My formal automata class might have used non-standard terminology, but what I was taught was that while A: Aa and A: ε are productions, A: Aa | ε is just a shorthand to combine the two. Since there is only one start variable, A: Aa | ε is the entire grammar as well. a* is the regular expression representing the language for this grammar.
> but what I was taught was that while A: Aa and A: ε are productions
Huh? This is the exactly what I also just said, in response to the different claim you made above, which was that the production is merely "A" rather that "A: Aa" or "A: ε". If you're claiming they are somehow equal (which they clearly are not... one is a symbol and the other is a rule mapping that symbol to a sentential form) then I'm confused how you think A and a* were any less equal to begin with...
