Is there a mathematical notation to express the domain without the range or the range without the domain?

Question

I can express the domain and range of a function like this $$f:X\rightarrow Y$$

What if I am only interested in the domain of the function? Is it mathematically accepted to write this? $$f:X$$

What if I am only interested in the range?

I am asking if there is a mathematical notation to represent these concepts individually without presenting both at the same time.

The range of $f$ is often expressed by $f(X).$ However, as you can see, it still uses the fact that $X$ is the domain of $f.$ — Pawel, Sep 05 '18 at 22:25
Looking through a book I have found the notation $D_{f}$ and $R_{f}$. Is this widely used? — Cedric Martens, Sep 05 '18 at 22:32
Actually, $Y$ is the codomain, which is a superset of the range. — mr_e_man, Sep 05 '18 at 22:41

score 9 · Accepted Answer · edited Sep 05 '18 at 23:41

9

One often sees $\operatorname{dom }f$ and $\operatorname{ran} f$ or $D(f)$ and $R(f)$ or $D_{f}$ and $R_{f}$ .

Of course, you can also say something like

When $f$ is a function, we will write “$\square f$” to mean the domain of $f$ and “$f\square$” to mean the codomain

or whatever. You're allowed to make up whatever notation you like, as long as you explain it clearly.

edited Sep 05 '18 at 23:41

answered Sep 05 '18 at 22:27

MJD

Is that supposed to appear as a white box? – qwr Sep 06 '18 at 02:30
The $\square$ is supposed to appear as a hollow square. – MJD Sep 06 '18 at 02:36
Indeed, ◻ is U+25FB: WHITE MEDIUM SQUARE. – Andreas Rejbrand Sep 06 '18 at 06:49

1 Answers1