Today I came across a question about the function \(f(x)\), which takes the value \(x\) when \(x \in Q\) and the value \(1-x\) when \(x \notin Q\). Is this function continuous at any point?
I thought that \(f(x)\) would be continuous at \(x=0.5\) since the left and right hand limits seem to approach \(0.5\) near \(x=0.5\).
Am I correct? If so, why? If not, why?