My TA (teacher's assistant) told me that these kind of problems (with rational/irrational) are always undefined. He's not around right now, so could anyone explain why this is the case?
If then there is some which is rational and there is an which is irrational. That is, in any open interval there is a rational and an irrational number. So there are two places 16 units apart. Continuous functions must have values 'close together' at points of continuity.