[Math] Why the set of irrational numbers is represented as $\mathbb{R}\setminus\mathbb{Q}$ instead of $\mathbb{R}-\mathbb{Q}$

Question

What does the "\" symbol means in this context?

I have seen it used for quotient sets like $X /{\sim}$ where $X$ is a set and $\sim$ is an equivalence relation but I don't know what it means applied to two sets.

$\mathbb{R}-\mathbb{Q}$ seems to be much more suitable, since the set of irrational numbers are just that: real numbers which are not rational.

Answer 1

Both symbols $\setminus$ \setminus and $-$ - are used for denoting set difference: $$A\setminus B = A - B = \{ x \mid x \in A,\,x \not\in B \}.$$

I, particularly, prefer $A \setminus B$. In some contexts, we can have something like: $$A-B = \{ x-y \mid x \in A,\, y \in B \},$$ so sticking to $\setminus$ there is zero chance of confusion.