My textbook states that the definition for $A_{n}$ occurs infinitely often is:
$\limsup\limits_{n \to \infty} A_{n} = \cap_{n=1}^{\infty}(\cup_{m \geq n}A_m) = \lim_{n \to \infty} (\cup_{m \geq n} A_m)$
I don't understand how we get the second equality. Is it just because another way to look at the limit is just an infinite intersection? And we don't have a similar equality for $\liminf\limits_{n \to \infty} A_n = \cup_{n=1}^{\infty}(\cap_{m \geq n} A_m)$ because we have an infinite union so we couldn't write that as a limit, is that right?