Simple homotopy theory
In mathematics, simple homotopy theory is a homotopy theory (a branch of algebraic topology) that concerns with the simple-homotopy type of a space. It was originated by Whitehead in his 1950 paper "S
Congruence (geometry)
In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other. More formally, two sets of points are ca
Quasi-isometry
In mathematics, a quasi-isometry is a function between two metric spaces that respects large-scale geometry of these spaces and ignores their small-scale details. Two metric spaces are quasi-isometric
Equality (mathematics)
In mathematics, equality is a relationship between two quantities or, more generally two mathematical expressions, asserting that the quantities have the same value, or that the expressions represent
System equivalence
In the systems sciences system equivalence is the behavior of a parameter or component of a system in a way similar to a parameter or component of a different system. Similarity means that mathematica
Normalization (statistics)
In statistics and applications of statistics, normalization can have a range of meanings. In the simplest cases, normalization of ratings means adjusting values measured on different scales to a notio
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Equivalent definitions of mathematical structures
In mathematics, equivalent definitions are used in two somewhat different ways. First, within a particular mathematical theory (for example, Euclidean geometry), a notion (for example, ellipse or mini
Quasi-isomorphism
In homological algebra, a branch of mathematics, a quasi-isomorphism or quism is a morphism A → B of chain complexes (respectively, cochain complexes) such that the induced morphisms of homology group
Isomorphism
In mathematics, an isomorphism is a structure-preserving mapping between two structures of the same type that can be reversed by an inverse mapping. Two mathematical structures are isomorphic if an is
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Ramanujan's congruences
In mathematics, Ramanujan's congruences are some remarkable congruences for the partition function p(n). The mathematician Srinivasa Ramanujan discovered the congruences This means that:
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Elementary equivalence
In model theory, a branch of mathematical logic, two structures M and N of the same signature σ are called elementarily equivalent if they satisfy the same first-order σ-sentences. If N is a substruct
Congruence relation
In abstract algebra, a congruence relation (or simply congruence) is an equivalence relation on an algebraic structure (such as a group, ring, or vector space) that is compatible with the structure in
Extensionality
In logic, extensionality, or extensional equality, refers to principles that judge objects to be equal if they have the same external properties. It stands in contrast to the concept of intensionality
Hyperfinite equivalence relation
In descriptive set theory and related areas of mathematics, a hyperfinite equivalence relation on a standard Borel space X is a Borel equivalence relation E with countable classes, that can, in a cert
A-equivalence
In mathematics, -equivalence, sometimes called right-left equivalence, is an equivalence relation between map germs. Let and be two manifolds, and let be two smooth map germs. We say that and are -equ
Equivalence (measure theory)
In mathematics, and specifically in measure theory, equivalence is a notion of two measures being qualitatively similar. Specifically, the two measures agree on which events have measure zero.
Equipollence (geometry)
In Euclidean geometry, equipollence is a binary relation between directed line segments. A line segment AB from point A to point B has the opposite direction to line segment BA. Two parallel line segm
Approximation
An approximation is anything that is intentionally similar but not exactly equal to something else.
K-equivalence
In mathematics, -equivalence, or contact equivalence, is an equivalence relation between map germs. It was introduced by John Mather in his seminal work in Singularity theory in the 1960s as a technic
Congruence of squares
In number theory, a congruence of squares is a congruence commonly used in integer factorization algorithms.
