partially ordered set

noun

(set theory, order theory, loosely) A set that has a given, elsewhere specified partial order. / (set theory, order theory, formally) The ordered pair comprising a set and its partial order.

A partially ordered set is a set equipped with a binary relation that satisfies certain properties.

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意味（1）

(set theory, order theory, loosely) A set that has a given, elsewhere specified partial order.

意味（2）

(set theory, order theory, formally) The ordered pair comprising a set and its partial order.

A partially ordered set means a pair (P,≻) consisting of a set P and a partial order ≻ in P. As usual, when the meaning is clear, we may suppress the notation of "≻" and speak of the partially ordered set P.

The ordered fields defined earlier are easily seen to be examples of partially ordered sets.

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partially ordered set

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