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- Dictionarywell ordered
adjective
- 1. arranged or organized in an orderly way: "the only rash decision of his well-ordered life"
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Learn the meaning of well-ordered as an adjective for having an orderly procedure or arrangement, or as a noun for a type of ordering of elements. See examples, synonyms, word history, and related entries.
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.
Well-ordered definition: arranged, planned, or occurring in a desirable way, sequence, etc.. See examples of WELL-ORDERED used in a sentence.
A well order is a total order where every non-empty subset has a least element. Learn how to define and use well orders, see examples and the well-ordering theorem, and find out how to check order isomorphism.
Well-ordered is an adjective that describes a relation or a set that has a least element for every nonempty subset. Learn the meaning, synonyms, examples and origin of well-ordered from Collins English Dictionary.
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 $.
Well-ordered means having a logical or orderly arrangement, especially in mathematics. Learn more about this word, its synonyms, and how to use it in sentences with Collins Dictionary.
