Faster access than browser!
61 relations: Adjoint functors, Analytic geometry, Associative property, Axiom of choice, Axiom of pairing, Axiom of power set, Axiom of union, Axiom schema of specification, Binary relation, Cardinal number, Cardinality, Cartesian closed category, Cartesian coordinate system, Cartesian product of graphs, Category theory, Codomain, Commutative property, Complement (set theory), Coproduct, Direct product, Dover Publications, Empty product, Empty set, Euclidean space, Euclidean vector, Exponential object, Finitary relation, Function (mathematics), Graph theory, Index set, Indexed family, Infinite set, Infinity, Initial and terminal objects, Intersection (set theory), Isomorphism, Mathematics, Natural number, Operation (mathematics), Ordered pair, Plane (geometry), Power set, Product (category theory), Product topology, Product type, Projection (mathematics), Pullback (category theory), Real number, René Descartes, Set (mathematics), ..., Set theory, Set-builder notation, Singleton (mathematics), Standard 52-card deck, Subset, Tensor product of graphs, Tuple, Ultraproduct, Union (set theory), Vertex (graph theory), Zermelo–Fraenkel set theory. Expand index (11 more) »
Adjoint functors
In mathematics, specifically category theory, adjunction is a possible relationship between two functors.
New!!: Cartesian product and Adjoint functors · See more »
Analytic geometry
In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system.
New!!: Cartesian product and Analytic geometry · See more »
Associative property
In mathematics, the associative property is a property of some binary operations.
New!!: Cartesian product and Associative property · See more »
Axiom of choice
In mathematics, the axiom of choice, or AC, is an axiom of set theory equivalent to the statement that the Cartesian product of a collection of non-empty sets is non-empty.
New!!: Cartesian product and Axiom of choice · See more »
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.
New!!: Cartesian product and Axiom of pairing · See more »
Axiom of power set
In mathematics, the axiom of power set is one of the Zermelo–Fraenkel axioms of axiomatic set theory.
New!!: Cartesian product and Axiom of power set · See more »
Axiom of union
In axiomatic set theory, the axiom of union is one of the axioms of Zermelo–Fraenkel set theory.
New!!: Cartesian product and Axiom of union · See more »
Axiom schema of specification
In many popular 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 comprehension is an axiom schema.
New!!: Cartesian product and Axiom schema of specification · See more »
Binary relation
In mathematics, a binary relation on a set A is a set of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A2.
New!!: Cartesian product and Binary relation · See more »
Cardinal number
In mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality (size) of sets.
New!!: Cartesian product and Cardinal number · See more »
Cardinality
In mathematics, the cardinality of a set is a measure of the "number of elements of the set".
New!!: Cartesian product and Cardinality · See more »
Cartesian closed category
In category theory, a category is considered Cartesian closed if, roughly speaking, any morphism defined on a product of two objects can be naturally identified with a morphism defined on one of the factors.
New!!: Cartesian product and Cartesian closed category · See more »
Cartesian coordinate system
A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.
New!!: Cartesian product and Cartesian coordinate system · See more »
Cartesian product of graphs
In graph theory, the Cartesian product G \square H of graphs G and H is a graph such that.
New!!: Cartesian product and Cartesian product of graphs · See more »
Category theory
Category theory formalizes mathematical structure and its concepts in terms of a labeled directed graph called a category, whose nodes are called objects, and whose labelled directed edges are called arrows (or morphisms).
New!!: Cartesian product and Category theory · See more »
Codomain
In mathematics, the codomain or target set of a function is the set into which all of the output of the function is constrained to fall.
New!!: Cartesian product and Codomain · See more »
Commutative property
In mathematics, a binary operation is commutative if changing the order of the operands does not change the result.
New!!: Cartesian product and Commutative property · See more »
Complement (set theory)
In set theory, the complement of a set refers to elements not in.
