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. A pair is unordered: For any sets $a$ and $b$,
\[\{a, b\} = \{b, a\}.\]References
- [1]
- Wikipedia contributors. Unordered pair. Wikipedia, The Free Encyclopedia.
- [2]
- Thomas Jech. Set Theory. 3rd Millennium ed, rev. and expanded. Springer, 2002. pp. 6–7.