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Axiom of pairing
Axiom of pairing In axiomatic set theory and the branches ... and computer science that use it, the axiom of pairing is one of the axioms of Zermelo ... language of the Zermelo-Frankel axioms, the axiom reads: |
Talk:Axiom of pairing
Talk:Axiom of pairing Creation of the set of unordered pairs ... MathMartin 14:35, 7 Jan 2005 (UTC) Axiom of pairing is written in a correct form ? In ... language of the Zermelo-Frankel axioms, the axiom reads: \forall A, \forall B, \exist ...
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Axiom of regularity
Axiom of regularity The axiom of regularity (also known as the axiom of foundation) is one of the axioms ... set theory. In first-order logic the axiom reads: |
Axiom of union
Axiom of union In axiomatic set theory and ... and computer science that use it, the axiom of union is one of the axioms ... the elements of x. Together with the axiom of pairing this implies that for any two sets ... language of the Zermelo-Fraenkel axioms, the axiom reads: |
Axiom of infinity
Axiom of infinity In axiomatic set theory and ... and computer science that use it, the axiom of infinity is one of the axioms ... language of the Zermelo-Fraenkel axioms, the axiom reads: |
Talk:Axiom of choice
Talk:Axiom of choice A question on User Talk ... precise meaning of the independence of the axiom of choice (among other things). By consent ... 2004 (UTC) Do Wikipedia articles assume the axiom of choice unless otherwise mentioned? Or should ... of those theorems. AC is an accepted axiom in mathematics. --AxelBoldt This last position seems ... Too much of mathematics relies on this axiom. The proofs which do not rely ...
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Talk:Axiom schema of replacement
Talk:Axiom schema of replacement The term "mapping" should ... mapping in the sense of the replacement axiom is a special well-formed-formula (with ... all but put the requirement into the axiom itself. AxelBoldt 17:45 Jan 8, 2003 ... of predicate symbol, subject to a certain axiom, which is what the Stanford link does ... symbol): ∅, which is used in the axiom of infinity. As with any derived ...
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Axiomatic set theory
... cardinality) when there is a way of pairing off members of A exhaustively with members ... say that Cantor was tacitly using the axiom of extensionality, the axiom of infinity, and the axiom schema of (unrestricted) comprehension. Some do not ... 1908. He included in this system the axiom of choice, a controversial axiom that ...
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Von Neumann–Bernays–Gödel set theory
... von Neumann–Bernays–Gödel set theory (NBG) is an axiom system for set theory designed to yield ... Zermelo-Fraenkel set theory, together with the axiom of choice (ZFC), but with only a ... finite number of axioms, that is without axiom schemas. First formulated by John von Neumann ... with the membership relation. Notions of equality, pairing, subclass, and such, are thus matters of ... of axioms concerning themselves primarily with classes. axiom of Extensionality: |
Talk:Zermelo-Fraenkel set theory
... separate point, isn't the empty set axiom redundant here? It seems to follow from ... it. I'll mention the redundancy on Axiom of the empty set. -- Toby 05:33 ... 21, 2003 (UTC) The singular, "Zermelo-Fraenkel axiom", does not make sense as the title ... a general concept of a Zermelo-Fraenkel axiom; we're defining a short list of ... t care less about ZF. Sure, the axiom of choice is interesting, but not ...
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