Proving that a limit does not exist 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

Here $\lim_{x\to 0^+}f(x)=1$ & $\lim_{x\to 0^-}f(x)=-1$ both limit are not equal.
therefore limit is not exists
