Question 67
Find all positive real numbers $t$ with the following property: there exists an infinite set $X$ of real numbers such that the inequality
$$
\max\{|x-(a-d)|, |y-a|, |z-(a+d)|\} \gt td
$$
holds for all (not necessarily distinct) $x, y, z \in X$, all real numbers $a$ and all positive real numbers $d$.
$$
\max\{|x-(a-d)|, |y-a|, |z-(a+d)|\} \gt td
$$
holds for all (not necessarily distinct) $x, y, z \in X$, all real numbers $a$ and all positive real numbers $d$.