are . $\qquad$
Solution: Only (1) satisfies all three properties; where (2) does not satisfy property (3), (3) does not satisfy property (2), thus the correct answer is (1).