Can the letter $\epsilon$ be defined as a parameter instead of the conventional meaning?

Question

If in some sections of my proof, $\epsilon$ represents the common meaning of the small variable approaching zero, while in another section of the proof, $\epsilon $ is defined as a parameter, would it be considered "unconventional notation" or "bad grammar"?

Answer 1

That is indeed an unconventional notation, but not bad grammar at all. On the other hand, it is not at all a good option to use, within a single proof, the same symbol for two different objects.