Prove that in any set of
![2000](/media/m/2/1/6/216477d1d2094f40c748772b62121291.png)
distinct real numbers there exist two pairs
![a > b](/media/m/3/7/5/37594d4b0c0b78e3811a7fc1f992335b.png)
and
![c > d](/media/m/4/5/7/4579d65dae70647d18815ebc05964d03.png)
with
![a \neq c](/media/m/2/5/9/259a0196c1f270c730e05d5d64726f04.png)
or
![b \neq d](/media/m/9/6/a/96ab429c569366709050a47205053c42.png)
such that
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Prove that in any set of $2000$ distinct real numbers there exist two pairs $a > b$ and $c > d$ with $a \neq c$ or $b \neq d$ such that $$
\left| \frac{a-b}{c-d} - 1 \right| < \frac{1}{100000} \text{.}
$$