Phrase guide

totally ordered

adj · 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

adj

Meaning 1

That is equipped with a total order, that is a subset of (the ground set of) a partially ordered set whose partial order is a total order with respect to said subset.

Definition source: English Wiktionary via Wiktextract

Usage: not-comparable

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

Examples

  • 1976, K. D. Stroyan, W. A. J. Luxemburg, Introduction to the Theory of Infinitesimals, Harcourt Brace Jovanovich (Academic Press), page 67, (A.2.5) THEOREM If A is a totally ordered ring and if I is a proper order ideal, then A/I is a totally ordered ring (with the operations and order given above).

Meaning relationships

Synonyms: none provided

Antonyms: none provided

Broader terms: partially ordered

History

Etymology

No etymology was provided for this word.

Across languages

Translations

2 source translations are retained for this English entry.

  • German: total geordnet — that is equipped with a total order
  • Polish: liniowy — that is equipped with a total order