Q: f is function from the reals to the reals. f(x) = x for x rational, f(x) = 1 - x otherwise. Find the set of all a such that f is continous at a.
A: I think f is continous at x = 1/2. Is this correct? Are there any other points? I thought not because if we choose any a not equal to one half, then we can always find some rational number between x and a, as we proceed to the limit. Is this correct reasoning?