I have a function that is defined as such,
$f(x)=x$, if x is rational, ie $x=\frac{p}{q}$ and $f(x)=1-x$, if x is irrational. What are all the points of continuity?
I would say that all the points of continuity are the points where $p\neq q$ since at any the limit of f(x) as x approaches 1 is 0, while the functional value of the limit of x, as x approaches 1 is 1. Since they do not agree, the function is discontinuous at any point $p=q$
Is that view correct?