Does the notation $f(x) = \frac{1}{x} \mathbb{1}_{\{ x \neq 0 \}}$ make sense?

Question

I have the function $f : \mathbb{R} \to \mathbb{R}$, $f(x) = \begin{cases} 1/x & (x \neq 0) \\ 0 & (x=0)\end{cases}$

So I would like to denote the function $f$ as more simple, 'one-line' notation,

$$ f(x) = \frac{1}{x} \mathbb{1}_{\{ x \neq 0 \}} $$

But I think this notation is impossible unless we give some priority to the indicator function.

Does it make sense to do so?

Answer 1

Not really, no. If the domain is $\mathbb{R}$, then you need to tell me how to evaluate the function at $0$. The easiest way is just to say $f(0) = 0$.