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)[reply]