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?