- axiom of power sets
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English-Polish dictionary for engineers. 2013.
axiom of power sets
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Axiom of power set — In mathematics, the axiom of power set is one of the Zermelo Fraenkel axioms of axiomatic set theory.In the formal language of the Zermelo Fraenkel axioms, the axiom reads::forall A , exists P , forall B , [B in P iff forall C , (C in B… … Wikipedia
Axiom of pairing — In axiomatic set theory and the branches of logic, mathematics, and computer science that use it, the axiom of pairing is one of the axioms of Zermelo Fraenkel set theory. Formal statement In the formal language of the Zermelo Frankel axioms, the … Wikipedia
Power set — In mathematics, given a set S , the power set (or powerset) of S , written mathcal{P}(S), P ( S ), or 2 S , is the set of all subsets of S . In axiomatic set theory (as developed e.g. in the ZFC axioms), the existence of the power set of any set… … Wikipedia
Axiom of choice — This article is about the mathematical concept. For the band named after it, see Axiom of Choice (band). In mathematics, the axiom of choice, or AC, is an axiom of set theory stating that for every family of nonempty sets there exists a family of … Wikipedia
Axiom schema of replacement — In set theory, the axiom schema of replacement is a schema of axioms in Zermelo Fraenkel set theory (ZFC) that asserts that the image of any set under any definable mapping is also a set. It is necessary for the construction of certain infinite… … Wikipedia
Axiom — This article is about logical propositions. For other uses, see Axiom (disambiguation). In traditional logic, an axiom or postulate is a proposition that is not proven or demonstrated but considered either to be self evident or to define and… … Wikipedia
Category of sets — In mathematics, the category of sets, denoted as Set, is the category whose objects are all sets and whose morphisms are all functions. It is the most basic and the most commonly used category in mathematics.Properties of the category of setsThe… … Wikipedia
Set of all sets — In set theory as usually formulated, referring to the set of all sets typically leads to a paradox. The reason for this is the form of Zermelo s axiom of separation: for anyformula varphi(x) and set A, the set {x in A mid varphi(x)}which contains … Wikipedia
Simple theorems in the algebra of sets — Elementary discrete mathematics courses sometimes leave students under an erroneous impression that the subject matter of set theory is the algebra of union, intersection, and complementation of sets. Those topics are treated below: they would… … Wikipedia
set theory — the branch of mathematics that deals with relations between sets. [1940 45] * * * Branch of mathematics that deals with the properties of sets. It is most valuable as applied to other areas of mathematics, which borrow from and adapt its… … Universalium
New Foundations — In mathematical logic, New Foundations (NF) is an axiomatic set theory, conceived by Willard Van Orman Quine as a simplification of the theory of types of Principia Mathematica. Quine first proposed NF in a 1937 article titled New Foundations for … Wikipedia
