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Given a relation $ R \subseteq A \times B $.

from wikipedia: The domain of R is the set of all x such that xRy for at least one y. The range of R is the set of all y such that xRy for at least one x.

Hence: $domain \subseteq A, range \subseteq B$

A cannot be called domain, since that name is taken by one of its subsets which is only equal to it in special cases. If you insist on calling A the domain then my new question is: what is the set of all x such that xRy for at least one y is called?

Wikipedia mentions "set of departure" for A and "set of destination" for B. But I am wondering if people would understand and accept if I would use those terms.

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    $\begingroup$ In Nicolas Bourbaki, Elements of Mathematics: Theory of sets (Engl.transl. 1968) we can find : "A correspondence between a set $A$ and a set $B$ is a triple $\Gamma = \langle G, A, B \rangle$ where $G$ is a graph such that $pr_1 G \subset A$ and $pr_2 G \subset B$. $G$ is said the graph of $\Gamma$, $A$ is the source, and $B$ is the target of $\Gamma$." $\endgroup$ – Mauro ALLEGRANZA Mar 13 '17 at 13:55
  • $\begingroup$ A graph is a set of ordered pairs and $pr_1 G = \{ x \mid (\exists y) (x,y) \in G \}$ is the domain of $G$ (and the same for $pr_2 G$, the range of $G$). $\endgroup$ – Mauro ALLEGRANZA Mar 13 '17 at 13:58
  • $\begingroup$ You can see also this related post : unambiguous-terminology-for-domains-ranges-sources-and-targets. $\endgroup$ – Mauro ALLEGRANZA Mar 13 '17 at 14:12

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