2013 IMO Shortlist A2

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 $$\left|\frac{a-b}{c-d}-1\right|<\frac{1}{100000}$$ (Lithuania)

证明在任何 2000 个不同实数的集合中，存在两对 $a>b$ 和 $c>d$，其中 $a \neq c$ 或 $b \neq d$，使得 $$\left|\frac{a-b}{c-d}-1\right|<\frac{1}{100000}$$ (立陶宛)