$f(x) = \begin{cases} \dfrac{\sin \left \lfloor x \right \rfloor}{\left \lfloor x \right \rfloor}, & \text{for} & \left \lfloor x \right \rfloor \neq 0 \\ \\ 0, & \text{for} & \left \lfloor x \right \rfloor = 0 \end{cases}$

If $f(x)$ is as defined above, find $\displaystyle \lim_{x \to 0^{-}}{f(x)}$.

**Notation:** $\lfloor \cdot \rfloor$ denotes the floor function.