Definition:Set Union/Family of Sets

Definition
Let $I$ be an indexing set.

Let $\left \langle {X_i} \right \rangle_{i \mathop \in I}$ be a family of subsets of a set $S$.

Then the union of $\left \langle {X_i} \right \rangle$ is defined as:


 * $\displaystyle \bigcup_{i \mathop \in I} X_i = \left\{{y: \exists i \in I: y \in X_i}\right\}$

Also denoted as
The set $\displaystyle \bigcup_{i \mathop \in I} X_i$ can also be seen denoted as:


 * $\displaystyle \bigcup_I X_i$

or, if the indexing set is clear from context:


 * $\displaystyle \bigcup_i X_i$

However, on this website it is recommended that the full form is used.