TITLE: Unambiguous terminology for domains, ranges, sources and targets.
QUESTION [7 upvotes]: Given a correspondence $f : X \rightarrow Y$ (which may or may not be a function) I generally use the following terminology.

$X$ is the source of $f$
$Y$ is the target
$\{x \in X \mid \exists y \in Y : xy \in f\}$ is the domain
and $\{y \in Y \mid \exists x \in X : xy \in f\}$ is the range.

However, it has come to my attention that some people use 'domain' to mean $X$, rather than the subset of $X$ described above. So, is there any standard, unambiguous terminology for these concepts that does not have this problem?

REPLY [3 votes]: No, there is no standard unambiguous terminology. The standard terms are "domain" and "range" but they are ambiguous between authors.