# limits of sequences

• Oct 11th 2011, 11:33 AM
MathSucker
limits of sequences
I have:

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

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

But what if:

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

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

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