Set
Elementary
A set is a collection of different objects, called its elements. Order and repetition do not matter: $\lbrace 1, 2 \rbrace$, $\lbrace 2, 1 \rbrace$, and $\lbrace 1, 1, 2 \rbrace$ are the same set.
Graduate (axiomatic set theory)
A set is an object of a set theory such as ZFC. By the axiom of extensionality, a set is determined entirely by its elements.
Properties
- Not every collection is a set: the collection of all sets is not a set (Russell’s paradox).