Talk:Rational set

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I think there is a typo: Kleene star is defined as ${\displaystyle A\in \mathrm {RAT} (N)}$ then ${\displaystyle A^{*}=\bigcup _{i=1}^{\infty }A^{i}\in \mathrm {RAT} (N)}$ where ${\displaystyle A^{1}=A}$ and ${\displaystyle A^{n+1}=A^{n}\cdot A}$ (${\displaystyle \cdot }$ meaning concatenation). It cannot be subsequent products since ${\displaystyle |A^{1}\times A^{n+1}|\leq \mathrm {max} (|A^{1}|,|A^{n+1}|)}$, but, Kleene star generates infinite strings. Wvxvw (talk) 19:37, 17 January 2016 (UTC)Reply

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)Reply

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)Reply

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)Reply

Corrected Arthur MILCHIOR (talk) 01:47, 11 July 2016 (UTC)Reply