I have:

$\displaystyle E_n=[0,2]$ if $\displaystyle n$ is odd, and $\displaystyle [1,4]$ if $\displaystyle n$ is even.

So: $\displaystyle lim \, inf \, E_n = [1,2]$ and $\displaystyle lim \, sup \, E_n = [0,4]$

But what if:

$\displaystyle E_n=[0,1]$ if $\displaystyle n$ is odd, and $\displaystyle [2,n]$ if $\displaystyle n$ is even.

Does that mean: $\displaystyle lim \, sup \, E_n = [0,\infty]$ ?

and$\displaystyle lim \, inf \, E_n$ be?