| 释义 |
▪ I. well-ˈordering, vbl. n.
a. gen. The property of being well-ordered.
a1586Sidney Apol. Poetrie (Arb.) 21 The well ordering of a banquet. 1614Markham (title) Cheape and Good Husbandry, for the well-Ordering of all Beasts, and Fowles. 1668Pepys Diary 16 Sept., The well-ordering of the men [at a muster of the Guards].
b. spec. in Math.; also, a well-ordered set. Freq. attrib.
1941Birkhoff & MacLane Survey Mod. Algebra i. 9 The integers have one further important property, not characteristically algebraic and not shared by other number systems. This is the well-ordering principle. 1963W. V. Quine Set Theory 145 Well-orderings are notable for their exemplary behavior. 1966Math. Rev. XXXI. 6/1 Only denumerable well-orderings are considered. 1970A. G. Howson Handbk. Terms Algebra & Analysis xvi. 80 Zermelo's Well-Ordering Theorem states that if X is any set whatsoever, then there exists a well-ordering of X.
So well-ˈorder v. trans., to arrange the elements of (a set) in such an order as to produce a well-ordered set.
1944Ann. Math. Stud. xiii. 117 For a finite set can be well-ordered in obvious fashion and hence must obey the axiom of choice. 1966McGraw-Hill Encycl. Sci. & Technol. XII. 206/1 One considers the collection Z of all subsets of X, selects a point xα = f(zα) from each element zα of Z, and well orders X so that [etc.].
▪ II. well-ˈordering, ppl. a.
1668R. Steele Husbandman's Calling x. (1672) 246 The over-ruling and well-ordering hand of God. |