# Tagged Questions

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### An exercise on liminf and limsup

Take a function $f:\mathbb{R}\rightarrow(0,+\infty)$ non-decreasing and such that $\mathrm{lim\;inf}_{n\rightarrow+\infty}(f(n+1)-f(n))>0$ then ...
1answer
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### Inequality involving $\limsup$ and $\liminf$

This may have been asked before, however I was unable to find any duplicate. This comes from pg. 52 of "Mathematical Analysis: An Introduction" by Browder. Problem 14: If $(a_n)$ is a sequence in ...
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### Question about $\liminf$ and $\limsup$ of a sequence

Suppose that a sequence $\{x_k\}$ has a clusterpoint (or more..) $c\in\mathbb{R}$. what conclusion, if any, can be drawn about either $\liminf x_k$ or $\limsup x_k$ ? I don't know the conclusion... ...
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### $\liminf$ of difference of two sequences

Let ${a_k}$, ${b_k}$ be two sequences in $\mathbb{R}$. Suppose ${a_k}$ converges to $a$ s.t. $\liminf_{k \to \infty} {a_k} = \lim_{k \to \infty} {a_k} = a$. Is it then true that \$\liminf_{k \to ...