Arithmetic operators and regex Let $L$ be the language over the alphabet $\{0, 1, 2, 3, (,), +, -, *, /\}$, $L$ is the set of operations with correctly formatted natural numbers. A single number is considered to belong to $L$.

2 - - 3 is an incorrect expression, 2 + 3 is correct, 2 + (-3) is correct. 
Is it possible to write a regular expression for this language?  If not, why?

I think that it is not possible to write a regular expression for this language, because of the operator / we cannot write 2 / 0 for example and are more than a finite number combinations to make this possible. Is it correct?
You haven't defined your language, but presumably
$$
L \cap [^*0+0](+0])^* = \{ [^n[0+0](+0])^n : n \geq 0 \},
$$
where I replaced parentheses with square brackets. The latter language is essentially $\{a^nb^n : n \ge 0 \}$ in disguise, and so isn't regular. It follows that $L$ isn't regular as well.