define well ordered - EAS

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    well or·der·ed
    [ˈwelˌôːrdərd]
    ADJECTIVE
    well ordered (adjective) · well-ordered (adjective)
    1. arranged or organized in an orderly way:
      "the only rash decision of his well-ordered life" · "this is a lovely book, beautifully designed and well ordered"
    Translate well ordered to
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    What does well order mean in math?
    Well-order. In mathematics, a well-order (or well-ordering or well-order relation) on a set S is a total order 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 well-order relation is then called a well-ordered set.
    en.wikipedia.org/wiki/Well-order
    Is a totally ordered set well ordered?
    A totally ordered set is said to be well ordered (or have a well-founded order) iff every nonempty subset of has a least element (Ciesielski 1997, p. 38; Moore 1982, p. 2; Rubin 1967, p. 159; Suppes 1972, p. 75). Every finite totally ordered set is well ordered.
    mathworld.wolfram.com/WellOrderedSet.html
    What is the least element of a well-ordered set?
    Every non-empty well-ordered set has a least element. Every element s of a well-ordered set, except a possible greatest element, has a unique successor (next element), namely the least element of the subset of all elements greater than s.
    en.wikipedia.org/wiki/Well-order
    What is the successor of a well-ordered set?
    Every element s of a well-ordered set, except a possible greatest element, has a unique successor (next element), namely the least element of the subset of all elements greater than s. There may be elements besides the least element which have no predecessor (see § Natural numbers below for an example).
    en.wikipedia.org/wiki/Well-order
  3. Properly or carefully organized

    Well-ordered Definition. Properly or carefully organized. Having a precise arrangement. (mathematics, not comparable) Having a well-order. Simple past tense and past participle of well-order.
    www.yourdictionary.com/well-ordered
    www.yourdictionary.com/well-ordered
  4. https://www.merriam-webster.com/dictionary/well-ordered

    Web1. : having an orderly procedure or arrangement. a well-ordered household. 2. : partially ordered with every subset containing a first element and exactly one of the relationships "greater than," "less than," or "equal to" holding for any given pair of elements. well …

  5. https://www.dictionary.com/browse/well-ordered

    Webwell-ordered. adjective. logic maths (of a relation) having the property that every nonempty subset of its field has a least member under the relation: less than is well …

  6. https://www.thefreedictionary.com/well-ordered
      1. (Logic) logic maths (of a relation) having the property that every nonempty subset of its field …
      2. (Mathematics) logic maths (of a relation) having the property that every nonempty subset of …
  7. https://www.thesaurus.com/browse/well-ordered

    WebSee definition of well-ordered on Dictionary.com as in businesslike as in systematic as in tidy synonyms for well-ordered Compare Synonyms diligent disciplined earnest …

  8. https://www.yourdictionary.com/well-ordered

    WebWell-ordered Definition welôrdərd Meanings Sentences Definition Source Adjective Verb Filter adjective Properly or carefully organized. Webster's New World Having a precise …

  9. https://en.wikipedia.org/wiki/Well-order

    WebIn mathematics, a well-order on a set S is a total order on S with the property that every non-empty subset of S has a least element in this ordering. The set S together with …

  10. well-ordered | Definition of well-ordered in English at ...

    https://advancedictionary.com/definition/well-ordered

    Web(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, …

  11. https://www.collinsdictionary.com/us/dictionary/english/well-ordered-set

    Webwell-ordered setin American English. noun. Math. a totally ordered setin which every nonemptysubsethas a smallest elementwith the propertythat there is no element in the …

  12. https://en.wikipedia.org/wiki/Well-ordering_principle

    WebIn mathematics, the well-ordering principle states that every non-empty set of positive integers contains a least element. [1] In other words, the set of positive integers is well …

  13. https://mathworld.wolfram.com/WellOrderedSet.html

    Web2 days ago · Well Ordered Set. A totally ordered set is said to be well ordered (or have a well-founded order) iff every nonempty subset of has a least element (Ciesielski 1997, p. …



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