Definition:Set Union/Countable Union

Definition
In the general definition of union, if the indexing set $I$ or the set of sets $\mathbb S$ is countable, then the term countable union is used.

The union of $X_1, X_2, X_3, \ldots$ is denoted:
 * $X_1 \cup X_2 \cup X_3 \cup \cdots$
 * $\displaystyle \bigcup_{k \mathop = 1}^\infty X_k$
 * $\displaystyle \bigcup_{k \mathop \in \N} X_k$

The first of these is informal and should be avoided.