Given a sequence $\{x_{n}\}_{n=1}^{\infty}$, then $\lim_{n\to\infty}\{x_n\}=-\infty$ if, for every K, there is an N such that, for every $n \geq N, x_n < K$.
Do we still have the same definition if the sequence indexed by $\mathbb Z$, i.e, $\{x_{n}\}_{n=-\infty}^{\infty}$?
More precisely, I'm looking for a definition of $\lim_{n\to-\infty}\{x_n\}=-\infty$, and $\lim_{n\to+\infty}\{x_n\}=+\infty$.