well-order

短语

[计] 良序

词形变化

well-orders 复数 well-orders well-ordered well-ordering well-orders 三单 well-ordering 现在分词 well-ordered 过去式 well-ordered 过去分词

别名

well order

释义与例句

n.
  1. 1.

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

    数学

    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.

    2001, Robert L. Vaught, Set Theory: An Introduction, Springer (Birkhäuser), 2nd Edition, Softcover, page 71, Some simple facts and terminology about well-orders were already given in and just before 1.8.4. Here are some more: In a well-order A, every element x is clearly of just one of these three kinds: x is the first element; x is a successor element - i.e., x has an immediate predecessor; or x is a limit element - i.e., x has a predecessor but no immediate predecessor. The structure (∅, ∅) is a well-order.

v.
  1. 1.

    To impose a well-order on (a set).

    及物 数学

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

    1950, Frederick Bagemihl (translator), Erich Kamke, Theory of Sets, 2006, Dover (Dover Phoenix), page 111, Starting from these special well-ordered subsets, it is then possible to well-order the entire set.

    1975 [The Williams & Wilkins Company], Dennis Sentilles, A Bridge to Advanced Mathematics, Dover, 2011, page 182, To carry the analogy a bit further, the axiom of choice implies the ability to well order any set.