Definition of a limit at infinity in which $x\to\infty$

Question

I was wondering, what is the definition of a limit in which $x$ tends to $+\infty$ and the result is $+\infty$?

Example:

$$\lim\limits_{x\to\infty}\ln x = \infty$$

Answer 1

For every $L>0$, there exists some $M>0$, for every $x\geq M$, then $f(x)\geq L$.

Whether or not those inequalities are strict does not matter.