Phrase guide

partially ordered set

noun · 2 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

Pronunciation

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1

noun

Meaning 1

A set that has a given, elsewhere specified partial order.

Definition source: English Wiktionary via Wiktextract

Usage: broadly

Topics: mathematics, order-theory, sciences, set-theory

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

2

noun

Meaning 2

The ordered pair comprising a set and its partial order.

Definition source: English Wiktionary via Wiktextract

Usage: formal

Topics: mathematics, order-theory, sciences, set-theory

Examples

  • 1959 [D. Van Nostrand], Edward James McShane, Truman Arthur Botts, Real Analysis, 2005, Dover, page 28, 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.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

No etymology was provided for this word.

Across languages

Translations

11 source translations are retained for this English entry.

  • Arabic: فِئَةٌ مُرَتَّبَةٌ جُزْئِيًّا (fiʔatun murattabatun juzʔiyyan) — set having a specified partial order
  • Arabic: مَجْمُوعَةٌ مُرَتَّبَةٌ جُزْئِيًّا (majmūʕatun murattabatun juzʔiyyan) — set having a specified partial order
  • Czech: uspořádaná množina — set having a specified partial order
  • Finnish: osittain järjestetty joukko — set having a specified partial order
  • German: partiell geordnete Menge — set having a specified partial order
  • Japanese: 半順序集合 (hanjunjo-shūgō) — set having a specified partial order
  • Polish: częściowy porządek — set having a specified partial order
  • Spanish: conjunto parcialmente ordenado — set having a specified partial order
  • Spanish: poset — set having a specified partial order
  • Spanish: copo — set having a specified partial order
  • Swedish: partiellt ordnad mängd — set having a specified partial order