The ordered pair associated to $A$ and $B$ is the set $(A,B)$ defined by
\[ (A,B)\mathrel {\smash {\overset {\mathclap {\scriptscriptstyle \text{def}}}=}}\left\{ \left\{ A\right\} ,\left\{ A,B\right\} \right\} . \]
-
(b)
We have $A=C$ and $B=D$.
4.3.4 Ordered Pairs
Let $A$ and $B$ be sets.
Let $A$ and $B$ be sets.
Proof of Proposition 4.3.4.1.2.
Item 1: Uniqueness
See Theorem 1.2.3 of [Ciesielski, Set Theory for the Working Mathematician].
