How is this called?

Question

In french, there is a word for what's called an "application" that can be bijective, injective or surjective, in english I only see the word "function".

In french, an application is defined as a relation between two sets, where each element of the first set is linked to a unique element of the second set, is there any word more precise than a function for this definition in English?

@OpenBall Thank you !! Its funny that we are using two different words in french! — Pop Flamingo, Jan 29 '17 at 18:05
Related: http://math.stackexchange.com/questions/95741/is-there-any-difference-between-mapping-and-function I suspect in fact in French they also define the same notion. — Wolfram, Jan 29 '17 at 18:06
You're welcome. Not too funny, as we also have the name "mapping". — , Jan 29 '17 at 18:07
@Wolfram Oh I see... well yes, the term used probably depends on the context of what we are studying... — Pop Flamingo, Jan 29 '17 at 18:07
Application, map and function are synonyms, at least in Italian, French and English. In Italian we use different terms according to the domains of such objects: real numbers, spaces of functions, geometric subspaces etc. — Jack D'Aurizio, Jan 29 '17 at 18:09
Also in Russian we have "отображение" aka mapping and "функция" aka "function". — Wolfram, Jan 29 '17 at 18:10
See Application : It seems to me that math English does not distinguish between the two cases : total (defined for every element of the source) and not. See also the ref to Bourbaki. — Mauro ALLEGRANZA, Jan 29 '17 at 18:16
@MauroALLEGRANZA Oh so there is a small difference then... but I see that in practice it does not matter much! — Pop Flamingo, Jan 29 '17 at 18:21
The original French Bourbaki E II.14 has fonction and application : "une fonction $f$ [de $A$ dans $B$] dont l'ensemble de départ est egal à $A$ ..." — Mauro ALLEGRANZA, Jan 29 '17 at 18:30
The (1968) English transl (page 81) has respectively : function and mapping of $A$ into $B$". — Mauro ALLEGRANZA, Jan 29 '17 at 18:33

How is this called?

0 Answers0