TITLE: Limit Notation: $ \lim_{x \to \infty} f(x) =\infty $ or $ \lim_{x \to \infty} f(x) \rightarrow \infty$?
QUESTION [12 upvotes]: If $f(x) \to \infty $ as $x \to \infty $, 
Which of the following statements would be more correct:
$I.$ $$ \lim_{x \to \infty} f(x) =\infty $$
Or
$II. $ $$ \lim_{x \to \infty} f(x) \rightarrow  \infty $$
I thought $II$ would be more appropriate?

REPLY [10 votes]: First one is correct; "→" generally means "tend(s) to".  Limits either equal something (or +/- inf) or don't exist; they do not tend to something.