## ORDEREDPAIR

### Ordered pair

In mathematics, an**ordered pair**is a pair of mathematical objects. The order in which the objects appear in the pair is significant: the ordered pair is different from the ordered pair unless

*a*=

*b*.

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### ordered pair

#### Noun

- 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*<math>\langle a, b\rangle</math>.- If an ordered pair were defined (in terms of sets) as <math> (x,y) := \{ \{a\}, \{a, \{b\}\}\} </math> then the "first element" of an ordered pair
*S*could be defined as CAR(S) where CAR(S) =*x*if and only if <math> (\forall y \in S. \, x \in y) </math>. Likewise, the "second element" of*S*could be defined as CDR(S) where CDR(S) =*x*if and only if <math> (\exists y \in S. \, (\exists z \in y. \, x \in z)) </math>. 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 <math> (x,y) := \{ \{a\}, \{a, \{b\}\}\} </math> then the "first element" of an ordered pair

*The above text is a snippet from Wiktionary: ordered pair*

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