Set

A set is an object $A$ for which statements of the form $x\in A$ (read “$x$ is an element of $A$”) are meaningful, and whose identity is determined by extensionality: for sets $A,B$,

Many basic constructions in set theory are specified by describing their elements, such as union , intersection , and the power set .

Examples:

• The set of natural numbers $\mathbb{N}$ (see natural numbers ).
• For a real number $a$, the singleton $\{a\}=\{x : x=a\}$ is the set containing exactly the element $a$.