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59 relations: Axiom of choice, Bijection, Bijection, injection and surjection, Binary relation, Cancellation property, Cardinal number, Cardinality, Cartesian product, Category (mathematics), Category of sets, Codomain, Cover (algebra), Covering space, Disjoint sets, Domain of a function, Dover Publications, Element (mathematics), Enumeration, Epimorphism, Equivalence class, Equivalence relation, Exponential function, Fiber bundle, Finite set, France, Function (mathematics), Function composition, General linear group, Graph of a function, Group (mathematics), Identity function, Image (mathematics), Index set, Injective function, Integer, Inverse function, Invertible matrix, Mathematician, Mathematics, Matrix (mathematics), Matrix exponential, Modular arithmetic, Morphism, Multivalued function, Natural logarithm, Nicolas Bourbaki, Parity (mathematics), Partition of a set, Prefix, Projection (mathematics), ..., Projection (set theory), Range (mathematics), Real number, Restriction (mathematics), Schröder–Bernstein theorem, Section (category theory), Set (mathematics), Subset, Uniqueness quantification. Expand index (9 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.
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Bijection
In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set.
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Bijection, injection and surjection
In mathematics, injections, surjections and bijections are classes of functions distinguished by the manner in which arguments (input expressions from the domain) and images (output expressions from the codomain) are related or mapped to each other.
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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.
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Cancellation property
In mathematics, the notion of cancellative is a generalization of the notion of invertible.
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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.
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Cardinality
In mathematics, the cardinality of a set is a measure of the "number of elements of the set".
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Cartesian product
In set theory (and, usually, in other parts of mathematics), a Cartesian product is a mathematical operation that returns a set (or product set or simply product) from multiple sets.
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Category (mathematics)
In mathematics, a category (sometimes called an abstract category to distinguish it from a concrete category) is an algebraic structure similar to a group but without requiring inverse or closure properties.
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Category of sets
In the mathematical field of category theory, the category of sets, denoted as Set, is the category whose objects are sets.
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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.
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Cover (algebra)
In abstract algebra, a cover is one instance of some mathematical structure mapping onto another instance, such as a group (trivially) covering a subgroup.
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Covering space
In mathematics, more specifically algebraic topology, a covering map (also covering projection) is a continuous function p from a topological space, C, to a topological space, X, such that each point in X has an open neighbourhood evenly covered by p (as shown in the image); the precise definition is given below.
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Disjoint sets
In mathematics, two sets are said to be disjoint sets if they have no element in common.
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Domain of a function
In mathematics, and more specifically in naive set theory, the domain of definition (or simply the domain) of a function is the set of "input" or argument values for which the function is defined.
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Dover Publications
Dover Publications, also known as Dover Books, is an American book publisher founded in 1941 by Hayward Cirker and his wife, Blanche.
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Element (mathematics)
In mathematics, an element, or member, of a set is any one of the distinct objects that make up that set.
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Enumeration
An enumeration is a complete, ordered listing of all the items in a collection.
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Epimorphism
In category theory, an epimorphism (also called an epic morphism or, colloquially, an epi) is a morphism f: X → Y that is right-cancellative in the sense that, for all morphisms, Epimorphisms are categorical analogues of surjective functions (and in the category of sets the concept corresponds to the surjective functions), but it may not exactly coincide in all contexts; for example, the inclusion \mathbb\to\mathbb is a ring-epimorphism.
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Equivalence class
In mathematics, when the elements of some set S have a notion of equivalence (formalized as an equivalence relation) defined on them, then one may naturally split the set S into equivalence classes.
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Equivalence relation
In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive.
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Exponential function
In mathematics, an exponential function is a function of the form in which the argument occurs as an exponent.
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Fiber bundle
In mathematics, and particularly topology, a fiber bundle (or, in British English, fibre bundle) is a space that is locally a product space, but globally may have a different topological structure.
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Finite set
In mathematics, a finite set is a set that has a finite number of elements.
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France
France, officially the French Republic (République française), is a sovereign state whose territory consists of metropolitan France in Western Europe, as well as several overseas regions and territories.
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Function (mathematics)
In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.
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Function composition
In mathematics, function composition is the pointwise application of one function to the result of another to produce a third function.
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General linear group
In mathematics, the general linear group of degree n is the set of invertible matrices, together with the operation of ordinary matrix multiplication.
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Graph of a function
In mathematics, the graph of a function f is, formally, the set of all ordered pairs, and, in practice, the graphical representation of this set.
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Group (mathematics)
In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element and that satisfies four conditions called the group axioms, namely closure, associativity, identity and invertibility.
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Identity function
Graph of the identity function on the real numbers In mathematics, an identity function, also called an identity relation or identity map or identity transformation, is a function that always returns the same value that was used as its argument.
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Image (mathematics)
In mathematics, an image is the subset of a function's codomain which is the output of the function from a subset of its domain.
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Index set
In mathematics, an index set is a set whose members label (or index) members of another set.
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Injective function
In mathematics, an injective function or injection or one-to-one function is a function that preserves distinctness: it never maps distinct elements of its domain to the same element of its codomain.
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Integer
An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").
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Inverse function
In mathematics, an inverse function (or anti-function) is a function that "reverses" another function: if the function applied to an input gives a result of, then applying its inverse function to gives the result, and vice versa.
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Invertible matrix
In linear algebra, an n-by-n square matrix A is called invertible (also nonsingular or nondegenerate) if there exists an n-by-n square matrix B such that where In denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication.
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Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Matrix (mathematics)
In mathematics, a matrix (plural: matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.
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Matrix exponential
In mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function.
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Modular arithmetic
In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value—the modulus (plural moduli).
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Morphism
In mathematics, a morphism is a structure-preserving map from one mathematical structure to another one of the same type.
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Multivalued function
In mathematics, a multivalued function from a domain to a codomain is a heterogeneous relation.
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Natural logarithm
The natural logarithm of a number is its logarithm to the base of the mathematical constant ''e'', where e is an irrational and transcendental number approximately equal to.
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Nicolas Bourbaki
Nicolas Bourbaki is the collective pseudonym under which a group of (mainly French) 20th-century mathematicians, with the aim of reformulating mathematics on an extremely abstract and formal but self-contained basis, wrote a series of books beginning in 1935.
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Parity (mathematics)
In mathematics, parity is the property of an integer's inclusion in one of two categories: even or odd.
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Partition of a set
In mathematics, a partition of a set is a grouping of the set's elements into non-empty subsets, in such a way that every element is included in one and only one of the subsets.
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Prefix
A prefix is an affix which is placed before the stem of a word.
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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).
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Projection (set theory)
In set theory, a projection is one of two closely related types of functions or operations, namely.
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Range (mathematics)
In mathematics, and more specifically in naive set theory, the range of a function refers to either the codomain or the image of the function, depending upon usage.
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Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
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Restriction (mathematics)
In mathematics, the restriction of a function f is a new function f\vert_A obtained by choosing a smaller domain A for the original function f. The notation f is also used.
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Schröder–Bernstein theorem
In set theory, the Schröder–Bernstein theorem states that, if there exist injective functions and between the sets and, then there exists a bijective function.
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Section (category theory)
In category theory, a branch of mathematics, a section is a right inverse of some morphism.
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Set (mathematics)
In mathematics, a set is a collection of distinct objects, considered as an object in its own right.
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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.
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Uniqueness quantification
In mathematics and logic, the phrase "there is one and only one" is used to indicate that exactly one object with a certain property exists.
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References
[1] https://en.wikipedia.org/wiki/Surjective_function
