

Axiom of extensionality
Axiom of extensionality In axiomatic set theory and the branches ... and computer science that use it, the axiom of extensionality, or axiom of extension, is one of the ...
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Talk:Axiom of extensionality
Talk:Axiom of extensionality it's been a while since I ...
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Extensionality
Extensionality In mathematics, extensionality usually refers to some form of the ... extensional. That is one sense in which extensionality may fail. Another one is that consideration ... if taken into account, will usually contradict extensionality. In axiomatic set theory, extensionality is expressed in the axiom of ...
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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 ... language of the ZermeloFraenkel axioms, the axiom reads: $\backslash forall\; A,\; \backslash exist\; B,\; \backslash forall\; ...\; a\; member\; of\; A.\; Thus,\; what\; the$axiom is really saying is that, given ...
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Axiom of pairing
Axiom of pairing In axiomatic set theory and ... and computer science that use it, the axiom of pairing is one of the axioms ... language of the ZermeloFrankel axioms, the axiom reads: $\backslash forall\; A,\; \backslash forall\; B,\; \backslash exist\; ...\; D\; is\; equal\; to\; B.\; What\; the$axiom is really saying is that, given two ... A and B. We can use the axiom of extensionality to show that this ...
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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 ZermeloFraenkel axioms, the axiom reads: $\backslash exist\; \backslash mathbf\{N\}:\; \backslash varnothing\; \backslash in\; ...\; called\; an\; inductive\; set.\; To\; understand\; this$axiom, first we define the successor of x ... as x ∪ {x}. Note that the axiom of pairing allows us to form ...
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Axiom schema of specification
Axiom schema of specification In axiomatic set theory ... and computer science that use it, the axiom schema of specification, or axiom schema of separation, or axiom schema of restricted comprehension, is a schema ... set theory. It is also called the axiom schema of comprehension, although that term ...
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Axiom schema of replacement
Axiom schema of replacement In axiomatic set theory ... and computer science that use it, the axiom schema of replacement is a schema of ... language of the ZermeloFraenkel axioms, the axiom schema reads: $(\backslash forall\; X,\; \backslash exist!\backslash ,\; Y\; ...\; and\; C.\; Note\; that\; there\; is\; one$axiom for every such predicate P; thus, this is an axiom schema. To understand this axiom, first ...
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Axiom of power set
Axiom of power set In mathematics, the axiom of power set is one of the ... language of the ZermeloFraenkel axioms, the axiom reads: $\backslash forall\; A,\; \backslash exists\backslash ;\; \{\backslash mathcal\{P\; ...\; is\; a\; subset\; of\; A.\; By\; the$axiom of extensionality this set is unique. We call ...
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Axiom of empty set
Axiom of empty set In set theory, the axiom of empty set is one of the ... language of the ZermeloFraenkel axioms, the axiom reads: $\backslash exist\; \backslash varnothing,\; \backslash forall\; A:\; \backslash lnot\; ...\; member\; of\; it.\; We\; can\; use\; the$axiom of extensionality to show that there is only ...
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