Definition
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[1Y2] Given \(I\) a non-empty family of indices and given \(C_ i\) sets (one for each \(iβ I\)), then the union
\[ β_{iβ I}C_ i \]
is a set, which contains all (and only) the elements of all sets \(C_ i\); in formula 1
\[ β_{iβ I}C_ i {\stackrel{.}{=}}\{ x : β iβ I, xβ C_ i\} \quad . \]
If only two sets are given \(C_ 1,C_ 2\), we usually write \(C_ 1βͺ C_ 2\) to indicate the union; and similarly when finite sets are given.