different between function vs surjection

English

Etymology

From Middle French function, from Old French fonction, from Latin functi? (“performance, execution”), from functus, perfect participle of fungor (“to perform, execute, discharge”).

Pronunciation

• (UK) IPA^(key): /?f??(k)??n/, /?f??k?n?/
• (US) IPA^(key): /?f??k??n/, [?f??k???n], [?f??k?n?]
• Hyphenation: func?tion
• Rhymes: -??k??n

Noun

function (plural functions)

1. What something does or is used for.

   Synonyms: aim, intention, purpose, role, use

2. A professional or official position.

   Synonyms: occupation, office, part, role

4. An official or social occasion.

   Synonyms: affair, occasion, social occasion, social function

5. Something which is dependent on or stems from another thing; a result or concomitant.
6. A relation where one thing is dependent on another for its existence, value, or significance.
7. (mathematics) A relation in which each element of the domain is associated with exactly one element of the codomain.

   Synonyms: map, mapping, mathematical function, operator, transformation

   Hypernym: relation

8. (computing) A routine that receives zero or more arguments and may return a result.

   Synonyms: procedure, routine, subprogram, subroutine, func, funct

9. (biology) The physiological activity of an organ or body part.
10. (chemistry) The characteristic behavior of a chemical compound.
11. (anthropology) The role of a social practice in the continued existence of the group.

Hyponyms

• subfunction

Derived terms

Related terms

Translations

References

• function on Wikipedia.Wikipedia

Verb

function (third-person singular simple present functions, present participle functioning, simple past and past participle functioned)

1. (intransitive) To have a function.

   Synonyms: officiate, serve

2. (intransitive) To carry out a function; to be in action.

   Synonyms: go, operate, run, work

   Antonym: malfunction

Related terms

• functional
• dysfunction, dysfunctional

Translations

Middle French

Noun

function f (plural functions)

1. function (what something's intended use is)

Descendants

• ? English: function
• French: fonction

English

Etymology

From French surjection, introduced by Nicolas Bourbaki in their treatise Éléments de mathématique.Ultimately borrowed from Latin superiecti? (“a throwing over or on; (fig.) an exaggeration, a hyperbole”).

Pronunciation

• IPA^(key): /s??(?).d??k.??n/

Noun

surjection (plural surjections)

1. (set theory) A function that is a many-to-one mapping; (formally) Any function ${\displaystyle f:X\rightarrow Y}$ for which for every ${\displaystyle y\in Y}$, there is at least one ${\displaystyle x\in X}$ such that ${\displaystyle f(x)=y}$.
   • 1992, Rowan Garnier, John Taylor, Discrete Mathematics for New Technology, Institute of Physics Publishing, page 220,

     In some special cases, however, the number of surjections ${\displaystyle A\rightarrow B}$ can be identified.

   • 1999, M. Pavaman Murthy, A survey of obstruction theory for projective modules of top rank, Tsit-Yuen Lam, Andy R. Magid (editors), Algebra, K-theory, Groups, and Education: On the Occasion of Hyman Bass's 65th Birthday, American Mathematical Society, page 168,

     Let ${\displaystyle J=\cap _{i}m_{i}}$ be the (irredundant) primary decomposition of ${\displaystyle J}$. We associate to the pair ${\displaystyle (J,\omega )}$ the element ${\displaystyle \textstyle \sum _{i}(m_{i},\omega _{i})\in G}$, where ${\displaystyle \omega _{i}}$ is the equivalence class of surjections from ${\displaystyle L/m_{i}L\oplus (A/m_{i})^{n-1}}$ to ${\displaystyle m_{i}/m_{i}^{2}}$ induced by ${\displaystyle \omega }$.

   • 2003, Gilles Pisier, Introduction to Operator Space Theory, Cambridge University Press, page 43,

     In Banach space theory, a mapping ${\displaystyle u:E\rightarrow F}$ (between Banach spaces) is called a metric surjection if it is onto and if the associated mapping from ${\displaystyle E/{\text{ker}}(u)}$ to ${\displaystyle F}$ is an isometric isomorphism. Moreover, by the classical open mapping theorem, ${\displaystyle u}$ is a surjection iff the associated mapping from ${\displaystyle E/{\text{ker}}(u)}$ to ${\displaystyle F}$ is an isomorphism.

Synonyms

• (function that is a many-to-one mapping): surjective function

Related terms

• bijection
• injection
• surject

Translations

References

French

Etymology

Formed after bijection and injection.

Pronunciation

• IPA^(key): /sy?.??k.sj??/

Noun

surjection f (plural surjections)

1. (set theory) surjection

Derived terms

• surjectif