mathematics, the power set (or powerset) of a set S is the set of all subsets of S, including the empty set and S itself. In axiomatic set theory (as developed...

Zermelo–Fraenkel set theory with the axiom of choice. (ZFC is the most widely-studied version of axiomatic set theory.) The power set of a set S is the set of all...

of power set is one of the Zermelo–Fraenkel axioms of axiomatic set theory. It guarantees for every set x {\displaystyle x} the existence of a set P (...

example, the power set of {1, 2} is { {}, {1}, {2}, {1, 2} }. Some basic sets of central importance are the set of natural numbers, the set of real numbers...

that set, where P {\displaystyle {\mathcal {P}}} represents the power set operator. Therefore, the existence of the Cartesian product of any two sets in...

mathematics, a set is countable if either it is finite or it can be made in one to one correspondence with the set of natural numbers. Equivalently, a set is countable...

In set theory, the complement of a set A, often denoted by A ∁ {\displaystyle A^{\complement }} (or A′), is the set of elements not in A. When all elements...

itself; equivalently, the power set of the empty set is the set containing only the empty set. The number of elements of the empty set (i.e., its cardinality)...

In mathematics, fuzzy sets (a.k.a. uncertain sets) are sets whose elements have degrees of membership. Fuzzy sets were introduced independently by Lotfi...

where Z 0 {\displaystyle Z_{0}} is any infinite set and P {\displaystyle {\mathcal {P}}} is the power set operation. Moreover, one of Zermelo's axioms invoked...

The set of all even integers, expressed in set-builder notation. In set theory and its applications to logic, mathematics, and computer science, set-builder...

mathematics, an uncountable set, informally, is an infinite set that contains too many elements to be countable. The uncountability of a set is closely related...

In set theory, the intersection of two sets A {\displaystyle A} and B , {\displaystyle B,} denoted by A ∩ B , {\displaystyle A\cap B,} is the set containing...

union is infinite. The power set of an infinite set is infinite. Any superset of an infinite set is infinite. If an infinite set is partitioned into finitely...

set concerns the power set of the set of all sets. Because this power set is a set of sets, it would necessarily be a subset of the set of all sets,...

) . {\displaystyle A\cup (B\cap C)=(A\cup B)\cap (A\cup C).} The power set of a set U {\displaystyle U} , together with the operations given by union...

addition modulo 2. The power set of any set becomes an abelian group under the operation of symmetric difference, with the empty set as the neutral element...

IBM POWER is a reduced instruction set computer (RISC) instruction set architecture (ISA) developed by IBM. The name is an acronym for Performance Optimization...

exponent or power. Exponentiation is written as bn, where b is the base and n is the power; this is pronounced as "b (raised) to the (power of) n". When...

finitely many finite sets is finite. A finite set with n elements has 2n distinct subsets. That is, the power set P(S) of a finite set S is finite, with...

function, from A to B. For example, the set N of all natural numbers has cardinality strictly less than its power set P(N), because g(n) = { n } is an injective...

follows. For a collection T of subsets of X (that is, for any subset of the power set P(X) of X), let T σ {\displaystyle T_{\sigma }} be all countable unions...

domain is called the universe denoted U. The range is the set of subsets of U called the power set of U and denoted P(U). Thus the relation ∈ {\displaystyle...

structural, hot rolled plates, iron ore pellets, and coils. Jindal Steel and Power set up the world's first coal-gasification based DRI plant at Angul, Odisha...

set of subsets of a given set (its power set) ordered by inclusion (see Fig. 1). Similarly, the set of sequences ordered by subsequence, and the set of...

between sets, popularized by John Venn (1834–1923) in the 1880s. The diagrams are used to teach elementary set theory, and to illustrate simple set relationships...

In set theory and its applications throughout mathematics, a class is a collection of sets (or sometimes other mathematical objects) that can be unambiguously...

Rings of Power is based on J. R. R. Tolkien's history of Middle-earth, primarily material from the appendices of the novel The Lord of the Rings. Set thousands...

Tyrone Edmund Power III (May 5, 1914 – November 15, 1958) was an American actor. From the 1930s to the 1950s, Power appeared in dozens of films, often...

Reliance Power Limited (R-Power), formerly Reliance Energy Generation Limited (REGL) is a part of the Reliance Anil Dhirubhai Ambani Group. It was established...