Dictionary

ordered pair en · NOUN

Meanings

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 ⟨a,b⟩.
   • 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 (∀y∈S.,x∈y). Likewise, the "second element" of S could be defined as CDR(S) where CDR(S) = x if and only if (∃y∈S.,(∃z∈y.,x∈z)). If the two elements happened to be equal, then the ordered pair would still have cardinality two as would be naturally expected.

Forms

Relateds

triplet · tuple · triple

Translations (20)

fi järjestetty pari (in set theory) · pl para uporządkowana (in set theory) · tl kapid na ayos (in set theory) · ko 순서쌍 (in set theory) · sv ordnat par (in set theory) · el διατεταγμένο ζεύγος (in set theory) · fr couple (in set theory) · hu rendezett pár (in set theory) · cmn 有序對 /有序对 (in set theory) · it coppia (in set theory) · pt par ordenado (in set theory) · gl par ordenado (in set theory) · mi takirua raupapa (in set theory) · it coppia ordinata (in set theory) · ja 順序対 (in set theory) · ru упоря́доченная па́ра (in set theory) · es par ordenado (in set theory) · de geordnetes Paar (in set theory) · cs uspořádaná dvojice (in set theory) · ru па́ра (in set theory)