Notation: $f(c^+)$ and $f(c^-)$

Question

My lecturer often does this: $$ \text{Let} \quad f(c^-) = \lim_{x \to c^-} f(x) \quad \text{and} \quad f(c^+) = \lim_{x \to c^+} f(x). $$ Is $f(c^-)$ and $f(c^+)$ standard notation for one-sided limits in calculus? Are there any alternatives that are widely used?

Answer 1

Usually, you write it like $$ f(c^-) = \lim_{x \uparrow c} f(x) \text{ and } f(c^+) = \lim_{x \downarrow c} f(x), $$ and it is just a way of writing the left-sided limit and the right-sided limit.

See this wikipedia article.