Talk:Rational set

Definition of Kleene star
I think there is a typo: Kleene star is defined as $$A\in \mathrm{RAT}(N)$$ then $$A^*=\bigcup_{i=1}^\infty A^i \in\mathrm{RAT}(N)$$ where $$A^1=A$$ and $$A^{n+1}=A^n \cdot A$$ ($$\cdot$$ meaning concatenation). It cannot be subsequent products since $$|A^1\times A^{n+1}|\leq \mathrm{max}(|A^1|, |A^{n+1}|)$$, but, Kleene star generates infinite strings. Wvxvw (talk) 19:37, 17 January 2016 (UTC)
 * I do not understand this remark. In particular, Kleene star does not generate infinite strings. It only generate infinite set of finite string Arthur MILCHIOR (talk) 01:47, 11 July 2016 (UTC)
 * Yes, at the time I wrote the comment I was reading an automata book for the class. I didn't have a good idea of what Kleene star does. So, what I wrote doesn't make sense... However, I have a suggestion to make: to make the example more complete it would be nice to add examples of monoid's operation and the product. When I think about it, I mentally translate monoid's operation into concatenation, but in the context of automata I don't really know what to make of the product (I don't think that the product as defined for automata is the same one meant here).Wvxvw (talk) 05:38, 11 July 2016 (UTC)

Wording in example section
Indeed this language may be defined by a finite regular expression.

But no language has been previously defined... what language is this talking about? Also regular expressions are necessarily finite, there is no need to emphasize this fact.

I imagine that the original idea of this passage was something like: "Indeed, all these languages are precisely the languages defined by regular expressions over A*". Does this make sense? Wvxvw (talk) 19:50, 17 January 2016 (UTC)
 * Corrected Arthur MILCHIOR (talk) 01:47, 11 July 2016 (UTC)