Well-order
noun, verb
noun, verb ·Rare ·Advanced level
Definitions
Noun
- 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 To impose a well-order on (a set). transitive
"The set of positive integers is well-ordered by the relation ≤."
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."