Question 19
Prove that in any set of $2000$ distinct real numbers there exist two pairs $a \gt b$ and $c \gt d$ with $a \neq c$ or $b \neq d$, such that
$$
\left|\frac{a-b}{c-d}-1\right|\lt \frac{1}{100000}
$$
$$
\left|\frac{a-b}{c-d}-1\right|\lt \frac{1}{100000}
$$