Indicator function maps subset elements to 1, others to 0. Common notations include IA, χA, KA, or just A. Equivalent to Iverson bracket notation ⟦x ∈ A⟧
A set A is a subset of B if all elements of A are in B. Inclusion (or containment) is the relationship between sets. A k-subset contains k elements. The empty set is a vacuously subset of any set
Complement of set A is elements not in A. Absolute complement of A in universe U is elements in U not in A. Absolute complement is denoted by or A′. Absolute complement is generally not a set itself
Empty set is the unique set with no elements and zero cardinality. Common notations include {} and ∅, introduced by Bourbaki group in 1939. Zero was previously used as symbol but now considered improper
Intersection is the set containing all elements present in two or more objects. In set theory, intersection means overlapping area of objects. In geometry, intersection can be point, line, or curve
Sets store multiple items in a single variable. Sets are unordered, unchangeable, and unindexed. Sets are written with curly brackets. Sets cannot contain duplicate values