Union

Let $A$ and $B$ be sets . Their union is

More generally, for an indexed family $(A_i)_{i\in I}$ of sets, the union is

Union is dual to intersection and interacts with subset via monotonicity: if $A \subseteq B$ then $A \cup C \subseteq B \cup C$.

Examples:

• $\{1,2\} \cup \{2,3\} = \{1,2,3\}$.
• $(0,1) \cup (1,2) = (0,2)\setminus\{1\}$.
• If $A_i = \{i\}$ for $i\in\{1,2,3\}$, then $\bigcup_{i} A_i = \{1,2,3\}$.