Chapter 1.3, Problem 122E

Piecewise Functions Let

$f\left(x\right)=\{\begin{array}{ll}0,\hfill & \text{if}x\text{is}\text{ratioinal}\hfill \\ 1,\hfill & \text{if}x\text{is}\text{ratioinal}\hfill \end{array}$

and

$g\left(x\right)=\{\begin{array}{ll}0,\hfill & \text{if}x\text{is}\text{ratioinal}\hfill \\ 1,\hfill & \text{if}x\text{is}\text{ratioinal}\hfill \end{array}$

Find (if possible) $\underset{x\to 0}{\lim }f\left(x\right)$ and $\underset{x\to 0}{\lim }g\left(x\right)$.