Using Kleene Star to define set of all tuples?

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How is a set $S$ of all the ordered tuples with elements from universe $\mathbb U$ defined? For instance, $S = \{(), (x), (x,y), (x, (x,y))...\} \land x,y \in \mathbb U$. Is the Kleene Star function composed $n$ times and summed $S =\cup_{i=1}^\infty \star^{(i)} (\mathbb U)$ the solution? If not, what is?