Definition:Set Union/Family of Sets/Subsets of General Set

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Definition

Let $I$ be an indexing set.

Let $\left \langle {S_i} \right \rangle_{i \mathop \in I}$ be an indexed family of subsets of a set $X$.


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

$\displaystyle \bigcup_{i \mathop \in I} S_i := \left\{{x \in X: \exists i \in I: x \in S_i}\right\}$


Also denoted as

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

$\displaystyle \bigcup_I S_i$

or, if the indexing set is clear from context:

$\displaystyle \bigcup_i S_i$


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


Sources