I'm taking a uni Calc. 1 course, and have come across something I have never seem before while reading on the arithmitic laws of infinite limits. One law states:

$$ 1/0^+=\infty $$

and another law states: $$ 1/\infty = 0^+ $$

What does $0^+$ mean?


Assume that we want to compute $$L=\lim_{x\to a}\frac{1}{f(x)}$$ with $$\lim_{x\to a}f(x)=0.$$

So $$L=\frac 10$$ and we cannot say neither $L=-\infty $, nor $ L=\infty $

But, if the function $ f $ is positive near the point $ a$, then we write $$L=\frac{1}{0^+}=+\infty$$ For example, we have $$\lim_{x\to 1^-}\frac{1}{\ln(2-x)}=\frac{1}{0^+}=+\infty$$ and if $ f $ is negative then $$L=\frac{1}{0^-}=-\infty$$