If f: [0,1] is continuous and has only rational [respectively, irrational] values, must f be constant? Prove your answer.
That is the advice I have give many, many a student in my years as a department chairperson.
To you own self be true. If this basic material is a real problem for you, I can tell you it only gets worst.
Donít make the mistake of waiting too late to change course.