Question 16
Let $a_1$, $a_2$, ... be an infinite sequence of real numbers, for which there exists a real number $c$ with $0 \leq a_i \leq c$ for all $i$, such that
$$ \left|a_{i}-a_{j}\right|\geq\frac{1}{i+j}\quad\text{for all }i,j\text{ with }i\neq j. $$
Prove that $ c \geq 1 $.
$$ \left|a_{i}-a_{j}\right|\geq\frac{1}{i+j}\quad\text{for all }i,j\text{ with }i\neq j. $$
Prove that $ c \geq 1 $.