my lecturer told us that one example of function that is discontinuous anywhere:

$\displaystyle f(x) = 1$ if x = rational function and $\displaystyle f(x) = -1$ if x = not a rational number

can anyone sketch the graph? i can't "see" what is the mean of 'discontinuous' from the graph? (e.g. give data for x)

any other example of function that discontinuos anywhere?