Question 4
Does there exist an infinite sequence of real numbers $\{x_n\}_{n=1}^{+\infty}$ such that $|x_n|\le0.666$ and
$$|x_m-x_n|\ge\frac1{n^2+n+m^2+m}$$
for all distinct positive integers $m,n$?
$$|x_m-x_n|\ge\frac1{n^2+n+m^2+m}$$
for all distinct positive integers $m,n$?