How can two sets be equal even when their members are listed in different orders?

In set theory, two sets are considered equal if they contain exactly the same members, regardless of the order in which those members are listed.1

This principle is rooted in the axiom of extensionality, which establishes that a set is determined solely by its members rather than by how they are arranged or described. Because a set is defined as a collection of objects, the membership relation is the only factor that dictates identity. If every element of set A is an element of set B, and every element of set B is an element of set A, then A and B are the same set (symbolized as A = B).21

Consequently, listing elements in a different order does not change the identity of the set because the underlying collection of objects remains identical.1