Pair

🅟 Feb 16, 2026

  🅤 Jun 23, 2026

Definition 1.

Let $a$ and $b$ be two sets. The pair of $a$ and $b$ is

\[\{a, b\} = \{x : x = a \lor x = b\}.\]

This is a set by Axiom of Pairing.


Proposition 2. Unorderedness.

For any sets $a$ and $b$,

\[\{a, b\} = \{b, a\}.\]