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

  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 <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.


The above text is a snippet from Wiktionary: ordered pair
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