limit notation syntax validity

Question

If you know $$\lim_{x \to \infty} f(x) = -\infty$$ and $$\lim_{x \to -\infty} f(x) = -\infty$$, is it valid syntax to write $$\lim_{x \to \pm \infty} f(x) = -\infty$$?

Answer 1

to me it's fine, althought if you want to phrase it differently you could also write $$ \lim_{|x| \rightarrow \infty} f(x) = - \infty$$ whatever you prefer I guess, both are perfectly readable in my opinion