This article includes a list of general references, but it lacks sufficient corresponding inline citations. Please help to improve this article by introducing more precise citations.(May 2020) (Learn how and when to remove this message)
The elements of the power set of the set {x, y, z} ordered with respect to inclusion.
In mathematics, the axiom of power set[1] is one of the Zermelo–Fraenkel axioms of axiomatic set theory. It guarantees for every set the existence of a set , the power set of , consisting precisely of the subsets of . By the axiom of extensionality, the set is unique.
The axiom of power set appears in most axiomatizations of set theory. It is generally considered uncontroversial, although constructive set theory prefers a weaker version to resolve concerns about predicativity.
^"Axiom of power set | set theory | Britannica". www.britannica.com. Retrieved 2023-08-06.
and 27 Related for: Axiom of power set information
the axiomofpowerset is one of the Zermelo–Fraenkel axiomsof axiomatic set theory. It guarantees for every set x {\displaystyle x} the existence of a...
axiomatic set theory and the branches of mathematics and philosophy that use it, the axiomof infinity is one of the axiomsof Zermelo–Fraenkel set theory...
In set theory, the axiom schema of replacement is a schema ofaxioms in Zermelo–Fraenkel set theory (ZF) that asserts that the image of any set under any...
axiomatic set theory and the branches of logic, mathematics, and computer science that use it, the axiomof pairing is one of the axiomsof Zermelo–Fraenkel...
the whole of mathematics, particularly in the form of Zermelo–Fraenkel set theory with the axiomof choice. Besides its foundational role, set theory also...
The axiomof constructibility is a possible axiom for set theory in mathematics that asserts that every set is constructible. The axiom is usually written...
the axiomof regularity (also known as the axiomof foundation) is an axiomof Zermelo–Fraenkel set theory that states that every non-empty set A contains...
versions of axiomatic set theory, the axiom schema of specification, also known as the axiom schema of separation, subset axiom scheme or axiom schema of restricted...
the axiomof choice, abbreviated AC or AoC, is an axiomofset theory equivalent to the statement that a Cartesian product of a collection of non-empty...
axiomatic set theory and the branches of logic, mathematics, and computer science that use it, the axiomof extensionality, axiomof extension, or axiomof extent...
inner model of ZF set theory (that is, of Zermelo–Fraenkel set theory with the axiomof choice excluded), and also that the axiomof choice and the generalized...
omitting the axioms Union, PowerSet, Elementary Sets (essentially Pairing) and Infinity and then taking a theorem of Z, Adjunction, as an axiom. The natural...
theorem does not rely on the axiomof choice. Cantor's theorem implies that no set is equinumerous to its powerset (the setof all its subsets). This holds...
The axiomof countable choice or axiomof denumerable choice, denoted ACω, is an axiomofset theory that states that every countable collection of non-empty...
In set theory, the axiomof limitation of size was proposed by John von Neumann in his 1925 axiom system for sets and classes. It formalizes the limitation...
list of articles related to set theory. Algebra ofsetsAxiomof choice Axiomof countable choice Axiomof dependent choice Zorn's lemma Axiomofpower set...
or the axiomof regularity and axiomof pairing. In Zermelo–Fraenkel set theory, the axiomof regularity and axiomof pairing prevent any set from containing...
the unary predicate. AXIOM I. Axiomof extensionality (Axiom der Bestimmtheit) "If every element of a set M is also an element of N and vice versa ......
the empty set exists by including an axiomof empty set, while in other theories, its existence can be deduced. Many possible properties ofsets are vacuously...
an axiom is a premise or starting point for reasoning. In mathematics, an axiom may be a "logical axiom" or a "non-logical axiom". Logical axioms are...
an axiom schema (plural: axiom schemata or axiom schemas) generalizes the notion ofaxiom. An axiom schema is a formula in the metalanguage of an axiomatic...
probability axioms are the foundations of probability theory introduced by Russian mathematician Andrey Kolmogorov in 1933. These axioms remain central...
In mathematics, the axiomof determinacy (abbreviated as AD) is a possible axiom for set theory introduced by Jan Mycielski and Hugo Steinhaus in 1962...
Global Information
