Glossary of mathematics

It has been suggested that List of mathematical jargon be merged into this article. (Discuss) Proposed since March 2023.

B

binary

A binary relation is a set of ordered pairs; an element x is said to be related to another element y if and only if (x,y) are in the set.

C

canonical

1.  A canonical map is a map or morphism between objects that arises naturally from the definition or the construction of the objects being mapped against each other.

2.  A canonical form of an object is some standard or universal way to express the object.

correspondence

A correspondence from a set [math]\displaystyle{ A }[/math] to a set [math]\displaystyle{ B }[/math] is a subset of a Cartesian product [math]\displaystyle{ A \times B }[/math]; in other words, it is a binary relation but with the specification of the ambient sets [math]\displaystyle{ A, B }[/math] used in the definition.

D

diagram

See mathematical diagram.

F

function

A function [math]\displaystyle{ f: A \to B }[/math] is an ordered triple [math]\displaystyle{ (A, B, f) }[/math] consisting of sets [math]\displaystyle{ A, B }[/math] and a subset [math]\displaystyle{ f }[/math] of the Cartesian product [math]\displaystyle{ A \times B }[/math] subject to the condition [math]\displaystyle{ (a, b), (a, b') \in f }[/math] implies [math]\displaystyle{ b = b' }[/math]. In other words, it is a special kind of correspondence where given an element [math]\displaystyle{ a }[/math] of [math]\displaystyle{ A }[/math], there is a unique element [math]\displaystyle{ b }[/math] of [math]\displaystyle{ B }[/math] that corresponds to it.

I

invariant

An invariant of an object or a space is a property or number of the object or a space that remains unchanged under some transformations.

M

map

A synonym for a function between sets or a morphism in a category. Depending on authors, the term "maps" or the term "functions" may be reserved for specific kinds of functions or morphisms (e.g., function as an analytic term and map as a general term).

mathematics

See mathematics.

multivalued

A "multivalued function” from a set A to a set B is a function from A to the subsets of B. It has typically the property that, for almost all points x of B, there is a neighbourhood of x such that the restriction of the function to the neighbourhood can be considered as a set of functions from the neighbourhood to B.

P

projection

A projection is, roughly, a map from some space or object to another that omits some information on the object or space. For example, [math]\displaystyle{ \mathbb{R}^2 \to \mathbb{R}, (x, y) \mapsto x }[/math] is a projection and its restriction to a graph of a function, say, is also a projection. The terms “idempotent operator” and “forgetful map” are also synonyms for a projection.

S

structure

A mathematical structure on an object is an additional set of objects or data attached to the object (e.g., relation, operation, metric, topology).

See also

• Glossary of areas of mathematics
• List of mathematical constants
• List of mathematical jargon
• List of mathematical symbols
• Category:Mathematical terminology

References

• Encyclopedia of Mathematics

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