Definition:Ordered Pair/Wiener Formalization

Definition

The concept of an ordered pair can be formalized by the definition:

$\tuple {a, b} := \set {\set {\O, \set a}, \set {\set b} }$

Also see

• Equivalence of Definitions of Ordered Pair

Source of Name

This entry was named for Norbert Wiener.

Historical Note

The Wiener formalization of the ordered pair was devised by Norbert Wiener in $1914$.

According to Set Theory and the Continuum Problem by Raymond M. Smullyan and Melvin Fitting, this was the first such scheme for axiomatising the concept of the ordered pair.

Sources

• 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $2$: Some Basics of Class-Set Theory: $\S 4$ The pairing axiom: Remark