Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Is there a special name for a binary operation on the set $S$ that is also into $S$, that is unambiguous with other uses. I.e. if it's "operator on $S$", I've heard that in other places meaning the operator could map to another set $T$. I'm working on a math library in the D language.

share|cite|improve this question
A binary operation on a set $S$ is, by definition, a map $S\times S\to S$. Is that what you are looking for? – Arturo Magidin Mar 25 '12 at 3:17
endomap: $S\times S \to S$ – user2468 Mar 25 '12 at 3:21
BTW the tag (computer-science) is not relevant. The context was already set by OP in his/her sentence: ".. the D language." – user2468 Mar 25 '12 at 3:25
@J.D.: I don't like that: "endomap" suggests a map form a set to itself. – Arturo Magidin Mar 25 '12 at 3:27
up vote 1 down vote accepted

Are you looking for the term closed binary operation? (other reference)

share|cite|improve this answer
"Closed binary operation" is rather strange terminology. Instead, mathematicians usually say that a (sub)set is closed under a binary operation. – Bill Dubuque Mar 25 '12 at 3:57
@BillDubuque I find it strange too, but it makes sense. At least, it does not makes any other sense. Shall we conclude there is no unanimous terminology? There is in French and German: internal. – jmad Mar 25 '12 at 4:30

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.