New!!: Cartesian product and Complement (set theory) · See more »
Coproduct
In category theory, the coproduct, or categorical sum, is a category-theoretic construction which includes as examples the disjoint union of sets and of topological spaces, the free product of groups, and the direct sum of modules and vector spaces.
New!!: Cartesian product and Coproduct · See more »
Direct product
In mathematics, one can often define a direct product of objects already known, giving a new one.
New!!: Cartesian product and Direct product · See more »
Dover Publications
Dover Publications, also known as Dover Books, is an American book publisher founded in 1941 by Hayward Cirker and his wife, Blanche.
New!!: Cartesian product and Dover Publications · See more »
Empty product
In mathematics, an empty product, or nullary product, is the result of multiplying no factors.
New!!: Cartesian product and Empty product · See more »
Empty set
In mathematics, and more specifically set theory, the empty set or null set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero.
New!!: Cartesian product and Empty set · See more »
Euclidean space
In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.
New!!: Cartesian product and Euclidean space · See more »
Euclidean vector
In mathematics, physics, and engineering, a Euclidean vector (sometimes called a geometric or spatial vector, or—as here—simply a vector) is a geometric object that has magnitude (or length) and direction.
New!!: Cartesian product and Euclidean vector · See more »
Exponential object
In mathematics, specifically in category theory, an exponential object or map object is the categorical generalization of a function space in set theory.
New!!: Cartesian product and Exponential object · See more »
Finitary relation
In mathematics, a finitary relation has a finite number of "places".
New!!: Cartesian product and Finitary relation · See more »
Function (mathematics)
In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.
New!!: Cartesian product and Function (mathematics) · See more »
Graph theory
In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.
New!!: Cartesian product and Graph theory · See more »
Index set
In mathematics, an index set is a set whose members label (or index) members of another set.
New!!: Cartesian product and Index set · See more »
Indexed family
In mathematics, an indexed family is informally a collection of objects, each associated with an index from some index set.
New!!: Cartesian product and Indexed family · See more »
Infinite set
In set theory, an infinite set is a set that is not a finite set.
New!!: Cartesian product and Infinite set · See more »
Infinity
Infinity (symbol) is a concept describing something without any bound or larger than any natural number.
New!!: Cartesian product and Infinity · See more »
Initial and terminal objects
In category theory, a branch of mathematics, an initial object of a category C is an object I in C such that for every object X in C, there exists precisely one morphism I → X. The dual notion is that of a terminal object (also called terminal element): T is terminal if for every object X in C there exists a single morphism X → T. Initial objects are also called coterminal or universal, and terminal objects are also called final.
New!!: Cartesian product and Initial and terminal objects · See more »
Intersection (set theory)
In mathematics, the intersection A ∩ B of two sets A and B is the set that contains all elements of A that also belong to B (or equivalently, all elements of B that also belong to A), but no other elements.
New!!: Cartesian product and Intersection (set theory) · See more »
Isomorphism
In mathematics, an isomorphism (from the Ancient Greek: ἴσος isos "equal", and μορφή morphe "form" or "shape") is a homomorphism or morphism (i.e. a mathematical mapping) that can be reversed by an inverse morphism.
New!!: Cartesian product and Isomorphism · See more »
Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
New!!: Cartesian product and Mathematics · See more »
Natural number
In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").
New!!: Cartesian product and Natural number · See more »
Operation (mathematics)
In mathematics, an operation is a calculation from zero or more input values (called operands) to an output value.
New!!: Cartesian product and Operation (mathematics) · See more »
Ordered pair
In mathematics, an ordered pair (a, b) is a pair of objects.
New!!: Cartesian product and Ordered pair · See more »
Plane (geometry)
In mathematics, a plane is a flat, two-dimensional surface that extends infinitely far.
New!!: Cartesian product and Plane (geometry) · See more »
Power set
In mathematics, the power set (or powerset) of any set is the set of all subsets of, including the empty set and itself, variously denoted as, 𝒫(), ℘() (using the "Weierstrass p"),,, or, identifying the powerset of with the set of all functions from to a given set of two elements,.
