Increasing/decreasing notation

Question

I've seen the following notation being used when someone is talking about right-continuous functions:

$$\lim_{x \rightarrow x_0^+} F_X(x) = F_X(x_0),$$

$$\lim_{x \downarrow x_0} F_X(x) = F_X(x_0).$$

Which is the preferred notation, or are both okay?