Wilf equivalence
In the study of permutations and permutation patterns, Wilf equivalence is an equivalence relation on permutation classes.Two permutation classes are Wilf equivalent when they have the same numbers of
Adequate equivalence relation
In algebraic geometry, a branch of mathematics, an adequate equivalence relation is an equivalence relation on algebraic cycles of smooth projective varieties used to obtain a well-working theory of s
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Matrix similarity
In linear algebra, two n-by-n matrices A and B are called similar if there exists an invertible n-by-n matrix P such that Similar matrices represent the same linear map under two (possibly) different
Logical equality
Logical equality is a logical operator that corresponds to equality in Boolean algebra and to the logical biconditional in propositional calculus. It gives the functional value true if both functional
Equivalent latitude
In differential geometry, the equivalent latitude is a Lagrangian coordinate .It is often used in atmospheric science,particularly in the study of stratospheric dynamics.Each isoline in a map of equiv
Equivalence class
In mathematics, when the elements of some set have a notion of equivalence (formalized as an equivalence relation), then one may naturally split the set into equivalence classes. These equivalence cla
Weak equivalence (homotopy theory)
In mathematics, a weak equivalence is a notion from homotopy theory that in some sense identifies objects that have the same "shape". This notion is formalized in the axiomatic definition of a model c
Equivalence test
Equivalence tests are a variety of hypothesis tests used to draw statistical inferences from observed data. In these tests, the null hypothesis is defined as an effect large enough to be deemed intere
Partial equivalence relation
In mathematics, a partial equivalence relation (often abbreviated as PER, in older literature also called restricted equivalence relation) is a homogeneous binary relation that is symmetric and transi
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Equivalence of categories
In category theory, a branch of abstract mathematics, an equivalence of categories is a relation between two categories that establishes that these categories are "essentially the same". There are num
Identity (mathematics)
In mathematics, an identity is an equality relating one mathematical expression A to another mathematical expression B, such that A and B (which might contain some variables) produce the same value fo
Isometry
In mathematics, an isometry (or congruence, or congruent transformation) is a distance-preserving transformation between metric spaces, usually assumed to be bijective. The word isometry is derived fr
Simple-homotopy equivalence
In mathematics, particularly the area of topology, a simple-homotopy equivalence is a refinement of the concept of homotopy equivalence. Two CW-complexes are simple-homotopy equivalent if they are rel
Isomorphism of categories
In category theory, two categories C and D are isomorphic if there exist functors F : C → D and G : D → C which are mutually inverse to each other, i.e. FG = 1D (the identity functor on D) and GF = 1C
Equivalence of metrics
In mathematics, two metrics on the same underlying set are said to be equivalent if the resulting metric spaces share certain properties. Equivalence is a weaker notion than isometry; equivalent metri
Matrix congruence
In mathematics, two square matrices A and B over a field are called congruent if there exists an invertible matrix P over the same field such that PTAP = B where "T" denotes the matrix transpose. Matr
Row equivalence
In linear algebra, two matrices are row equivalent if one can be changed to the other by a sequence of elementary row operations. Alternatively, two m × n matrices are row equivalent if and only if th
Similarity (geometry)
In Euclidean geometry, two objects are similar if they have the same shape, or one has the same shape as the mirror image of the other. More precisely, one can be obtained from the other by uniformly
S-equivalence
S-equivalence is an equivalence relation on the families of semistable vector bundles on an algebraic curve.
Naimark equivalence
In mathematical representation theory, two representations of a group on topological vector spaces are called Naimark equivalent (named after Mark Naimark) if there is a closed bijective linear map be
Morita equivalence
In abstract algebra, Morita equivalence is a relationship defined between rings that preserves many ring-theoretic properties. More precisely two rings like R, S are Morita equivalent (denoted by ) if
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Characterization (mathematics)
In mathematics, a characterization of an object is a set of conditions that, while different from the definition of the object, is logically equivalent to it. To say that "Property P characterizes obj
Homomorphic equivalence
In the mathematics of graph theory, two graphs, G and H, are called homomorphically equivalent if there exists a graph homomorphism and a graph homomorphism . An example usage of this notion is that a
Equivalence relation
In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive. The equipollence relation between line segments in geometry is a common example of an equivale
Borel equivalence relation
In mathematics, a Borel equivalence relation on a Polish space X is an equivalence relation on X that is a Borel subset of X × X (in the product topology).
Quantile normalization
In statistics, quantile normalization is a technique for making two distributions identical in statistical properties. To quantile-normalize a test distribution to a reference distribution of the same
Matrix equivalence
In linear algebra, two rectangular m-by-n matrices A and B are called equivalent if for some invertible n-by-n matrix P and some invertible m-by-m matrix Q. Equivalent matrices represent the same line
Similarity (network science)
Similarity in network analysis occurs when two nodes (or other more elaborate structures) fall in the same equivalence class. There are three fundamental approaches to constructing measures of network
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Logical equivalence
In logic and mathematics, statements and are said to be logically equivalent if they have the same truth value in every model. The logical equivalence of and is sometimes expressed as , , , or , depen
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Exponentially equivalent measures
In mathematics, exponential equivalence of measures is how two sequences or families of probability measures are "the same" from the point of view of large deviations theory.
Logical biconditional
In logic and mathematics, the logical biconditional, sometimes known as the material biconditional, is the logical connective used to conjoin two statements P and Q to form the statement "P if and onl
Equals sign
The equals sign (British English, Unicode) or equal sign (American English), also known as the equality sign, is the mathematical symbol =, which is used to indicate equality in some well-defined sens