New posts in Limsup And Liminf

lim sup and lim inf of sequence of sets.

Properties of $\liminf$ and $\limsup$ of sum of sequences: $\limsup s_n + \liminf t_n \leq \limsup (s_n + t_n) \leq \limsup s_n + \limsup t_n$

Intuitive meaning of Limit Supremum?

limit inferior and superior for sets vs real numbers

Comparing two limsup's

How can we show that if $f$ is convex, then $\liminf_{|x|\to\infty}\frac{x\cdot\nabla f(x)}{|x|}>0$?