Editing Map (mathematics) (section)

{{Short description|Function, homomorphism, or morphism}}
{{Other uses|map (disambiguation)}}
[[File:Function_color_example_3.svg|thumb|A map is a function, as in the association of any of the four colored shapes in X to its color in Y]]

In [[mathematics]], a '''map''' or '''mapping''' is a [[function (mathematics)|function]] in its general sense.<ref>The words ''map'', ''mapping'', ''correspondence'', and ''operator'' are often used synonymously. {{harvnb|Halmos|1970|p=30}}. Some authors use the term ''function'' with a more restricted meaning, namely as a map that is restricted to apply to numbers only.</ref>  These terms may have originated as from the process of making a [[map|geographical map]]: ''mapping'' the Earth surface to a sheet of paper.<ref name=":1">{{Cite web|url=https://www.britannica.com/science/mapping|title=Mapping {{!}} mathematics|website=Encyclopedia Britannica|language=en|access-date=2019-12-06}}</ref>

The term ''map'' may be used to distinguish some special types of functions, such as [[homomorphism]]s. For example, a [[linear map]] is a homomorphism of [[vector space]]s, while the term [[linear function]] may have this meaning or it may mean a [[linear polynomial]].<ref>{{cite book |first=T. M. |last=Apostol |author-link=Tom M. Apostol |title=Mathematical Analysis |year=1981 |publisher=Addison-Wesley |isbn=0-201-00288-4 |page=35 }}</ref><ref>{{Cite web|url=http://www.cs.toronto.edu/~stacho/macm101-2.pdf|title=Function, one-to-one, onto|last=Stacho|first=Juraj|date=October 31, 2007|website=cs.toronto.edu|access-date=2019-12-06}}</ref> In [[category theory]], a map may refer to a [[morphism]].<ref name=":1" /> The term ''transformation'' can be used interchangeably,<ref name=":1" /> but ''[[transformation (function)|transformation]]'' often refers to a function from a set to itself. There are also a few less common uses in [[logic]] and [[graph theory]].