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How does the maximum distance between adjacent values vary for increasing $n$

That is, when is the $\underset{n \to \infty}{\lim} \max (X_i-X_{i-1})\rightarrow 0$, where $1<i\leq n$, and $X_i\geq X_{i-1}$ and when is the limit $\neq 0$? The question supposes that the ...
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