The sum property of limits can only be applied when the limits exist, right? As follows:
$$ \lim_{x \to a} [f(x) + g(x)] = \lim_{x \to a} f(x) + \lim_{x \to a} g(x) $$
But only if $\lim_{x \to a}f(x)$ and $\lim_{x \to a}g(x)$ exist simultaneously. Then, how to find the following limit
$$\lim_{x \to 2} (\lfloor x \rfloor + \lfloor -x \rfloor)$$
knowing that both of them doesn't exist?
Is there a way to manipulate the expression? I'm not familiar with floor functions.