A binary operator $f$ on a set $X$ is commutative if $f(x, y)=f(y, x)$ for all $x, y \in X .$ In state whether the given function $f$ is a binary operator on the set $X .$ If $f$ is not a binary operator, state why. State whether or not each binary operator is commutative.
$$
f(x, y)=x / y, \quad X=\{0,1,2, \ldots\}
$$