How does the notation of limits read in plain English? (3)

Question

How does the following notation read in plain English:

I can't interpret it myself.

$$a^+ = \lim\limits_{0 < \epsilon \to 0} a + \epsilon$$

Ref. Hwei Hsu. Page-39. ... (B) Properties of $F_{X}(x)$

Answer 1

The $0<\epsilon\to 0$ says "epsilon, greater than zero, approaches 0."

Epsilon is approaching 0, and at the same time, epsilon is always positive. We could also say epsilon is approaching 0 "from the right" as this is how we visualize it on the number line.

This line is introducing the notation $0^+$ (or $a^+$) as $\epsilon \to 0^+$ is less clunky to write.

Answer 2

$0 < \epsilon \to 0$ in the subscript means $\epsilon$ approaches $0$ from the right, so, as already mentioned, this reads as "the limit of $a + \epsilon$ as $\epsilon$ approaches $0$ from the right".