Is there a common way to denote the domain or range of a function? I've seen things like
$ \cal{D}\left(f\right) $ and $ \cal{R}\left(f\right) $ for the domain and range, respectively, but I wasn't sure if there was a more explicit syntax for this (e.g., the way that cardinality has a specific syntax instead of just $\mathrm{card}\left(X\right)$, for instance).
I know that you alternatively mention the domain and range in the "mapping" notation of the function, e.g.:
$$
f: \cal{D} \to \cal{R}
$$
But I'm really just looking for a way to explicitly indicate the domain/range of a given function.
Best Answer
Notations vary. You should pick something straightforward, and state it clearly up front. One common choice would be $$\operatorname{dom} f\\ \operatorname{ran} f$$
another reasonable choice might be $$\mathscr{D}(f)\\\mathscr{R}(f)$$
Principia Mathematica used: