Consider [sets](Sets.md) $A$ and $B.$ The _intersection_ between $A$ and $B$ is the set containing all elements that are in both $A$ and $B.$ This is denoted as $A\cap B$ ^980462 %%Should you bother even including that this is commutative? this is too obvious of a property%% # Disjoint sets Two sets are said to be _disjoint_ if $A\cap B=\emptyset$ where $\emptyset$ is the [empty set.](The%20null%20set.md) # Intersections of multiple sets We denote an [intersection](Intersection%20of%20sets.md) between multiple sets as: $\bigcap_{i=1}^n S_i = S_1 \cap S_2 \cap ... \cap S_n$ Since the [intersection](Intersection%20of%20sets.md) of multiple sets necessarily includes only elements that are common among of these sets, the intersection is associative, meaning that $(S_1 \cap S_2)\cap S_3= S_1 \cap (S_2\cap S_3)= S_1 \cap S_2\cap S_3$ #MathematicalFoundations/SetTheory