Given real numbers $x$ and $y$, such that
$$
x+y, x-y, x y, \frac{x}{y}
$$

three of the four numbers are identical, find all pairs $(x, y)$ that satisfy this property.
One, Solution: Since $\frac{x}{y}$ is meaningful, then $y \neq 0$, thus $x+y \neq x-y$.
Therefore, $x y=\frac{x}{y}$, which means $x\left(y^{2}-1\right)=0$.
So, $x=0$ or $y= \pm 1$.
(1) If $x=0$, then from $x y=x+y$ or $x y=x-y$, we get $y=0$, which makes $\frac{x}{y}$ meaningless;
(2) If $y=1$, then from $x y=x+y$ we get $x=x+1$, or from $x y=x-y$ we get $x=x-1$, both leading to contradictions;
(3) If $y=-1$, then from $x y=x+y$ we get $x=\frac{1}{2}$,
and from $x y=x-y$ we get $x=-\frac{1}{2}$,
so the pairs that meet the requirements are only $\left(\frac{1}{2},-1\right)$ and $\left(-\frac{1}{2},-1\right)$.