Consider the function f defined by

$f\left(x\right)=\{\begin{array}{cc}0,& whenx=0orisirrational\\ \frac{1}{n},& whenxisnon-zerorationalnumber\frac{m}{n},n>0and\frac{m}{n}isinlowestterm\end{array}$
which of the following statement(s) is(are) true?

For  $x=\alpha \in Q^c,f\left(\alpha \right)=0$ and  ${\lim }_{x\to \alpha }f\left(x\right)$  is also zero because if  x moves towards $\alpha$ through irrational numbers then it is zero, or if through rational numbers then the denominator can be made as large as possible.