Definition:Set Union/Family of Sets/Universal Set

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Definition

Let $\mathbb U$ be a universal set.

Let $I$ be an indexing set.

Let $\family {S_i}_{i \mathop \in I}$ be an indexed family of subsets of $\mathbb U$.


Then the union of $\family {S_i}$ is defined and denoted as:

$\displaystyle \bigcup_{i \mathop \in I} S_i := \set {x \in \mathbb U: \exists i \in I: x \in S_i}$


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