Set

A set is an idea from mathematics. A set has members (also called elements). A set is defined by its members, so any two sets with the same members are the same (e.g., if set ${\displaystyle {\mathit {X}}}$ and set ${\displaystyle {\mathit {Y}}}$ have the same members, then ${\displaystyle {\mathit {X}}={\mathit {Y}}}$).

A set cannot have the same member more than once. Membership is the only thing that matters. For example, there is no order or other difference among the members. Anything can be a member of a set, including sets themselves (though if a set is a member of itself, paradoxes such as Russell's paradox can happen).