limit as x approaches infinity from the left (Notation)

Question

This question doesn't involve a specific problem, instead focuses on notation. With limits that approach infinity, is it incorrect to say that the limit approaches infinity from the positive/negative direction?

Answer 1

I'm assuming that you are talking about limits of real quantities (like in a usual calculus class). Then $\infty = +\infty$ can only be approached from the negative direction, and $-\infty$ only from the positive direction. So, for example, writing $x \to \infty^-$ would be redundant, and $x \to \infty^+$ wouldn't make sense.

Answer 2

So, if it is approacing $+ \infty$ then it can only approach it from the negative side. If it is approaching $- \infty$ then it can only approach it from the positive side.

This is due to the fact that when approaching any value, you have to traverse along finite values. Anything in between, and not including, $- \infty$ and $+ \infty$ is considered to be a finite value. So if you were to lie outside of the interval $(- \infty, + \infty)$ you are inevitably dealing with non-finite values which has no place in mathematical expressions, except for comparing cardinalities.