Subsection 2.3.6 (003E): Unions of Families

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Table of Contents
Part 1: Sets
Chapter 2: Constructions With Sets
Section 2.3: Operations With Sets
Subsection 2.3.6: Unions of Families (cite)

2.3.6 Unions of Families

Let $\webleft\{ A_{i}\webright\} _{i\in I}$ be a family of sets.

Definition 2.3.6.1.1 ▶ Unions of Families

The union of the family $\webleft\{ A_{i}\webright\} _{i\in I}$ is the set $\bigcup _{i\in I}A_{i}$ defined by

\[ \bigcup _{i\in I}A_{i} \mathrel {\smash {\overset {\mathclap {\scriptscriptstyle \text{def}}}=}}\webleft\{ x\in F\ \middle |\ \text{there exists some $i\in I$ such that $x\in A_{i}$}\webright\} , \]

where $F$ is the set in the axiom of union, of .

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