Union

A union is the set obtained by collecting all elements that lie in at least one set in a given collection. For sets $A,B$,

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

Union is dual to intersection and interacts with complement via De Morgan’s laws in an ambient universe.

Examples:

• $\{1,2\}\cup\{2,3\}=\{1,2,3\}$.
• If $A_n=\{n\}$ for $n\in\mathbb{N}$, then $\bigcup_{n\in\mathbb{N}} A_n=\mathbb{N}$.