definition. These definitions are equivalent in the context of a given mathematical structure (Euclidean space, in this case). Second, a mathematical...

Abstract structure Isomorphism Equivalent definitions of mathematical structures Forgetful functor Intuitionistic type theory Mathematical object Algebraic...

of mathematics itself. For more information on mathematical structures see Wikipedia: mathematical structure, equivalent definitions of mathematical structures...

demonstrating strong similarities between the mathematical structures concerned. In some cases, these structures may appear to be unrelated at a superficial...

A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation...

definitions of the basic mathematical objects were insufficient for ensuring mathematical rigour. This became the foundational crisis of mathematics....

include uses of logic to characterize correct mathematical reasoning or to establish foundations of mathematics. Since its inception, mathematical logic has...

generalize the algebraic structures such as groups, rings, fields and vector spaces. The term universal algebra is used for structures of first-order theories...

The utility of the concept of a topology is shown by the fact that there are several equivalent definitions of this mathematical structure. Thus one chooses...

authors instead define "positive" to be a synonym of "non-negative"; these definitions are not equivalent. Suppose that p {\displaystyle p} and q {\displaystyle...

A mathematical joke is a form of humor which relies on aspects of mathematics or a stereotype of mathematicians. The humor may come from a pun, or from...

object with a pre-existing structure. Definitions by transport of structure are regarded as canonical. Since mathematical structures are often defined in reference...

objects are homotopy equivalent if they both result from "squishing" some larger object. Topology, as a well-defined mathematical discipline, originates...

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...

A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The...

used in logic. The mathematical field that studies topoi is called topos theory. Since the introduction of sheaves into mathematics in the 1940s, a major...

the elements of the monoid), and so can any preorder. There are many equivalent definitions of a category. One commonly used definition is as follows...

torus. Much of mathematics is grounded in the study of equivalences, and order relations. Lattice theory captures the mathematical structure of order relations...

Such a definition does not prove that such a complete ordered field exists, and the existence proof consists of constructing a mathematical structure that...

(1994) The Words of Mathematics: An etymological dictionary of mathematical terms used in English, page 43, The Mathematical Association of America ISBN 0-88385-511-9...

In mathematical physics, the causal structure of a Lorentzian manifold describes the possible causal relationships between points in the manifold. Lorentzian...

and Heyting algebras." Mathematical Structures in Computer Science, 20. Johnstone 1982. M. Hochster (1969). Prime ideal structure in commutative rings....

In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are sets with specific operations...

several mathematical domains. This includes different branches of mathematical analysis, which are based on fields with additional structure. Basic theorems...

representation of the shape (they contain all the information necessary to reconstruct the shape). Skeletons have several different mathematical definitions in the...

measure") is often used to assert that two distinct mathematical objects can be regarded as equivalent—if their difference is accounted for by an additional...

allows mathematical analysis to be performed on the manifold. A smooth structure on a manifold M {\displaystyle M} is a collection of smoothly equivalent smooth...

data of this type, and the behavior of these operations. This mathematical model contrasts with data structures, which are concrete representations of data...

topology). Glossary of areas of mathematics List of mathematical constants List of mathematical symbols Category:Mathematical terminology Goldfeld,...

In mathematics a Dirac structure is a geometric structure generalizing both symplectic structures and Poisson structures, and having several applications...