Exact notation of the domain of a function

Question

For example, we have $f(x)=\frac{1}{x^2-1}$

Would the domain be $$\mathcal D(f)=\{x\in\mathbb{R}\mid x\neq(1,-1)\}$$ or rather $$\mathcal D(f)=\{x\in\mathbb{R}\mid x\neq \{1,-1\}\}$$ or $$ D(f)=\{x\in\mathbb{R}\mid x \setminus \{1,-1\}\}$$ or are all notations correct?

Answer 1

Hint: The flaws in OP's proposals have already been identified in the comment section. Note, it is often convenient to write

$$\mathcal D(f)=\mathbb{R}\setminus\{-1,1\}$$

Answer 2

For example, we have $f(x)=\frac{1}{x^2-1}$

The domain $\mathcal D$ would be (suggested from Mauro ALLEGRANZA):

$$\mathcal{D}(f)=\left\{x\in\mathbb{R}\mid x\neq 1 \wedge x\neq -1\right\}$$