Hi

Kinda of a fundamental question here.

When does one say that a limit exists or not exist?

For example)

$\displaystyle \displaystyle\lim_{x\to 0^{+}} \frac{1}{x} = \infty $

This limit exists and is equal to infinity?

Is a typical case of a limit NOT existing $\displaystyle \displaystyle\lim_{x\to 0} \frac{|x|}{x} $ ? Because the limit is either negative one or plus one depending on if you approach zero from left or right.

How can we really say that a limit 'equals' infinity? Infinity is not a number.

Thx