To check whether the function is piecewise continuous or not

Question

Let \begin{equation} f(x) \triangleq \begin{cases} 1, & x \in \mathbb{Q} \\ -1, & x \notin \mathbb{Q} \end{cases} \end{equation}

where $\mathbb{Q}$ denotes the set of rational numbers. The function is definitely discontinuous at every point of the real line( if I am not wrong).

But I need help regarding piecewise concept of continuity

Thanks

Answer 1

Hint:

By definition:

A function is piecewise continuous if it is continuous on all but a finite number of points.

So if a function is discontinuous at any real number.......