Well-order

noun, verb

noun, verb ·Rare ·Advanced level

Definitions

Noun
  1. 1
    A total order of some set such that every nonempty subset contains a least element.

    "1986, G. Richter, Noetherian semigroup rings with several objects, G. Karpilovsky (editor), Group and Semigroup Rings, Elsevier (North-Holland), page 237, ̲X is well-order enriched iff every morphism set ̲X(X,Y) carries a well-order ≤_(XY) such that f≨_(XY)g⇒h•f≨_(XY)h•g for every h:Y→Z."

Verb
  1. 1
    To impose a well-order on (a set). transitive

    "The set of positive integers is well-ordered by the relation ≤."

Synonyms

All synonyms
well-ordering

Example

More examples

"1986, G. Richter, Noetherian semigroup rings with several objects, G. Karpilovsky (editor), Group and Semigroup Rings, Elsevier (North-Holland), page 237, ̲X is well-order enriched iff every morphism set ̲X(X,Y) carries a well-order ≤_(XY) such that f≨_(XY)g⇒h•f≨_(XY)h•g for every h:Y→Z."

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Data sourced from Wiktionary, WordNet, CMU, and other open linguistic databases. Updated March 2026.