Ordered Pair Definition

ôrdərd

noun

A pair of numbers that come in a specific order and are usually written in parentheses, such as (3, 5).

American Heritage

(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 .

If an ordered pair were defined (in terms of sets) as then the "first element" of an ordered pair S could be defined as CAR(S) where CAR(S) = x if and only if . Likewise, the "second element" of S could be defined as CDR(S) where CDR(S) = x if and only if . If the two elements happened to be equal, then the ordered pair would still have cardinality two as would be naturally expected.

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