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In mathematics, a well-order (or well-ordering or well-order relation) on a set S is a total ordering on S with the property that every non-empty subset of S has a least element in this ordering. The set S together with the ordering is then called a well-ordered set.
The meaning of WELL-ORDERED is having an orderly procedure or arrangement. How to use well-ordered in a sentence.
A set \(T\) of real numbers is said to be well-ordered if every nonempty subset of \(T\) has a smallest element. Therefore, according to the principle of well-ordering, \(\mathbb{N}\) is well-ordered.
Well-ordered definition: arranged, planned, or occurring in a desirable way, sequence, etc.. See examples of WELL-ORDERED used in a sentence.
Jan 8, 2017 · Well-ordered set. A set $ \mathbb {P} $ equipped with a binary relation $ \leq $ that satisfies the following conditions: For any $ x,y \in \mathbb {P} $, either $ x \leq y $ or $ y \leq x $. For any $ x,y \in \mathbb {P} $, if $ x \leq y $ and $ y \leq x $, then $ x = y $.
(of a relation) having the property that every nonempty subset of its field has a least member under the relation: less than is well-ordered on the natural numbers but not on the reals, since an open set has no least member
verb. Simple past tense and past participle of well-order. Wiktionary. Advertisement. Well-ordered Sentence Examples. No trace exists of the splendour of the ancient city, with its regular streets, well-ordered plan and numerous public buildings.
Jun 3, 2024 · Definitions of well-ordered. Definitions of. well-ordered. adjective. ordered well. “ well-ordered work habits”. synonyms: regular. in accordance with fixed order or procedure or principle.
Definition of well-ordered adjective in Oxford Advanced American Dictionary. Meaning, pronunciation, picture, example sentences, grammar, usage notes, synonyms and more.
well–ordered. 1 ENTRIES FOUND: well–ordered (adjective) well–ordered /ˌwɛl ˈ oɚdɚd/ adjective. Britannica Dictionary definition of WELL–ORDERED. [more well–ordered; most well–ordered] : carefully organized or controlled. a well-ordered household. well-ordered lives.
