ordered pair

Noun

This text is extracted from the Wiktionary and it is available under the CC BY-SA 3.0 license | Terms and conditions | Privacy policy 0.005

Noun

**ordered pair** (*plural* ordered pairs)

- (
*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.

- If an ordered pair were defined (in terms of sets) as (x,y) := \{ \{a\}, \{a, \{b\}\}\} then the "first element" of an ordered pair

- French: couple
- German: geordnetes Paar
- Italian: coppia, coppia ordinata
- Portuguese: par ordenado
- Russian: упоря́доченная па́ра
- Spanish: par ordenado

This text is extracted from the Wiktionary and it is available under the CC BY-SA 3.0 license | Terms and conditions | Privacy policy 0.005