\begin{definition}[Definition:Set Union/Finite Union]
Let $S = S_1 \cup S_2 \cup \ldots \cup S_n$.
Then:
:$\ds S = \bigcup_{i \mathop \in \N^*_n} S_i = \set {x: \exists i \in \N^*_n: x \in S_i}$
where $\N^*_n = \set {1, 2, 3, \ldots, n}$.
If it is clear from the context that $i \in \N^*_n$, we can also write $\ds \bigcup_{\N^*_n} S_i$.
{{explain|We need a proof that $S_1 \cup S_2 \cup \cdots \cup S_n$ equals the indexed union. See talk page. I've thought about it, Dfeuer's right.}}
\end{definition}