Equivalence (mathematics)

In mathematics, an isomorphism is a structure-preserving mapping or morphism between two structures of the same type that can be reversed by an inverse mapping. Two mathematical structures are isomorphic if an isomorphism exists between them, and this is often denoted as . The word is derived .

reflexive, symmetric and transitive relation

when two figures or objects in geometry have the same shape and size, or if one has the same shape and size as the mirror image of the other

idea in geometry

An approximation is anything that is intentionally similar but not exactly equal to something else.

mathematical symbol used to indicate equality

mathematical relationship asserting that two quantities have the same value

equation that is satisfied for all values of the variables

thumb|upright=1.4|A Function composition|composition of two opposite isometries is a direct isometry. A reflection in a line is an opposite isometry, like (reflection w.r.t the center diagonal line) or (reflection w.r.t the right diagonal line) on the image. Translation is a direct isometry: a rigid motion.

equivalence relation between matrices

concept in logic

mathematical concept

equivalence relation in algebra

equivalence relation between matrices

term

Concept in model theory

statistical procedure

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, which is concerned with whether the internal definitions of objects are the same. ==In mathematics== The extensional definition of function equality, discussed above, is commonly used in mathematics. A similar extensional definition is usually employed for relations: two relations are said to be equal if they have the same extensions.

abstract mathematics relationship

Mathematical equivalence relation

equivalence of matrices under row operations

property of parallel segments that have the same length and the same direction

equivalence relation on rings

logical operator in propositional calculus

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

in number theory, a congruence commonly used in integer factorization algorithms

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 if there exists a quasi-isometry between them. The property of being quasi-isometric behaves like an equivalence relation on the class of metric spaces.

term in mathematics

relation of categories in category theory