Last Updated：2025/11/20

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(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 ⟨a,b⟩.

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ordered pair

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Source Word

ordered pair

Noun

(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 ⟨a,b⟩.

Japanese Meaning

順序対：2つの要素が固定された順序で並んでいる組。要素が異なる場合、並び替えると異なる対となる（例：(a, b)）。

What is this buttons?

The professor explained that an ordered pair (a, b) represents two elements in a fixed order, so (a, b) and (b, a) are different when a ≠ b.

Google Translation / DeepL Translation

教授は、順序対 (a, b) が固定された順序で2つの要素を表し、a ≠ b の場合には (a, b) と (b, a) が異なると説明した。

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Sense（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 ⟨a,b⟩.

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 (∀y∈S.,x∈y). Likewise, the "second element" of S could be defined as CDR(S) where CDR(S) = x if and only if (∃y∈S.,(∃z∈y.,x∈z)). 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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ordered pairs

（ plural ）

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ordered pair

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