Phrase guide

total order

noun · 1 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 partial order, ≤, (a binary relation that is reflexive, antisymmetric, and transitive) on some set S, such that any two elements of S are comparable (for any x, y ∈ S, either x ≤ y or y ≤ x).

Definition source: English Wiktionary via Wiktextract

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

Examples

  • 2013, Nick Huggett, Tiziana Vistarini, Christian Wüthrich, 15: Time in Quantum Gravity, Adrian Bardon, Heather Dyke (editors), A Companion to the Philosophy of Time, Wiley, 2016, Paperback, page 245, A binary relation R defines a total order on a set X just in case for all x, y, z ∈ X, the following four conditions obtain: (1) Rxx (reflexivity), (2) Rxy & Ryz → Rxz (transitivity), (3) Rxy & Ryx → x = y (weak antisymmetry), and (4) Rxy ∨ Ryx (comparability). Bearing in mind that the relata of the total order are not events in E, but entire equivalence classes E/S of simultaneous events, it is straightforward to ask ≤ to be a total order of E/S.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

No etymology was provided for this word.

Across languages

Translations

8 source translations are retained for this English entry.

  • Czech: lineární uspořádání — partial order that applies an order to any two elements
  • Czech: úplné uspořádání — partial order that applies an order to any two elements
  • Esperanto: tuteca ordo — partial order that applies an order to any two elements
  • Finnish: täydellinen järjestys — partial order that applies an order to any two elements
  • German: Totalordnung — partial order that applies an order to any two elements
  • German: totale Ordnung — partial order that applies an order to any two elements
  • Polish: porządek liniowy — partial order that applies an order to any two elements
  • Spanish: orden total — partial order that applies an order to any two elements