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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.

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    A *binary operation* on a set $S$ is, by definition, a map $S\times S\to S$. Is that what you are looking for?2012-03-25
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    endomap: $S\times S \to S$2012-03-25
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    BTW the tag `(computer-science)` is not relevant. The context was already set by OP in his/her sentence: ".. the D language."2012-03-25
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    @J.D.: I don't like that: "endomap" suggests a map form a set to *itself*.2012-03-25

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

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    "Closed binary operation" is rather strange terminology. Instead, mathematicians usually say that a (sub)set is closed under a binary operation.2012-03-25
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    @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](http://fr.wikipedia.org/wiki/Loi_de_composition_interne) and [German](http://de.wikipedia.org/wiki/Zweistellige_Verkn%C3%BCpfung): internal.2012-03-25