Expressing tricky sets as intervals precisely.

Question

Fix $\delta \in \mathbb{R}$. Consider $f(x)$ is a real-valued function which is defined whenever $x \in [\delta, \infty) \cup$ or $x\in (-\infty, -\delta]\setminus \left\{-\frac{1}{n^2}:n \in \mathbb{Z}^+\right\}$. Is it possible to express the domain of $f(x)$ using proper (rigorous) notation as a union of intervals? I think $\left\{-\frac{1}{n^2}:n \in \mathbb{Z}^+\right\}$ is a set while $(-\infty, -\delta]$ and $[\delta, \infty)$ are intervals, so I won't be correct to say that the domain of $f(x)$ is $(-\infty, -\delta] \setminus \left\{-\frac{1}{n^2}:n \in \mathbb{Z}^+\right\} \cup [\delta, \infty)$.

Answer 1

I don't know if I really understood your question, is this ok? $$\operatorname{Dom}f=[\delta,\infty)\cup\left(\left(\bigcup_{n\in\mathbb{Z}^+} \left(-\frac{1}{n^2},-\frac{1}{(n+1)^2}\right)\right) \cap (-\infty,\delta]\right)$$