Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Zermelo–Fraenkel_set_theory> ?p ?o. }
Showing items 1 to 34 of
34
with 100 items per page.
- Zermelo–Fraenkel_set_theory abstract "In mathematics, Zermelo–Fraenkel set theory with the axiom of choice, named after mathematicians Ernst Zermelo and Abraham Fraenkel and commonly abbreviated ZFC, is one of several axiomatic systems that were proposed in the early twentieth century to formulate a theory of sets without the paradoxes of naive set theory such as Russell's paradox. Specifically, ZFC does not allow unrestricted comprehension. Today ZFC is the standard form of axiomatic set theory and as such is the most common foundation of mathematics.ZFC is intended to formalize a single primitive notion, that of a hereditary well-founded set, so that all entities in the universe of discourse are such sets. Thus the axioms of ZFC refer only to sets, not to urelements (elements of sets which are not themselves sets) or classes (collections of mathematical objects defined by a property shared by their members). The axioms of ZFC prevent its models from containing urelements, and proper classes can only be treated indirectly. Formally, ZFC is a one-sorted theory in first-order logic. The signature has equality and a single primitive binary relation, set membership, which is usually denoted ∈. The formula a ∈ b means that the set a is a member of the set b (which is also read, "a is an element of b" or "a is in b").There are many equivalent formulations of the ZFC axioms. Most of the ZFC axioms state the existence of particular sets defined from other sets. For example, the axiom of pairing says that given any two sets a and b there is a new set {a, b} containing exactly a and b. Other axioms describe properties of set membership. A goal of the ZFC axioms is that each axiom should be true if interpreted as a statement about the collection of all sets in the von Neumann universe (also known as the cumulative hierarchy). The metamathematics of ZFC has been extensively studied. Landmark results in this area established the independence of the continuum hypothesis from ZFC, and of the axiom of choice from the remaining ZFC axioms.".
- Zermelo–Fraenkel_set_theory wikiPageID "152214".
- Zermelo–Fraenkel_set_theory wikiPageRevisionID "604825926".
- Zermelo–Fraenkel_set_theory id "317".
- Zermelo–Fraenkel_set_theory id "Zermelo-FraenkelSetTheory".
- Zermelo–Fraenkel_set_theory id "p/z130100".
- Zermelo–Fraenkel_set_theory title "ZFC".
- Zermelo–Fraenkel_set_theory title "Zermelo-Fraenkel Axioms".
- Zermelo–Fraenkel_set_theory title "Zermelo-Fraenkel Set Theory".
- Zermelo–Fraenkel_set_theory subject Category:Systems_of_set_theory.
- Zermelo–Fraenkel_set_theory subject Category:Z_notation.
- Zermelo–Fraenkel_set_theory comment "In mathematics, Zermelo–Fraenkel set theory with the axiom of choice, named after mathematicians Ernst Zermelo and Abraham Fraenkel and commonly abbreviated ZFC, is one of several axiomatic systems that were proposed in the early twentieth century to formulate a theory of sets without the paradoxes of naive set theory such as Russell's paradox. Specifically, ZFC does not allow unrestricted comprehension.".
- Zermelo–Fraenkel_set_theory label "Aksjomaty Zermelo-Fraenkela".
- Zermelo–Fraenkel_set_theory label "Axiomas de Zermelo-Fraenkel".
- Zermelo–Fraenkel_set_theory label "Axiomas de Zermelo-Fraenkel".
- Zermelo–Fraenkel_set_theory label "Teoria degli insiemi di Zermelo - Fraenkel".
- Zermelo–Fraenkel_set_theory label "Théorie des ensembles de Zermelo-Fraenkel".
- Zermelo–Fraenkel_set_theory label "Zermelo-Fraenkel-Mengenlehre".
- Zermelo–Fraenkel_set_theory label "Zermelo-Fraenkel-verzamelingenleer".
- Zermelo–Fraenkel_set_theory label "Zermelo–Fraenkel set theory".
- Zermelo–Fraenkel_set_theory label "策梅洛-弗兰克尔集合论".
- Zermelo–Fraenkel_set_theory sameAs Zermelo%E2%80%93Fraenkel_set_theory.
- Zermelo–Fraenkel_set_theory sameAs Zermelova-Fraenkelova_teorie_množin.
- Zermelo–Fraenkel_set_theory sameAs Zermelo-Fraenkel-Mengenlehre.
- Zermelo–Fraenkel_set_theory sameAs Axiomas_de_Zermelo-Fraenkel.
- Zermelo–Fraenkel_set_theory sameAs Théorie_des_ensembles_de_Zermelo-Fraenkel.
- Zermelo–Fraenkel_set_theory sameAs Teoria_degli_insiemi_di_Zermelo_-_Fraenkel.
- Zermelo–Fraenkel_set_theory sameAs 체르멜로-프렝켈_집합론.
- Zermelo–Fraenkel_set_theory sameAs Zermelo-Fraenkel-verzamelingenleer.
- Zermelo–Fraenkel_set_theory sameAs Aksjomaty_Zermelo-Fraenkela.
- Zermelo–Fraenkel_set_theory sameAs Axiomas_de_Zermelo-Fraenkel.
- Zermelo–Fraenkel_set_theory sameAs Q191849.
- Zermelo–Fraenkel_set_theory sameAs Q191849.
- Zermelo–Fraenkel_set_theory wasDerivedFrom Zermelo–Fraenkel_set_theory?oldid=604825926.