well-founded set wikipedia - EAS

46,800,000 kết quả
  1. Xem thêm
    Xem tất cả trên Wikipedia

    Well-founded relation - Wikipedia

    https://en.wikipedia.org/wiki/Well-founded_relation

    In mathematics, a binary relation R is called well-founded (or wellfounded) on a class X if every non-empty subset S ⊆ X has a minimal element with respect to R, that is, an element m not related by sRm (for instance, "s is not smaller than m") for any s ∈ S. In other words, a relation is well founded if Some

     ...

    Xem thêm
    Induction and recursion

    An important reason that well-founded relations are interesting is because a version of transfinite induction can be used on them: if (X, R) is a well-founded relation, P(x) is some property of elements of X, and we want to show that

     ...

    Xem thêm
    Examples

    Well-founded relations which are not totally ordered include:
    • The positive integers {1, 2, 3, ...}, with the order defined by a < b if and only if a divides b and a ≠ b.
    • The set of all finite stringsover a fixed alphabet, with the order defined by s < t if and only if s is a

     ...

    Xem thêm
    Other properties

    If (X, <) is a well-founded relation and x is an element of X, then the descending chains starting at x are all finite, but this does not mean that their lengths are necessarily bounded.

     ...

    Xem thêm
    Reflexivity

    A relation R is said to be reflexiveif aRa holds for every a in the domain of the relation. Every reflexive relation on a nonempty domain has infinite descending chains, because any

     ...

    Xem thêm
    Văn bản Wikipedia theo giấy phép CC-BY-SA
    Mục này có hữu ích không?Cảm ơn! Cung cấp thêm phản hồi

  2. Non-well-founded set theory - Wikipedia

    https://en.wikipedia.org/wiki/Non-well-founded_set_theory

    Non-well-founded set theories are variants of axiomatic set theory that allow sets to be elements of themselves and otherwise violate the rule of well-foundedness. In non-well-founded set theories, the foundation axiom of ZFC is replaced by axioms implying its negation.
    The study of non-well-founded sets was initiated by Dmitry Mirimanoffin a series of papers between 1917 and 1920, in which he formulated the distinction between well-founded and non-…

    Wikipedia · Nội dung trong CC-BY-SA giấy phép

  3. Non-well-founded set theory wiki | TheReaderWiki

    https://thereaderwiki.com/en/Non-wellfounded_set_theory

    A set, x 0, is well-founded if it has no infinite descending membership sequence . {\displaystyle \cdots \in x_{2}\in x_{1}\in x_{0}.} In ZFC, there is no infinite descending ∈ …

  4. Non-well-founded set theory — Wikipedia Republished // WIKI 2

    https://wiki2.org/en/Non-well-founded_set_theory

    From Wikipedia, the free encyclopedia Non-well-founded set theories are variants of axiomatic set theory that allow sets to contain themselves and otherwise violate the rule of …

  5. Non-well-founded set theory - WikiMili, The Best Wikipedia ...

    https://wikimili.com/en/Non-well-founded_set_theory

    In set theory and related branches of mathematics, the von Neumann universe, or von Neumann hierarchy of sets, denoted by V, is the class of hereditary well-founded sets. This collection, which is formalized by Zermelo–Fraenkel set theory (ZFC), is often used to provide an interpretation or motivation of the axioms of ZFC.

  6. Théorie des ensembles non bien fondés — Wikipédia

    https://fr.wikipedia.org/wiki/Théorie_des_ensembles_non_bien_fondés

    La théorie des ensembles non bien fondés est une variante de la théorie axiomatique des ensembles qui permet aux ensembles de s'appartenir les uns aux autres sans limite. Autrement dit, c'est une théorie des ensembles qui viole l'axiome de fondation. Plus précisément, dans la théorie des ensembles non bien fondés, l'axiome de fondation de ZFC est remplacé par un …

  7. Tìm kiếm có liên quan cho well-founded set wikipedia

  8. Một số kết quả đã bị xóa


Results by Google, Bing, Duck, Youtube, HotaVN