Talk:Equality of Ordered Pairs

Wouldn't it be fair to say that this is the (or an) abstract definition of ordered pairs? The Kuratowski construction is common, but it was not the first (Smullyan and Fitting say the first construction was by Wiener, defining $\langle x, y \rangle$ as $\{\{\varnothing, \{x\}\}, \{\{y\}\}\}$). I believe that some texts that fully accept the axiom of foundation define $\langle x, y \rangle$ as $\{x, \{x, y\}\}$. In any case, the notion of an ordered pair predates set theory, and is a concept deserving independent axioms (specifically, this one). --Dfeuer (talk) 16:52, 22 March 2013 (UTC)


 * Work in progress. --prime mover (talk) 18:52, 25 January 2020 (EST)