ordered pair

Noun

 * 1)  An object containing exactly two elements in a fixed order, so that, when the elements are different, exchanging them gives a different object. Notation: (a, b) or $$\langle a, b\rangle$$.
 * If an ordered pair were defined (in terms of sets) as $$ (x,y) := \{ \{a\}, \{a, \{b\}\}\} $$ then the "first element" of an ordered pair S could be defined as CAR(S) where CAR(S) = x if and only if $$ (\forall y \in S. \, x \in y) $$. Likewise, the "second element" of S could be defined as CDR(S) where CDR(S) = x if and only if $$ (\exists y \in S. \, (\exists z \in y. \, x \in z)) $$. If the two elements happened to be equal, then the ordered pair would still have cardinality two as would be naturally expected.

Translations

 * Chinese:
 * Mandarin: 有序對
 * Czech: uspořádaná dvojice
 * Finnish: järjestetty pari
 * French:
 * Galician: par ordenado
 * German:
 * Greek:
 * Hungarian:
 * Italian:, coppia ordinata
 * Japanese: 順序対
 * Korean: 순서쌍
 * Maori: takirua raupapa
 * Polish: para uporządkowana
 * Portuguese: par ordenado
 * Russian: упоря́доченная па́ра,
 * Spanish: par ordenado
 * Swedish: ordnat par
 * Tagalog: kapid na ayos