New!!: Cartesian product and Power set · See more »
Product (category theory)
In category theory, the product of two (or more) objects in a category is a notion designed to capture the essence behind constructions in other areas of mathematics such as the cartesian product of sets, the direct product of groups, the direct product of rings and the product of topological spaces.
New!!: Cartesian product and Product (category theory) · See more »
Product topology
In topology and related areas of mathematics, a product space is the cartesian product of a family of topological spaces equipped with a natural topology called the product topology.
New!!: Cartesian product and Product topology · See more »
Product type
In programming languages and type theory, a product of types is another, compounded, type in a structure.
New!!: Cartesian product and Product type · See more »
Projection (mathematics)
In mathematics, a projection is a mapping of a set (or other mathematical structure) into a subset (or sub-structure), which is equal to its square for mapping composition (or, in other words, which is idempotent).
New!!: Cartesian product and Projection (mathematics) · See more »
Pullback (category theory)
In category theory, a branch of mathematics, a pullback (also called a fiber product, fibre product, fibered product or Cartesian square) is the limit of a diagram consisting of two morphisms and with a common codomain.
New!!: Cartesian product and Pullback (category theory) · See more »
Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
New!!: Cartesian product and Real number · See more »
René Descartes
René Descartes (Latinized: Renatus Cartesius; adjectival form: "Cartesian"; 31 March 1596 – 11 February 1650) was a French philosopher, mathematician, and scientist.
New!!: Cartesian product and René Descartes · See more »
Set (mathematics)
In mathematics, a set is a collection of distinct objects, considered as an object in its own right.
New!!: Cartesian product and Set (mathematics) · See more »
Set theory
Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects.
New!!: Cartesian product and Set theory · See more »
Set-builder notation
In set theory and its applications to logic, mathematics, and computer science, set-builder notation is a mathematical notation for describing a set by enumerating its elements or stating the properties that its members must satisfy.
New!!: Cartesian product and Set-builder notation · See more »
Singleton (mathematics)
In mathematics, a singleton, also known as a unit set, is a set with exactly one element.
New!!: Cartesian product and Singleton (mathematics) · See more »
Standard 52-card deck
A deck of French playing cards is the most common deck of playing cards used today.
New!!: Cartesian product and Standard 52-card deck · See more »
Subset
In mathematics, a set A is a subset of a set B, or equivalently B is a superset of A, if A is "contained" inside B, that is, all elements of A are also elements of B. A and B may coincide.
New!!: Cartesian product and Subset · See more »
Tensor product of graphs
In graph theory, the tensor product G × H of graphs G and H is a graph such that.
New!!: Cartesian product and Tensor product of graphs · See more »
Tuple
In mathematics, a tuple is a finite ordered list (sequence) of elements.
New!!: Cartesian product and Tuple · See more »
Ultraproduct
The ultraproduct is a mathematical construction that appears mainly in abstract algebra and in model theory, a branch of mathematical logic.
New!!: Cartesian product and Ultraproduct · See more »
Union (set theory)
In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection.
New!!: Cartesian product and Union (set theory) · See more »
Vertex (graph theory)
In mathematics, and more specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs of vertices), while a directed graph consists of a set of vertices and a set of arcs (ordered pairs of vertices).
New!!: Cartesian product and Vertex (graph theory) · See more »
Zermelo–Fraenkel set theory
In mathematics, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in the early twentieth century in order to formulate a theory of sets free of paradoxes such as Russell's paradox.
New!!: Cartesian product and Zermelo–Fraenkel set theory · See more »
Redirects here:
Cartesian Product, Cartesian Products, Cartesian power, Cartesian product algorithm, Cartesian products, Cartesian square, CartesianProduct, Cylinder (algebra), Graphing the total product, Graphing total product, Product of sets, Product set.
References
[1] https://en.wikipedia.org/wiki/Cartesian_product
