Given the function $f(x)= \left\{\begin{matrix} 1 & x \gt 0 \\ 0 & x =0 \\ -1 & x \lt 0 \end{matrix}\right\}$
What is $\lim_{a}f$ for all $a \in \mathbb{R},a \gt 0$?
It seems easy enough to guess that the limit is $1$, but how do I take into account the fact that $f(x)=-1$ when $x \lt 0$? Thanks