lim sup of a sequence of sets $(E_n)$ is defined as $$\bigcap_{n = 1}^{\infty}\bigcup_{k = n}^{\infty} E_k$$
and this means that an element ins lim sup $E_n$ is a member of infinitely many of the sets $E_k$. Or in probability theory its the probability that the event occurs infinitely often.
But just as for the sake of understanding I'm wondering what difference it would make if we considered starting from say, $n = 5$ instead.
$$\bigcap_{n = 5}^{\infty}\bigcup_{k = n}^{\infty} E_k$$
It seems like this won't make a difference as we only really care about what happens as n gets very large?