English
ordered pair
Noun

ordered pair (plural ordered pairs)

1. (set theory) 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.
Related terms Translations
• French: couple
• German: geordnetes Paar
• Italian: coppia, coppia ordinata