Intersection

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

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

Intersection is related to union by De Morgan-type dualities once a complement is fixed.

Examples:

• $\{1,2\} \cap \{2,3\} = \{2\}$.
• $[0,2] \cap (1,3) = (1,2]$.
• If $A_i = \mathbb{R}\setminus\{i\}$ for $i\in\{1,2\}$, then $\bigcap_i A_i = \mathbb{R}\setminus\{1,2\}$.