Can a limit approaching positive infinity be right sided?

Question

In other words is $\lim_{x \to \infty^{+}} f(x)$ ever meaningful/defined? Seems like it's intrinsically an implicit left sided limit to approach positive infinity. Also curious for the mirror case, left hand limit approaching negative infinity.

Answer 1

This kind of convention is not used and is meaningless since $\infty$ is not a numbers but if we want to define accordingly to the others, forcing the definition, we should consider it as a “left side limit” as for $1^-$ on the interval $(0,1)$.

A definition for $(0, \infty)$ could be something like this

• $lim_{\infty^-}:= \lim_{a^-}$ as $a\to \infty$

But It doesn’t seem to be needed to define nor useful.